Controller Design for Hysteresis Compensation of Piezo Actuators for

Micro/Nano Positioning Thesis submitted to the

School of Mechatronics & Robotics Indian Institute of Engineering Science and Technology, Shibpur,

(Formerly Bengal Engineering and Science University, Shibpur ) Howrah – 711103

West Bengal India

in the partial fulfillment of the requirements For the Degree

of Master of Technology in Mechatronics and Robotics

by

ANIRBAN BHAKTA Roll no. – 191225002; Registration no. – 235512002

Under the esteemed guidance of

Mr. Saikat Kr Shome Scientist, Electronics& Instrumentation Group

and Dr. Arpita Mukherjee

Senior Scientist, Electronics& Instrumentation Group

Central Mechanical Engineering Research Institute, (CMERI),

Durgapur- 713 209 India

May 2014

School of Mechatronics & Robotics Indian Institute of Engineering Science and Technology, Shibpur

&

CSIR-Central Mechanical Engineering Research Institute, (CMERI), Durgapur

I, hereby forward the Progress Report of the Thesis entitled “Controller design for Hysteresis Compensation of Piezo Actuators for Micro/Nano Positioning.” Prepared by Anirban Bhakta under my and supervision in partial fulfillment of the requirements for the degree of Master of Technology in Mechatronics.

Mr. Saikat Kr Shome Scientist, Electronics &Instrumentation Group

CSIR-CMERI, Durgapur

Dr. Arpita Mukherjee Senior Scientist, Electronics &Instrumentation Group

CSIR-CMERI, Durgapur Countersigned by,

Director, School of Mechatronics & Robotics Indian Institute of Engineering Science and Technology, Shibpur, Howrah

(Dean of Faculty of Engg. & Technology Indian Institute of Engineering Science and Technology Shibpur, Howrah

School of Mechatronics & Robotics Indian Institute of Engineering Science and Technology, Shibpur

Howrah – 711103

Certificate of Approval

The foregoing Progress Report is hereby approved as a creditable study of engineering subject carried out and presented in a manner satisfactory to warrant its acceptance as a prerequisite for the Thesis work for which it has been submitted. It is understood that by this approval the undersigned do not necessarily endorse or approved any statement made, opinion expressed or conclusion drawn therein but approve the Progress Report only for the purpose for which it is submitted (Thesis Work).

……………………………....

Board of Examiners ………………………………

……………………………….

School of Mechatronics & Robotics Indian Institute of Engineering Science and Technology, Shibpur

Howrah – 711103

Student Declaration

I, hereby declare that the work presented in this project entitled “Controller design for Hysteresis Compensation of Piezo Actuators for Micro/Nano Positioning”, submitted towards completion of Partial Fulfillment Of the Requirement of the Degree of Master of Technology at Indian Institute of Engineering Science and Technology, Shibpur is an authentic record of my work carried out under the guidance of Dr. A.Mukherjee and Mr. S.K.Shome. The project was done in full compliance with the requirements and constraints of the prescribed curriculum.

Place: Durgapur

Date:

Anirban Bhakta Registration number

235512002

ACKNOWLEDGEMENT

This M.Tech project titled “Controller design for Hysteresis Compensation of Piezo Actuators for Micro/Nano Positioning” required a lot of commitment, patience and hard work. First and foremost, I would like to thank Dr. Pijush Pal Roy, Director, CSIR-CMERI, Durgapur, for giving me the opportunity to carry out my project in this esteemed organization.

I express sincere gratitude and indebtness to my project guide Dr. A.Mukherjee and Mr. S.K.Shome, CMERI Durgapur, for their constant encouragement and active involvement in every step of the project, making it a great learning experience, and also an enjoyable one.

I am very thankful to Prof. Debjani Ganguly, Director, School of Mechatronics and Robotics, Indian Institute of Engineering Science and Technology, Dr. Subhasis Bhaumik, Coordinator, School of Mechatronics and Robotics, Indian Institute of Engineering Science and Technology and Dr. S.N. Shome, Coordinator, School of Mechatronics and Robotics at CMERI, Durgapur for providing me an opportunity to undertake the project in this esteemed organization.

My journey of one and half year in CMERI is quite an experience, and there are lots of life outside the lab and the working hours. I take this opportunity to thank my friends Biswarup and Bipin for extending their help in every way they could, and sometimes even without asking. Without them, life at Durgapur could have been much more difficult. Finally I would like to thank my parents for the support and encouragement, they provided in this period that enabled me to successfully complete this thesis work.

DEDICATION This thesis is dedicated

to my beloved ever caring parents

Mr. Biswanath Bhakta and

Mrs. Putul Bhakta

ABSTRACT

One of the crucial aspects of research in nano technology is precision control and

manipulation of devices at the nano scale i.e nano positioning. Nano technology is the science of

understanding matter and the control of matter at dimensions of 100 nm or less. Encompassing

nano scale science, engineering, and technology, nanotechnology involves imaging, measuring,

modeling, and manipulation of matter at this level of precision. An important aspect of research

in nanotechnology involves precision control and manipulation of devices and materials at a

nano scale, i.e., nanopositioning. Nano positioners are precision mechatronic systems designed to

move objects over a small range with a resolution down to a fraction of an atomic diameter. The

desired attributes of a nano positioner are extremely high resolution, accuracy, stability, and fast

response. The key to successful nanopositioning is accurate position sensing and feedback

control of the motion.

Piezo electric actuators (PZA) are capable of positioning with (sub) nanometer resolution,

large blocking force, high stiffness, and rapid response characteristics. Nevertheless, PZT

introduces nonlinearity into the actuation mainly due to its hysteresis property occurring at

voltage-driven strategy, which attenuates the positional accuracy of the manipulator if not

carefully treated. This research focuses on effective minimization of this hysteretic effect aimed

at improving tracking performance of the actuator.

One of the regular ways to overcome the nonlinearity is to model the hysteresis

mathematically first and then construct a hysteresis compensation scheme. There are a number of

hysteresis models are available in literature like Dahl model, Bouc-Wen model, Preisach model,

Maxwell model, Duhem model and Prandtl–Ishlinskii model. Amongst which the 2nd order Dahl

model is preferred over the others because hysteresis can be better expressed by this model as it

involves lesser number of parameters.

The piezo electric actuator is modeled as a second order system using its mechanical

equivalence having three major parameters i.e equivalent mass, damping ratio and stiffness

constant. Then the hysteresis model is introduced with the main plant which generates the

hysteresis force from the output displacement of the plant.

Consequently, several control algorithms have been developed to compensate the non

linearity. Some conventional control strategies like Feedforward control, feedforward with

feedback control and a few non linear control laws like Internal model control (IMC), Fuzzy

control are adopted. Feedforward control operates with the principle of inverse plant model. It is

an open loop system so to remove the shortcomings feedback controller is introduced with it. On

the other hand, IMC reflects the system non linerities more precisely by comparing the output

obtained from the actual plant model and nominal (mathematical) plant model. A number of

simulations are performed to validate the effectiveness of the controllers and finally some of the

controllers have been realized on hardware platform.

In this work, the controllers are developed in LABVIEW platform and Compact-Rio

processor is used to generate the control signals. This signal is fed to the Physik Instrumente

(PI) manufactured piezo amplifier and finally it actuates the PI based piezo actuator attached

with the micro-positioning stage. This micro/nano positioning stage has wide range of

applications like positioning of wafers, IC chip assembly line, biological cell operator, cell

tracking system etc.

Contents Chapter One: 1. Introduction and Background

Fundamentals of Piezo-electricity ..............................................................................................01

Material properties .................................................................................................................... 02

Low voltages and high voltages Piezo-actuators....................................................................... 03

Mechanical considerations ........................................................................................................ 04

Stiffness ........................................................................................................................04

Load capacity and force generation ............................................................................ 04

Protection from mechanical damage ........................................................................... 04

Power requirement .................................................................................................................... 04

Basic design of Piezo-electric positioning elements ................................................................. 04

Stack design ................................................................................................................ 04

Laminar design .............................................................................................................05

Scanner tube design ..................................................................................................... 06

Bender type actuator ................................................................................................... 07

Piezo-actuator with integrated lever motion amplifier ................................................ 07

PZT flexure nano-positioners ...................................................................................... 08

Advantages of Piezo-electric positioning system ...................................................................... 08

Difficulties in Piezo-actuators ................................................................................................... 09

Creep ........................................................................................................................... 09

Non linear creep............................................................................................. 09

Linear creep ................................................................................................... 10

Non linear vs linear creep models ................................................................. 10

Hysteresis .................................................................................................................... 10

Hysteresis modeling ....................................................................................... 11

Modeling errors ........................................................................................................... 12

Parameter variation ......................................................................................... 12

Unmodeled dynamics .......................................................................................12

Vibrations .................................................................................................................... 12

Self heating ................................................................................................................. 13

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Band width- precision- range tradeoff ........................................................................ 14

Present state of art of hysteresis compensation techniques ................................................... 14

Motivations ............................................................................................................................. 15

Thesis organization. ................................................................................................................ 16

Chapter Two: 2. System modeling and Identifications ............................................................. 17

Dynamic plant modeling ......................................................................................................... 17

Hysteresis modeling ................................................................................................................ 17

Preisach model .......................................................................................................................... 17

Prandtl- Ishlinsky hysteresis model .......................................................................................... 18

Bouc- Wen model ..................................................................................................................... 18

Dahl hysteresis model ............................................................................................................... 19

Nth order Dahl model ............................................................................................................... 19

2nd order Dahl model ................................................................................................................ 20

Model identification ................................................................................................................ 21

Particle Swarm Optimization .................................................................................................... 21

Model identification with PSO ................................................................................................. 22

Construction of Dahl hysteresis model ................................................................................... 23

Model comparison .................................................................................................................. 24

Chapter Three: 3. Design of Controllers ................................................................................... 25

Feedforward controller ............................................................................................................. 25

Feedforward with feedback compensation .............................................................................. 25

Internal Model Control approach ............................................................................................ 27

IMC background ....................................................................................................................... 27

The IMC strategy ...................................................................................................................... 28

Practical design of IMC ................................................................................................................ 30

Sensitivity and complementary sensitivity function ................................................................. 30

Modified Internal Model Control ............................................................................................. 31

Fuzzy logic control .................................................................................................................. 32

Fuzzy logic theory ................................................................................................................... 33

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Fuzzy relations........................................................................................................................ 34

A closed loop set point tracking system ................................................................................ 35

Design principle of Fuzzy logic controllers ............................................................................ 38

The Fuzzification module ......................................................................................................... 38

The Fuzzy logic rule base ......................................................................................................... 39

The Defuzzification module ............................................................................ 40

Chapter Four: 4. Simulation using MATLAB/SIMULINK ...................................................... 41

Input reference signal.................................................................................................................... 42

Matlab models of the controller ................................................................................................ 43

Feedforward model ................................................................................................................ 43

Feedforward with feedback model ..........................................................................................43

Internal Model Controller ...................................................................................................... 43

Two degree of freedom IMC controller ................................................................................. 44

Modified IMC controller ......................................................................................................... 44

Fuzzy logic controller ............................................................................................................ 45

Simulation results ..................................................................................................................... 46

Hysteresis plots ...................................................................................................................... 46

Tracking errors ........................................................................................................................ 48

Deviation between i/p and o/p trajectories ................................................................................ 48

Set point errors 49

Variation of plant parameters.................................................................................................... 51

Chapter Five: 5. Hardware modeling and Implementation ...................................................... 52

feedforward controller in TMS320c6713 DSK board .............................................................. 52

Overview of TMS320C6713 DSK .......................................................................................... 52

TMS320C6713 features ......................................................................................................... 54

Code composer studio(CCS) ................................................................................................... 55

Feedforward controller in CCS .............................................................................................. 55

Implementation....................................................................................................................... 56

Operating Piezo-electric stages with LabVIEW ....................................................................... 57

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Hardware description ................................................................................................................ 57

Piezo-actuator (PI-P840) ........................................................................................................... 57

Piezo-amplifier module (PI E505.00) ....................................................................................... 58

Piezo-servo controller module (PI E509.S1) ............................................................................ 58

Digital piezo controller operation module (PI E 517.I3) .......................................................... 58

Piezo actuation stage (PI M-014) .............................................................................................. 59

Controller design in LabVIEW ................................................................................................. 59

Hardware interface with LabVIEW .......................................................................................... 60

NI CompactRIO .......................................................................................... 60

LabVIEW FPGA interface ........................................................................... 64

Proposed work flowchart ............................................................................. 66

Chapter Six: 6. Conclusion and Future scopes........................................................................... 68

Contribution of the present work .............................................................................................. 68

Future scopes ............................................................................................................................ 68

Bibliography ................................................................................................................................. 69

Appendix 1.Description of the Piezo actuator system from PI

Appendix 2. Description of the I/O modules of CRIO from NI

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List of Figures:

Fig 1. Piezo-electric elementary cell.

Fig 2. Electric dipole in Weiss domain.

Fig 3. Direct and converse piezoelectric effect.

Fig 4. Electrical and mechanical structure of stack actuators.

Fig 5. Laminar design structure.

Fig 6. Scanner tube design.

Fig 7. Bimorph design.

Fig 8. Simple lever motion amplifier.

Fig 9. Basic parallelogram flexure guiding system.

Fig 10. Steady state I/O plots for phase lag creep model.

Fig 11. Hysteresis curve of an open loop piezo actuator for various peak voltages.

Fig 12. Piezo actuator model.

Fig 13. Schematic of piezo actuator.

Fig 14. Dahl hysteresis model.

Fig 15. Feedforward control.

Fig 16. Inverse Dahl model.

Fig 17. Plant with feedforward control.

Fig 18. Feedforward with feedback control.

Fig 19.open loop control strategy.

Fig 20. Schematic of IMC controller.

Fig 21. Conventional IMC structure.

Fig 22. Modified IMC structure.

Fig 23. A Fuzzification “a is slightly greater than b”.

Fig 24. A closed loop set point tracking system.

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Fig 25. General structure of fuzzy logic controller.

Fig 26. Clustering and membership value of I/P variable.

Fig 27. Clustering and membership value of o/p variable.

Fig 28. Reference input trajectory.

Fig 29. Simulink model of feedforward controller.

Fig 30. Simulink model of feedforward with feedback controller.

Fig 31. Simulink model of IMC controller.

Fig 32. Simulink model of two degree of freedom IMC controller.

Fig 33. Simulink model of modified IMC controller.

Fig 34. Simulink model of fuzzy logic controller.

Fig 35.FIS file structure.

Fig 36. FIS editor for input and output variables.

Fig 37. Membership function for input and output variables.

Fig 38. Fuzzy rule editor panel.

Fig 39. Hysteresis plot for feedforward control.

Fig 40. Hysteresis plot for feedback control.

Fig 41. Hysteresis plot for IMC control.

Fig 42. Hysteresis plot for modified IMC control.

Fig 43. Set point tracking of feedforward control.

Fig 44. Set point tracking of feedforward with feedback control.

Fig 45. Set point tracking of conventional IMC control.

Fig 46. Set point tracking of modified IMC control.

Fig 47. Set point tracking of fuzzy logic control.

Fig 48. Tracking error of feedforward control.

Fig 49. Tracking error of feedforward with feedback control.

Fig 50. Tracking error of fuzzy logic control.

Fig 51. Tracking error of conventional IMC control.

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Fig 52. Tracking error of modified IMC control.

Fig 53. Schematic diagram of TMS320C6713 DSK.

Fig 54. Code Composer Studio window.

Fig 55. Feedforward controller in DSK platform.

Fig 56. Feedforward controller in LabVIEW.

Fig 57. Dahl hysteresis model in LabVIEW.

Fig 58. Reconfigurable embedded system architecture.

Fig 59. Reconfigurable FPGA chassis.

Fig 60. Host to target configuration of CRIO.

Fig 61. CRIO devices with required I/O modules.

Fig 62. Window for selection of programming mode.

Fig 63. Analysis of performance in LabVIEW platform.

Fig 64. Proposed hardware setup.

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List of Tables

1. Table 1. The Dahl model parameters adopted for the micro nano manipulator system.

2. Table 2. Controller performance comparison and the error values of peak to peak error and RMS error.

3. Table 3. Controller performance under parameter variation (in terms of rms error).

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N Chapter One

1. INTRODUCTION AND BACK GROUND

ano technology is the science of understanding matter and the control of matter at dimensions of 100 nm or less. Encompassing nanoscale science, engineering, and technology, nanotechnology involves imaging, measuring, modeling, and manipulation

of matter at this level of precision. An important aspect of research in nanotechnology involves precision control and manipulation of devices and materials at a nanoscale, i.e., nanopositioning. Nanopositioners are precision mechatronic systems designed to move objects over a small range with a resolution down to a fraction of an atomic diameter. The desired attributes of a nanopositioner are extremely high resolution, accuracy, stability, and fast response. The key to successful nanopositioning is accurate position sensing and feedback control of the motion. Most micro and nano manipulators employ a flexure-based mechanism and piezoelectric actuators (PZTs) to deliver a submicron or sub nanometer resolution positioning. In addition to vacuum compatibility, flexure mechanism eliminates clearance, backlash, friction, and lubrication requirements for the device. As a type of linear actuator, PZT is capable of positioning with (sub) nanometer resolution, large blocking force, high stiffness, and rapid response characteristics.

Fundamentals of Piezoelectricity

The piezoelectric effect is often encountered in daily life. For example, in small butane

cigarette or gas grill lighters, a lever applies pressure to a piezoelectric crystal creating an electric field strong enough to produce a spark to ignite the gas. Furthermore, alarm clocks often use a piezoelectric element. When AC voltage is applied, the piezoelectric material moves at the frequency of the applied voltage and the resulting sound is loud enough to wake even the strongest sleeper. With high-reliability PZT materials a strain on the order of 1/1000 (0.1%) can be achieved; this means that a 100 mm long PZT actuator can expand by 100 micrometers when the maximum allowable field is applied.

The word "piezo" is derived from the Greek word for pressure. In 1880, Jacques and Pierre Curie discovered that pressure applied to a quartz crystal creates an electrical charge in the crystal; they called this phenomenon the piezo effect. Later they also verified that an electrical field applied to the crystal would lead to a deformation of the material. This effect is referred to as the inverse piezo effect. After the discovery it took several decades to utilize the piezoelectric phenomenon. The first commercial applications were ultrasonic submarine detectors developed during World War I and in the 1940’s scientists discovered that barium titanate ceramics could be made piezoelectric in an electric field.

As stated above, piezoelectric materials can be used to convert electrical energy into mechanical energy and vice versa. For nanopositioning, the precise motion which results when

1

an electric field is applied to a piezoelectric material is of great value. Actuators using this effect first became available around 20 years ago and have changed the world of precision positioning.

Material Properties: Since the piezo effect exhibited by natural materials such as quartz, tourmaline, Rochelle

salt, etc. is very small, polycrystalline ferroelectric ceramic materials such as BaTiO3 and Lead Zirconate Titanate (PZT) have been developed with improved properties. Ferroelectric ceramics become piezoelectric when poled. PZT ceramics are available in many variations and are still the most widely used materials for actuator or sensor applications today. PZT crystallites are centro- symmetric cubic (isotropic) before poling and after poling exhibit tetragonal symmetry (anisotropic structure) below the Curie temperature. Above this temperature they lose the piezoelectric properties.

Fig 1Piezoelectric elementary cell; (a) before poling (b) after poling

Charge separation between the positive and negative ions is the reason for electric dipole behavior. Groups of dipoles with parallel orientation are called Weiss domains. The Weiss domains are randomly oriented in the raw PZT material, before the poling treatment has been finished. For this purpose an electric field (> 2000 V/mm) is applied to the (heated) piezo ceramics. With the field applied, the material expands along the axis of the field and contracts perpendicular to that axis. The electric dipoles align and roughly stay in alignment upon cooling. The material now has a remanent polarization (which can be degraded by exceeding the mechanical, thermal and electrical limits of the material). As a result, there is a distortion that causes growth in the Dimensions aligned with the field and a contraction along the axes normal to the electric field. When an electric voltage is applied to a poled piezoelectric material, the Weiss domains increase their alignment proportional to the voltage. The result is a change of the Dimensions (expansion, contraction) of the PZT material.

a. b.

2

Fig 2 Electric dipoles in Weiss domains; (1) unpoled ferroelectric cermic, (2) during and (3) after poling (piezoelectric ceramic)

Fig 3 direct and converse piezo-electric effect, a. direct effect b. converse effect

Low voltage and High voltage Piezo-actuators Two main types of piezo actuators are available: low voltage (multilayer) devices

requiring about 100 volts for full motion and high voltage devices requiring about 1000 volts for full extension. Modern piezo ceramics capable of greater motion replace the natural material used by the Curies, in both types of devices. Lead zirconate titanate (PZT) based ceramic materials are most often used today. Actuators made of this ceramic are often referred to as PZT actuators. The maximum electrical field PZT ceramics can withstand is on the order of 1 to 2 kV/mm. In order to keep the operating voltage within practical limits, PZT actuators consist of thin layers of electroactive ceramic material electrically connected in parallel. The net positive displacement is the sum of the strain of the individual layers. The thickness of the individual layer determines the maximum operating voltage for the actuator. High voltage piezo actuators are constructed from 0.5 to 1.0 mm layers while low voltage piezo actuators are monolithic (diffusion bonded) multilayer designs constructed from 20 to 100 μm layers. Both types of piezo actuators can be used for many applications: Low voltage actuators facilitate drive electronics design, high voltage types operate to higher temperatures (150 °C compared to 80 °C). Due to manufacturing technology high voltage ceramics can be designed with larger cross-sections for higher load applications (up to several tons) than low voltage ceramics.

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Mechanical Considerations Stiffness

In a first approximation, a piezo actuator can be regarded as a spring/mass system. The stiffness or spring constant of a piezo actuator depends on the Young's Modulus of the ceramic (approximately 25 % that of steel), the cross section and length of the active material and a number of other nonlinear parameters.

Load capacity and Force generation PZT ceramics can withstand high pushing forces and carry loads to several tons. Even when

fully loaded, the PZT will not lose any travel as long as the maximum load capacity is not exceeded. Load capacity and force generation must be distinguished. The maximum force (blocked force) a piezo can generate is determined by the product of the stiffness and the total travel. A piezo actuator (as most other actuators) pushing against a spring load will not reach its nominal displacement. The reduction in displacement is dependent on the ratio of the piezo stiffness to the spring stiffness. As the spring stiffness increases, the displacement decreases and the generated force increases.

Protection from Mechanical Damage Since PZT ceramics are brittle and cannot withstand high pulling or shear forces, the

mechanical actuator design must isolate these undesirable forces from the ceramic. For example, spring preloads can be integrated in the mechanical actuator assembly to compress the ceramic inside and increase the ceramic’s pulling capabilities for dynamic push/pull applications.

Power Requirement Piezo actuators operate as capacitive loads. Since the current leakage rate of the ceramic

material is very low (resistance >> 10 MΩ ), piezo actuators consume almost no energy in a static application and therefore produce virtually no heat. In dynamic applications the power consumption increases linearly with frequency and actuator capacitance. High-load actuators with larger ceramic cross sections have higher capacitance than small actuators. For example, a typical medium load LVPZT actuator with a motion range of 15 microns and 10 kg load capacity requires only five watts to be driven at 1000 Hz while a high load actuator capable of carrying a few tons may require hundreds of watts for the same frequency.

Basic Designs of Piezoelectric Positioning Elements

Stack design The active part of the positioning element consists of a stack of ceramic disks separated by

thin metallic electrodes. Maximum operating voltage is proportional to the thickness of the disks. PI stack actuators are manufactured with layers from 0.02 to 1 mm thickness. Stack elements can withstand high pressure and show the highest stiffness of all piezo actuator designs. Since the ceramics cannot withstand large pulling forces, spring preloaded actuators are available. Stack

4

models can be used for static and dynamic operation. Displacement of a PZT stack actuator can be estimated by the following equation

∆L ≈ d33*n * U (i) Where, d33 = strain coefficient (field and deflection in polarization direction) [m/V], n = number of ceramic layers, U = operating voltage [V]

Fig 4 a. Electrical design of stack Translator. b. Mechanical structure

Laminar Design (Contraction Type Actuator) The active material in the laminar actuators consists of thin ceramic strips. The

displacement of these actuators is perpendicular to the direction of polarization and electric field. When the volt-age is increased the strip contracts the piezo strain coefficient d31 (negative!) describes the relative change in length. It is on the order of 50% of d33. The maximum travel is a function of the length of the strips, while the number of strips arranged in parallel determines the stiffness and the stability of the element. Displacement of a PZT contraction actuator can be estimated by the following Equation ∆L ≈ d31*L * U/d (ii)

Where, d31 = strain coefficient (deflection normal to polarization direction) [m/V] L = length of the PZT ceramics [m] U = operating voltage [V] d = thickness of one ceramic layer [m]

a. b.

5

Scanner tube design Fig 5. Laminar design

Tube actuators are not designed to withstand large forces. Application examples are scanning microscopy, ink jet printers etc. The scan range of a scanner tube is defined by the equation

Where,

∆ x ≈ ( 2 2 .d31.U.L2)/(Π.ID.d) (iii)

∆ x = scan range in X and Y (for symmetrical electrodes) [m] d31 = strain coefficient (deflection normal to polarization direction) [m/V] U = operating voltage [V] L = length [m] ID = inner diameter [m] d = wall thickness [m]

Fig 6 Scanner tube.

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Bender Type Actuators (Bimorph and Multimorph Design) A PZT bimorph operates similarly to a bimetallic strip in a thermostat. When ceramic is

energized the metal substrate is deflected with a motion proportional to the applied volt-age. Bimorph actuators providing motion up to 1000 μm are available and greater travel range is possible. Apart from the classical strip form, bimorph disk actuators are available, where the center arches when a voltage is supplied.

Fig 7 Bimorph design

Instead of a PZT/metal combination PZT/PZT combinations are possible where individual PZT layers are operated in opposite mode (contraction/expansion). Two basic versions are available: the two electrode bimorph (serial bimorph) and the three electrode bimorph (parallel bimorph). In the serial type, one of the two ceramic plates is always operated opposite to the direction of polarization. To avoid depolarization the maximum electric field is limited to a few hundred volts per millimeter. Serial bimorph benders are widely used as force sensors.

Piezo Actuators with Integrated Lever Motion Amplifier

Piezo actuators or positioning stages can be designed in a way that a lever motion amplifier is integrated into the system, increasing the PZT displacement by a factor of typically 2 to 20. To maintain sub-nanometer resolution with the increased travel range, the leverage system must be stiff, backlash- and friction-free which is why ball or roller bearings cannot be used. PI employs a proprietary Finite Element Analysis (FEA) computer program to design PZT Flexure Nano Positioners with or without integrated lever motion amplifiers.

Fig 8 Simple lever motion amplifier

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PZT Flexure Nano Positioners Flexure positioners are far superior to traditional positioners (a ball bearing, crossed roller

bearings, dovetails etc.) in terms of resolution, straightness and flatness. Inherent friction and stiction in these traditional designs limit applications to those requiring repeatability on the order of 0.5 to 0.1 μm. A flexure is a frictionless, stictionless device based on the elastic deformation (flexing) of a solid material. Sliding and rolling are entirely eliminated. In addition to absence of internal friction, flexure devices exhibit high stiffness and load capacity. Flexures are also less sensitive to shock and vibration than other guiding systems.

Basic parallelogram flexure actuators show a second-order cross coupling (parasitic motion) between axes. This movement is called arcuate motion (travel is in an arc motion). It can lead to small out-of-plane errors on the order of 0.1% of the distance traveled (The error can be estimated by the following equation:

∆ H ≈ (± ∆ L/2)2 /2H (iv) Where, ∆ H = Lateral run out (out-of-plane error) [m] ∆ L = Distance traveled [m] H = Length of the flexures [m] The amplification r (transmission ratio) is given by (a+b)/a.

Fig 9. Basic parallelogram flexure guiding system with motion amplification

Advantages of Piezoelectric Positioning Systems

1. Unlimited Resolution: A piezoelectric actuator (PZT) can produce extremely fine position changes down to the sub nanometer range. The smallest changes in operating voltage are converted into smooth movements. Motion is not influenced by stiction/ friction or threshold voltages.

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2. Large Force Generation: PZTs can generate a force of several 10,000 N. PI offers units that can bear loads up to several tons and position within a range of more than 100 μm with sub nanometer resolution 3. Fast Expansion: Piezo actuators offer the fastest response time available (microsecond time constants). Acceleration rates of more than 10,000 g's can be obtained. 4. No Magnetic Fields: The piezo effect is related to electrical fields. PZT actuators don't produce magnetic fields nor are they affected by magnetic fields. They are especially well suited for applications where magnetic fields cannot be tolerated. 5. Low Power Consumption: The piezo effect directly converts electrical energy into motion only absorbing electrical energy during movement. Static operation, even holding heavy loads, does not consume power. 6. No Wear and Tear: A piezo actuator has neither gears nor rotating shafts. Its displacement is based on solid state dynamics and shows no wear and tear. PI has conducted endurance tests on PZTs in which no change in performance was observed after several billion cycles. 7. Vacuum and Clean Room Compatible: Piezo actuators are ceramic elements that do not need any lubricants and show no wear and abrasion. This makes them clean room compatible and ideally suited for Ultra High Vacuum applications. 8. Operation at Cryogenic Temperatures: The piezo effect is based on electric fields and functions down to almost zero Kelvin (with reduced specifications).

Difficulties in Piezo actuators

Creep

Creep is an undesirable property common with piezoelectric actuators. It can result in significant loss in precision when positioning is required over extended periods of time. In particular, during slow operation of SPMs, creep can result in significant distortions in the image generated. Piezoelectric creep is related to the effect of the applied voltage on the remnant polarization of the piezoceramic actuator. If the operating voltage of a piezoelectric actuator is increased, the remnant polarization continues to increase. This manifests itself in a slow creep after the voltage change is complete. A negative step change in the applied voltage would have the opposite effect.

Nonlinear Creep Model

A number of approaches have been proposed to deal with this phenomenon. One approach is based on the approximate description of the creep effect by the following nonlinear equation

(1)

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Here, t0 represents the time at which the creep effect is apparent, y0 is the value of the actuator displacement at time t0, and the creep rate, γ is a fixed value, that can be identified by observing the step response of the actuator.

Linear Creep Model

The linear model captures the low-frequency response of a piezoelectric actuator using creep models applied in mechanics. In particular, the creep effect can be modeled as a series connection of a number of springs and dampers

Where,

(2)

k0 models the elastic behavior of the actuator at low frequencies, ki is the spring constant, and ci is the damping constant. It has been shown that a model order of three, i.e. N=3, would capture the creep effect with reasonable accuracy

Nonlinear Versus Linear Creep Models

A challenge with the nonlinear creep model (1) is its dependence on the choice of the time-parameter t0 used to fit the model. For example, the creep rate γ tends to depend on the choice of the time-parameter t0. Additionally, for any fixed t0, the model is not valid as time t becomes small—the output y becomes unbounded as t → 0 . Similarly, the output becomes unbounded as time becomes large, i.e. t → ∞ . These modeling difficulties can be alleviated by using a linear creep model (2).

Hysteresis

Hysteresis is the main form of nonlinearity in piezoelectric transducers. The original meaning of the word refers to “lagging behind” or “coming after.”However, it must not be confused with “phase lag,” which is not nonlinearity and is present in many linear systems. Hysteresis is based on crystalline polarization effects and molecular friction. The absolute displacement generated by an open loop PZT depends on the applied electric field and the piezo gain which is related to the remanent polarization. Since the remanent polarization and therefore the piezo gain is affected by the electric field applied to the piezo, its deflection depends on whether it was previously operated at a higher or a lower voltage (and some other effects).

Hysteresis is typically on the order of 10 to 15 % of the commanded motion. E.g. if the drive voltage of a 50 μm piezo actuator is changed by 10 %, ( 5 μm motion) the position repeatability is still on the order of only 1 % full travel or better than 1 μm. Classical motor driven lead screw positioners will hardly beat this repeatability.

10

Fig 10 Steady state, I/O plots corresponding to phase lag from creep model G in (5): (top plot) input

sin(0.4.pi.t); and (bottom plot) input sin(2.pi.t)is higher frequency.

Fig 11 Hysteresis curves of an open loop piezo actuator for various peak voltages

Hysteresis Modeling

One regular way to overcome the nonlinearity is to model the hysteresis first and then construct a feedforward compensation scheme. A number of hysteresis models are available in the literature, such as the Preisach model, Maxwell model, Duhem model, Prandtl–Ishlinskii model, and Bouc–Wen model, etc. The schematic of the piezo actuator model is shown in Fig 10

11

Modeling Errors

Fig 12 Piezo actuator model

The system performance (controller design) should be robust to the presence of modeling errors due to parameter variations and unmodeled dynamics.

Parameter Variations:

A major difficulty in modeling piezoelectric-actuator dynamics is that parameters (such as the applied-voltage to induced-strain constant and the external load) are not known accurately. Therefore, it is challenging to develop a priori accurate models for controller design. Even when the parameters are known, they can change over relatively long time intervals because of aging effects. More-over, piezoelectric parameters are very sensitive to variations in temperature. Therefore, experimental modeling and parameter identification are important aspects of the controller design, thus making robust, adaptive, and learning techniques well suited for the control of piezoelectric-actuator-based systems.

Unmodeled Dynamics:

When designing controllers for the vibrational dynamics of piezoelectric actuators, high- frequency vibrational modes are often neglected to obtain a simplified model (for controller design). However, the high-frequency vibrational modes can affect the stability of the closed-loop system as well as impose limitations on the achievable performance of the closed-loop system. Therefore, the spillover effects on these unmodeled modes should be considered in the controller design.

Vibrations

In the high speed application of piezo actuators, vibration is one of the major constraints. Vibrations induced when the positioning bandwidth is increased relative to the first resonant mode of the piezoelectric actuator and become significant at approximately 1/10th of this frequency. The degradation of the positional accuracy is comparatively low at lower operating frequency. As a result to eliminate the non linearity like vibration, the operating bandwidth has to be bound much smaller than the first resonating frequency of the piezo electric actuator.

12

To appreciate the complications that can arise during high speed nanopositioning applications, note that in SPM a probe is moved over the sample in a raster pattern. To achieve this specific movement of the probe, a slowly increasing ramp signal is applied to the x-electrode of a piezoelectric tube scanner, while the y-electrode is driven by a fast triangular waveform. When the frequency of this latter waveform is high, the lateral movement of the tube is distorted.

Self Heating Self-heat generation is a phenomenon which occurs in PEAs when they are continuously

driven at high frequency under high electric field. Substantial temperature rise is observed in which may affect the performance and durability of the actuator. Moreover, the hysteresis behavior may change due to temperature variation which affects the phenomenological model and feedforward control of the actuator. Also, due to temperature variation, the model parameter such as piezoelectric capacitance is also affected. It is reported that the self-heating phenomenon is a function of frequency, electric field and effective volume of the actuator. It is shown that a temperature rise increases the current in the actuator. Self-heat generation results from losses such as mechanical damping and dielectric losses. At high frequencies close to resonance, it is thought that the mechanical losses play a major role in heat generation while at frequencies lower than the resonance frequency, the dielectric losses contribute most to heat generation. The dielectric loss is caused by the ferroelectric hysteresis loss which primarily occurs due to domain switching. A theoretical model is developed to model the self-heating phenomenon which is based on the law of energy conservation. The model assumes that rate of heat generation is proportional to the frequency and the hysteresis loss per driving cycle per unit volume; u. also studied the geometric changes in different actuators. They conclude that the steady-state temperature rise is a linear function of ratio of effective actuator volume to surface area. They also show that hysteresis varies with temperature. However, the temperature effect on the hysteresis loss is not considered in their model. The self-heating model is extended which includes a heat sink attached to the actuator in order to reduce the actuator temperature due to self-heat generation. Instead of the loss term, u, displacement hysteresis, Df (an equivalent parameter to u calculated from the strain-electric field hysteresis) is introduced in the model. The model predicts the self-heating phenomenon in the presence of a heat sink and concludes that the self-heating temperature increase is reduced by 39% by the introduction of the heat-sink. However, the model does not account for the mechanical losses due to friction between the heat sink and the actuator. A different temperature prediction model is proposed where it is shown that temperature change due to self-heating increases the current flow. The change in the current measurement is used to measure the change in temperature. it is shown that the temperature rise due to self-heating in non resonant applications is a function

of driving frequency, f, electric field, E and effective volume to surface area ratio

predict the temperature is shown in Equation

ve . A model to A

13

T −T0 = ufve

kT A [1− exp(−

kT A vρ.c

t)]

(3)

where, u is the loss of the sample per driving cycle per unit volume, kT is the overall heat transfer coefficient, ½ is the density of the PZT material, v is the actuator volume and t is the time.

Bandwidth-Precision-Range Tradeoffs

Controller design has to consider tradeoffs between the bandwidth, precision, and range of a piezoelectric actuator. Positioning precision depends inversely on the bandwidth, not only because of the difficulty in controlling higher frequency modes of the piezoelectric actuator (which leads to a loss in precision), but also because the sensor noise tends to be proportional to the bandwidth. Moreover, precision also depends inversely on the positioning range because of quantization noise in digital controller implementations. For example, analog-to-digital conversion (when using analog sensors such as thermal and capacitive sensors) as well as digital- to-analog conversion (for actuation) introduce noise, which adversely affects the controller performance. The bandwidth tends to be inversely dependent on the range because the first vibrational resonance of the piezoelectric actuator tends to be higher for a smaller actuator. Note that vibrations tend to degrade positioning accuracy as the main frequency content of the input becomes close to the first resonance frequency of the system. One approach to reduce vibration- induced error is to choose system inputs that avoid exciting the piezoelectric positioner’s vibrational dynamics. Specifically, vibrations can be decreased by limiting the input frequency content to well below the system resonance (low-speed operation). Alternatively, to enable higher-speed operation, the first resonance frequency of the system can be increased by optimizing the geometry of the piezoelectric positioner (to make it stiffer). This optimization, however, usually results in a smaller (or stiffer) piezoelectric positioner, which also tends to have a smaller maximum positioning range. Therefore, the tradeoffs are between the maximum range and the achievable bandwidth of the piezoelectric positioner

Present state of art of Hysteresis compensation techniques

There are several novel control strategies that has been proposed in different literatures,

which includes robust control, sliding mode control, adaptive control and dither based control. Sliding mode control (SMC) is a nonlinear control approach that drives the system’s state trajectory upon a specified sliding surface and maintains the trajectory on this surface for the subsequent time. SMC with feedforward compensation is reported in [1].The feedforward controller eliminates hysteresis nonlinear term but it is not enough to eliminate the nonlinearities completely. Practical hysteresis effect is different from the estimated hysteresis effect. Sliding mode controller adds efficiency to have robustness for the remaining nonlinearity and fast response which a feedforward controller cannot have. SMC design using the Extended Kalman

14

filter is reported in [2]. Sliding mode control with perturbation estimation (SMCPE) is employed for a precise tracking control of a piezo-driven micro positioning stage. EKF is employed to estimate the states of the nonlinear system including both the velocity and hysteresis term. The estimated states are then used by the designed SMCPE controller to obtain the tracking control voltage for the piezo actuator. [3] describes the adaptive PI based SMC. However Conventional SMC creates some undesired oscillations in the control signal. Besides, the design of the boundary layer technique of SMC requires the prior knowledge of bounds on system uncertainties and disturbances. Adaptive PI control is used in place of the discontinuous control term for the SMC. The main utility of this approach is to suppress the chattering which is not desirable in practical situation. Dither controller is described in [4,5] where, Dithering is a process of intentionally adding artificially generated noise to an otherwise uncorrupted signal to improve the performance of an end overall system. The notion of stochastic resonance for nanopositioning is studied to determine the optimal dither level for efficient plant performance. Dither mechanism is devised to determine a suitable voltage and displacement dither variance that matches the minimum tracking error level. The optimal control for hysteresis compensation is highlighted in [6], where Optimal control is attractive as it aims to minimize some cost functional like energy consumption or final time. Adaptive inverse control with hysteresis operator is presented in [7] where the inverse hysteretic observer are identified during operation by a stable adaption law and transformed to the controller parameter. As a result maximum non linearity error by hysteresis is lowered about one order of magnitude. Antiwindup strategy and repetitive control is reported in [8].Due to the limits of voltage applied to the PZT, a saturation function is added to restrict the signal of controller output between the two input extremes. However, the interaction of integration and saturation may cause the phenomenon of windup for the PID controller. Here the back calculation Antiwindup scheme is employed. It is observed that an additional feedback loop is added in the system, which is formed by generating a voltage error between the actual input signal (v) to the PZT and the controller output. On the other hand the repetitive control has the major advantage that it gives the control input using the error signal information in the previous period. Thus, the control signal can be adjusted repetitively by the RC for the tracking of a periodic reference motion.

Motivation

For compensating the non linear effect in terms of hysteresis, it is very important to develop the hysteresis model accurately. Dahl model is preferred over the other models because to establish the non linear hysteretic system, Dahl model is very accurate and inverse Dahl model can be constructed to develop the feedforward controller. Secondly, non symmetric hysteresis loop can be better described by Dahl model than Bouc-Wen model with same numbers of model parameters. In the above study, it is found that Dahl hysteresis model is rarely used for controller design purpose. So this particular model is mainly focused in this work to achieve better elimination of hysteresis and positional accuracy.

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Fine positional accuracy is very much essential in the applications like positioning of wafers, scanning probe microscopy, biological cell operators, IC chip assembly line etc. Therefore, the set point tracking performance and the noise rejection should be very high. Internal model control approach with Dahl hysteresis model gives satisfactory performance under the constraints like process and measurement noise, plant parameter uncertainty and temperature effect etc.

Thesis organization

The work carried out in this thesis has been organized into six chapters. The present chapter

introduces the general aspects of nano positioning and prevalent control approaches. It also presents a brief state-of-art survey on this area of research and sets the motivation behind the present work.

Chapter two presents the system modeling and identification of model parameters for

developing a piezoelectric actuator with its mechanical equivalence. It also highlights the construction of Dahl hysteresis model and comparison of the same with other existing models.

Chapter three presents the approaches of controller design. Several controllers have been

implemented like Feedforward control, feedback control, Internal model control, Fuzzy control etc.

In Chapter four, the controller’s performance is verified in Matlab/Simulink platform. The performance is examined with comparison of the following parameters like are under hysteresis curve, set point tracking error, peak to peak error and r.m.s error. This model also verified under the plant parameter variation.

Chapter five primarily contains the hardware implementation of some of the controllers. The

feedforward controller is developed on TMS320C6713 DSP platform. It also contains the operation and control of PI based piezo actuator with LabVIEW model.

Chapter six concludes the work with proposed work to be done in future.

16

n

Chapter Two 2. System modeling and Identification

Dynamic Plant Modeling

In the current research, instead of investigating the individual PZT actuator, the entire micro manipulator system including the components of mechanical amplifiers, compound parallelogram flexures, and PZT actuators is studied. Considering the mechanical part as linear and of second order, and the nonlinearity arising from the PZT actuator, the dynamic model of whole system with nonlinear hysteresis can be established as follows:[8]

M.x + D.x + K.x = T.u − Fh (4)

Where, the parameters M, D, K, and x represent the equivalent mass, damping coefficient,

stiffness, and x-axis displacement of the XY micromanipulator, respectively. In addition, T is the piezo-electric coefficient, u denotes the input voltage, and Fh indicates the hysteretic effect of the system in terms of force.

Traditionally, the system model of can be identified by finding the model parameters through the experiments. Specifically, dividing by M, the left hand side equation can be obtained as a linear second-order system in the form

x + 2.ξ .ωn .x + ω2 = T .u − Fh

M M

(5)

Where, ωn the natural frequency of oscillation and ξ is the damping ratio of the second order system.

Hysteresis Modeling Smart material-based actuators which are widely used for industrial applications

exhibit strong hysteresis property under increasing and decreasing inputs. The hysteresis properties of smart actuators are known to cause inaccuracies and oscillations in the system responses that may even lead to instability of the closed loop system. To describe hysteresis phenomenon in smart actuators, a number of hysteresis models have been utilized, which can be roughly classified into 1. Physics based models and 2. Phenomenological models. Some of the most popular hysteresis models are Preisach model, Prandtl-ishlinski model, Bouc-Wen model and Dahl model.

Preisach Model Preisach hysteresis model, which is the most well-known phenomological based-operator

model, has been formulated to characterize hysteresis phenomenon in smart actuators. In this

17

model, hysteresis is modeled as a cumulative effect (density function) of all possible delayed relay elements which are parameterized by a pair of threshold variables.

The output of the Preisach model can be calculated by a double integral defined over the Preisach triangle

y(t) = ∫α ≥β µ(α, β )γ (α, β , x(t))dα.dβ (6)

Where, µ (α , β ) is the distribution function determined from measurements, and γ (α , β , x(t)) is the characteristics of one elementary hysteron. The variables α and β are called switching fields of the rectangular hysteron.

Prandtl-Ishlinskii Hysteresis Model Another popular phenomenological hysteresis model is the Prandtl–Ishlinskii model. This

model is a superposition of elementary play or stop operators, which are parameterized by a single threshold variable. PI model is a subset of the Preisach model and is defined in terms of an integral of play operator or stop operator with a density function determining the shape of the hysteresis.

The Prandtl-Ishlinskii model utilizes the play operator F [v](t) r to describe relationship between output yp and input v

R

y p = q.v + ∫ p(r)Fr [v](t)dr o

(7)

Where, p(r) is a density function, satisfying p(r) ≥ 0 , which is generally identified from experimental data. q is a positive constant.

c-Wen Model

the Bouc-Wen hysteresis model can also be employed to describe the plant dynamics in a simple manner.

mx + bx + kx = k (d .u − h) n −1 n

(8)

h = α .d .u − β u h h − γ .u . h Where, the parameters m, b, k, and x represent the mass, damping coefficient, stiffness,

and x-axis displacement of the XY micromanipulator, respectively, d is the piezoelectric coefficient, u denotes the input voltage, and h indicates the hysteretic loop in terms of displacement, whose magnitude and shape are determined by the parameters α , β , γ and the order n, where n governs the smoothness of the transition from elastic to plastic response. For the elastic structure and material, n=1 is usually assigned.

18

∑ m k

Hysteresis Model In this work, Dahl hysteresis model is used as it describes the system non linearity more accurately. The classical Dahl model is expressed as

F x dx ψ =1− ( ) sgn( )

Fc dt (9)

dF(x) = σψ i sgn[ψ ]

dx (10)

Now, dt>0 implies sgn(dx/dt)= sgn(dx). This derivation uses the standard simplification of Dahl’s model setting i=1 to simplify calculations.

For positive displacement, dx>0 Dahl’s model is a first order ordinary differential equation in x.

dF(x) = σ(1− F(x))

(11) dx Fc

Where, Fc is the steady state value of F(x).

For negative displacement, dx<0 Dahl’s model becomes

dF(x) = σ(1+ F(x))

(12) dx Fc

Now, -Fc is the steady state value for F(x).

N-th order Dahl’s model

Consider the n-th order linear differential equation in x

y(n) (x) + n−1

k =1 ak y

(n−k ) (x) = ∑k =0 b u(m−k ) (x) (13)

Which is stable in forward integration with m<n

A state space equation of the model is more useful for computational and simulation purposes. Converting the transfer function to standard controllable state space form, the hysteresis model becomes the following in the displacement domain

dq

= A.q

+ B.u dt

y =C.q +[0].u

(14)

(15)

19

n

q

.

m

0

2

2

0 Where, q

is an intermediate state variable. .

1 . . . .

0

; B =

0 0

.

A = . 0

. . 0 1

− sgn(dx) an . . . − sgn(dx)a1 1

sgn( dx ) n b sgn(

dx ) .

n −1 m −1

C = sgn(

dx ) n − m b .

0

The hysteresis model also has a time domain representation multiplying by dx/dt

dq = dq . dx (16) dt dx dt

dq = Aq dx + Bu dx (17) dt dt dt

y = Cq +[0].u

(18)

Second order Dahl’s model

It has been shown that the hysteretic force term Fh can be predicted accurately by the second- order. The differential equation for second order Dahl’s model

d F + sgn(dx)a dF + a

F = sgn(dx)b

dx + b u

(19)

dt2 1 dt 2 1 dt 0

Time domain state space representation of the equation

q q1 ( x) = ( x) (20)

dq

dx dx = Aq + Bu

(21)

Where, dt dt

F

b

0

20

=

C.q

(22)

21

0 1 0 A = ; B =

− a2 − sgn( dx ).a1 1

C = [b1 sgn(dx)b0 ]

Where, the hysteresis model parameters can be derived based on the following formulas

a = 2 ln( peakn−1

1 T )

peakn

2π 2 a1

a2 = T

+ 2

b1 = Gdc .a2

b0 = s0

nth

T denotes the period of the damped oscillation, peakn represents the overshoot with respect to the steady state values, Gdc denotes the D.C gain and S0 denotes the initial slope respectively.

The overall plant model with Dahl hysteresis model can be expressed in Fig 13

Fig 13 Schematic of the piezo actuator

Model Identification

Particle Swarm Optimization (PSO) method PSO is a stochastic global optimization method which is based on simulation of social

behavior. As in GA and ES, PSO exploits a population of potential solutions to probe the search space. In contrast to the aforementioned methods in PSO no operators inspired by natural evolution are applied to extract a new generation of candidate solutions. Instead of mutation PSO relies on the exchange of information between individuals, called particles, of the population, called swarm. In effect, each particle adjusts its trajectory towards its own previous best position, and towards the best previous position attained by any member of its neighborhood. In the global variant of PSO, the whole swarm is considered as the neighborhood. Thus, global sharing of information takes place and particles profit from the discoveries and previous experience of all other companions during the search for promising regions of the landscape. To visualize the operation of the method consider the case of the singleobjective minimization case; promising regions in this case possess lower function values compared to others, visited previously.

2

22

x

*

=

Initially, let us define the notation adopted in this paper: assuming that the search space is Ddimensional, the i-th particle of the swarm is represented by a Ddimensional vector Xi = (xi1; xi2; : : : ; xiD) and the best particle of the swarm, i.e. the particle with the lowest function value, is denoted by index g. The best previous position (i.e. the position corresponding to the best function value) of the i-th particle is recorded and represented as Pi = (pi1; pi2; : : : ; piD), and the position change (velocity) of the i-th particle is Vi = (vi1; vi2; : : : ; viD).

The particles are manipulated according to the following equations (the superscripts denote the iteration)

k+1 k k k k k k k

Vi = χ(w.Vi +ciri1 ( pi − xi ) +c2ri2 ( pg − xi )) (23) k +1 k i i + Vi

k +1

(24) Where, i = 1; 2; : : :;N, and N is the size of the population; χ is a constriction factor which is used to control and constrict velocities; w is the inertia weight; c1 and c2 are two positive constants, called the cognitive and social parameter respectively; ri1 and ri2 are random numbers uniformly distributed within the range [0; 1]. Eq. (23) is used to determine the i-th particle's new velocity, at each iteration, while Eq. (24) provides the new position of the i-th particle, adding its new velocity, to its current position. The performance of each particle is measured according to a fitness function, which is problem dependent. In optimization problems, the fitness function is usually identical with the objective function under consideration.

The role of the inertia weight w is considered important for the PSO's convergence behavior. The inertia weight is employed to control the impact of the previous history of velocities on the current velocity. Thus, the parameter w regulates the tradeoff between the global (wide ranging) and the local (nearby) exploration abilities of the swarm. A large inertia weight facilitates exploration (searching new areas), while a small one tends to facilitate exploitation, i.e. fine tuning the current search area. A proper value for the inertia weight w provides balance between the global and local exploration ability of the swarm, and, thus results in better solutions. Experimental results imply that it is preferable to initially set the inertia to a large value, to promote global exploration of the search space, and gradually decrease it to obtain refined solutions. The initial population can be generated either randomly or by using a Sobol sequence generator, which ensures that the D-dimensional vectors will be uniformly distributed within the search space.

el Identification with PSO

The fitness function for minimization is chosen as

1 n

f (M , D, K ,T ) = n ∑(xi − xi ) (25)

i=1

x

2

23

x * i.e., r.m.s of the Dahl model output i deviations with respect to the experimental results xi, where n denotes the total number of samples. The optimization problem is stated below: Minimize: f(M,D,K,T) represented by Eq. (25) Variables to be optimized: M, D, K, T Subject to:

M ∈ [0.1, 0.2], D∈[1000, 5000], K∈[10000, 50000], and T∈ [0.01,0.1]

In order to apply PSO for the model identification, several fundamental parameters are required to be assigned at first. In the current four-dimensional optimization problem, a particle can be described by Xi=(xi1 ,xi2 ,xi3 ,xi4) with the particle velocity Vi =(vi1 ,vi2 ,vi3 ,vi4), which corresponds to a set of the system dynamic parameters (M,D,K,T). In the n th generation, there are N particles popn=(X1 , X2 ,_,XN), where the population size N is set to be 10 for the current problem. The inertia weight w determines the impact of previous velocities on the current velocity, and its initial and final values are selected as 0.9 and 0.4, respectively, where 500 epoches are allowed to take from the initial value to the final one linearly. In addition, the local and global acceleration constants are assigned as c1=2.0 and c2=2.0, respectively. As far as the termination criterion is concerned, three items are set. One criterion is the maximum number of iterations (2000) for the optimization procedure, another one is the minimum global error gradient (10−6), which is the error between two neighboring gBest, and the third one is the maximum number of iterations without error change, which is chosen as 500.

Construction of Dahl Hysteresis Model Now, with four dynamic parameters M, D, K, and T obtained from PSO method and four

hysteresis parameters a1, a2, b1, and b0 obtained based on the above conventional approach, the whole system can be determined finally. A block diagram of the dynamic system is illustrated in Fig 13. Where, the details of the Dahl hysteresis model are shown in Fig.14. Based on the block diagrams, the system model can be easily implemented with MATLAB/SIMULINK software.

Fig 14. Dahl Hysteresis model

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Parameters values unit M 0.1828 Kg D 2.5973 x103

N.s/m K 2.6065 x 104

N/m T 0.0468 c/m a1 121.9874 - a2 1.1773 x106

- b1 1.8485 x106

- b0 0 -

Table 1. The Dahl model parameters adopted for the micro nano manipulator system

Model Comparison

As simpler hysteresis models, both Bouc–Wen and Dahl models can describe the system with the same number of parameters (eight). For the purpose of comparison, a Bouc–Wen hysteresis model of the system as identified by the PSO approach. It can be observed that the Dahl model represents the system more accurately with a better generalization property. From this point of view, the Dahl model is more superior to the Bouc–Wen model in dealing with non symmetric hysteresis.

25

T Chapter Three

3. Design of Controllers

he objective of motion control is to force the output platform of the micromanipulator to track a given position trajectory. Once the trajectory is assigned, the determination of the input voltage applied to the PZT is the target of the controller design. These controllers

are designed based on the voltage driven strategies. Feedforward Control

Feed-forward is a term describing an element or pathway within a control system which passes a controlling signal from a source in its external environment, often a command signal from an external operator, to a load elsewhere in its external environment. A control system which has only feed-forward behavior responds to its control signal in a pre-defined way without responding to how the load reacts; it is in contrast with a system that also has feedback, which adjusts the output to take account of how it affects the load, and how the load itself may vary unpredictably; the load is considered to belong to the external environment of the system. In a feed-forward system, the control variable adjustment is not error-based. Instead it is based on knowledge about the process in the form of a mathematical model of the process and knowledge about or measurements of the process disturbances. The characteristics of feedforward control are Future oriented, Limiting activities in advance and prevent the problems before they arise.

The basic idea of feedforward controller is shown in Fig 15.

Fig 15 Feedforward Control

Here we have considered the plant that takes voltage signal as input and produces some positional output. Our target is to obtain a controller which can perform the reverse action that of the plant i.e. to generate a voltage signal taking a positional data. We can develop the inverse Dahl model as the feedforward controller. Therefore what ever the set point is provided to the inverse model, it will produce the voltage and accordingly the plant is forced to follow the path. The operating principle of the feedforward control can be expressed by the Eq. 26

26

1 U FF = (M x d

T + D x d + Kx d + Fh

)

(26)

Where, U FF is the output voltage from controller, Fh is the hysteresis force and x d is the desired trajectory. Instead of designing a Dahl model-based hysteresis observer as in the feedforward controller is developed in DSK. This simplifies the controller implementation process by eliminating the requirement of the velocity observer design. Here the hysteresis force can be obtained from the Dahl model. Feedforward controller is basically is the inverse transfer function for the plant along with the hysteresis model. A block schematic of the controller has been shown in Fig 16. The overall model operated by feedforward controller is shown in Fig 17.

Fig 16 Inverse Dahl Model

Fig 17Plant with Feedforward control

Feedforward with Feedback Compensation

There are some drawbacks of feedforward control like it requires infinitely accurate mathematical models, requires infinitely accurate measurements and estimation of the current situation. As it is an open loop system, no corrective measure cannot be taken in feedback if

27

there is any set point error occurs. Due to the existence of errors for the identified model output with respect to experimental results, the hysteresis effect cannot be totally compensated by the feedforward voltage computed by Eq.26. Therefore, an additional feedback control is adopted to compensate for the model imperfection and other disturbances of the system. Here PID controller is used as a feedback control.

P-I-D controller has the optimum control dynamics including zero steady state error, fast response (short rise time), no oscillations and higher stability. The necessity of using a derivative gain component in addition to the PI controller is to eliminate the overshoot and the oscillations occurring in the output response of the system. One of the main advantages of the P-I-D controller is that it can be used with higher order processes including more than single energy storage. The feedback control input can be written as

t

U FB (t ) = K p [ e (t ) + 1

∫ e (τ ) d τ + Td

de (t ) ]

Where,

Ti 0 dt (27)

t is the time variable. The tracking error is defined as e(t)= xd(t) − x(t) with x denoting the measured position. Kp is the proportional gain. Ti is the integral time constant. Td is the derivative time constant.

By adopting an incremental PID algorithm, the overall control signal is given in a discredited form (Fig 18)

Fig 18. Block diagram of the FF plus feedback FB control scheme

Internal Model Control (IMC) Approach

Background

In process control applications, model based control systems are often used to track set points and reject low disturbances. The internal model control (IMC) philosophy relies on the internal model principle which states that if any control system contains within it, implicitly or explicitly, some representation of the process to be controlled then a perfect control is easily achieved. In particular, if the control scheme has been developed based on the exact model of the process then perfect control is theoretically possible.

28

G p

Fig 19 Open loop control strategy

For above open loop control system: Output = Gc . Gp . Set-point (multiplication of all three parameters) Gc = controller of process Gp = actual process or plant Gp* = model of the actual process or plant A controller Gc is used to control the process Gp. Suppose Gp* is the model of Gp then by setting: Gc =inverse of Gp* (inverse of model of the actual process) And if Gp = Gp* (the model is the exact representation of the actual process)

Now it is clear that for these two conditions the output will always be equal to the set point. It show that if we have complete knowledge about the process (as encapsulated in the process model) being controlled, we can achieve perfect control. This ideal control performance is achieved without feedback which signifies that feedback control is necessary only when knowledge about the process is inaccurate or incomplete.

Although the IMC design procedure is identical to the open loop control design procedure, the implementation of IMC results in a feedback system. Thus, IMC is able to compensate for disturbances and model uncertainty while open loop control is not. Also IMC must be detuned to assure stability if there is model uncertainty.

Strategy

In practice, process model mismatch is common; the process model may not be invertible and the system is often affected by unknown disturbances. Thus the above open loop control arrangement will not be able to maintain output at set-point. Nevertheless, it forms the basis for the development of a control strategy that has a potential to achieve perfect control. This strategy is known as Internal Model Control and the structure is depicted in Fig 20.

In this diagram, d(s) is an unknown disturbance affecting the system. The manipulated input U(s) is introduced to both the process and its model. The process output, Y(s) is compared

with the output of the model, resulting in a signal d (s) . That is,

d (s) = [G (s) − ~ (s)]U (s) + d (s) (28) p

29

Gp

c Gp

Gp

Gp

Gp

Gp

G p

G p

G p

Fig 20. Schematic of the IMC

If, d(s) is zero for example, then d (s) is measure of the difference in behavior between

the process and its model. If Gp (s) = ~ (s), then d (s) is equal to the unknown disturbance.

Thus d (s) may be regarded as the information that is missing in the model, ~ (s) and

can therefore be used to improve control. This is done by subtracting d (s) from the set-point R(s), which is very similar to affecting a set-point trim. The resulting control signal is given by,

U (s) = [R(s) − d(s)]G (s) = R(s) −[Gp (s) − ~ (s)]U (s) − d (s)Gc

(s)

(29)

Thus, U (s) = [R(s) − d (s)]Gc (s) (30) 1 + [G p (s) −

~ (s)]G (s)

Since, Y (s) = Gp (s)U (s) + d(s) (31) The closed loop transfer function for the IMC scheme is therefore

[R(s) − d (s)]Gc (s)Gp (s)

Or,

Y (s) = 1 +[Gp (s) −

~ (s)]Gc (s) + d (s)

Gc (s)Gp (s)R(s) + [1 − Gc (s) ~ (s)]d (s) Y (s) =

1 + [Gp (s) − ~ (s)]Gc (s)

(32)

From this closed loop expression, we can see that if Gc (s) = ~ (s) −1 , and if G (s) =

~ (s),

c

p

30

G p

G p

Gp

G p

G p

Gp

imc Gp Gp

G p G p

G p

G p G p

G p

G p

then perfect set point tracking and disturbance rejection is achieved. Theoretically, even if

G p (s) ≠ ~ (s), perfect disturbance rejection can still be realized provided Gc (s) =

~ (s) −1 , .

Additionally, to improve robustness, the effects of the process model mismatch should be minimized. Since discrepancies between process and model behavior usually occur at the high frequency end of the system’s frequency response, a low-pass filter Gf(s) is usually added to attenuate the effects of process model mismatch. Thus the internal model controllers usually designed as the inverse of the process model in series with a low-pass filter, i.e. GIMC (s) = Gc (s)Gf (s) . The order of the filter is usually chosen such that Gc(s)Gf(s) is proper, to prevent excessive differential control action. The resulting closed loop then becomes

G IMC (s)G p (s) R (s) + [1 − G IMC (s) ~

(s)]d (s)

Y (s) = 1 + [G p (s) −

~ (s)]G IMC (s)

(33)

tical Design of IMC Designing an internal model control is relatively easy. Given a model of the process,

~ (s) , first ~ (s) is factorized into ‘invertible’ and ‘non-invertible’ components, i.e. ~ (S ) =

~ + (s). ~ − (s) (34) GP G p G p

The non-invertible component, ~ − (s) , contains terms which if inverted, will lead to instability

and realisability problems, e.g. terms containing positive zeros and time-delays. Next, set

Gc (s) = ~ + (s) −1 and then GIMC (s) = Gc (s)Gf (s) , where Gf(s) is a low pass function of appropriate order.

Sensitivity and Complementary Sensitivity functions for IMC

Sensitivity functions of IMC are calculated to compare it with the conventional feedback

control.

ε (s) = E(s) = Y (s) R(s) − d (s) d (s)

For IMC, since Y (s) = G IMC (s)G p (s) R (s) + [1 − G IMC (s) ~ (s)]d (s)

1 + [G p (s) − ~ (s)]G

IMC (s)

Y (s) 1 − G IMC (s) ~ (s)

ε (s) = = d (s) 1 + G

IMC (s)[G p (s) −

~ (s)] (35)

Further, supposing that Gp (s) = ~ (s), then

∈~ (s) = 1− G (s) ~ (s) and η(s) = G imc (s) ~ (s)

31

Therefore, in the IMC strategy, the controllers appear linearly in the respective functions. Comparing this with the corresponding functions for the conventional control scheme,

ε (s) = 1

Gc (s)Gp (s) + 1 and η (s) =

Gc (s)Gp (s)

Gc (s)G p (s) + 1

(36)

Since the sensitivity function determines performance whilst the complementary sensitivity function determines robustness, this implies that (compared to the conventional control scheme) the IMC provides a much easier framework for the design of the robust control systems.

Modified Internal Model Control

In this approach the IMC controller C(s) has been replaced by a negative feedback closed loop combination of C(s) and Gm(s). From the perfect set point tracking point of view, this model is found to be more efficient in the presence of process and measurement noise. Consider the conventional control model in Fig 21.

Fig 21 Conventional IMC structure

The output obtained from the fig 21 can be expressed as

Y(s) = G(s)C(s)R(s) + 1+ C(s)(G(s) −Gm (s))

(1−C(s)Gm (s))D(s)

1+ C(s)(G(s) −Gm (s)) − G(s)C(s)N(s) 1+ C(s)(G(s) − Gm (s))

(37) Here we are considering both external noise input and measurement noises are present

and they have non zero values. If Gm(s)=G(s) and C(s)=1/Gm(s), N(s)=D(s) ≠ 0 from Eqn.37.

we are having Y(s) =R(s)−N(s).

From the present modification the IMC controller becomes

C′(s) = C(s)

1+ C(s)Gm (s) = C(s) / 2

Now substituting C(s) by Y (s) = ( R (s) + D (s) − N (s)) / 2

C′(s)

in the Eq. 37 the output becomes

32

As, D(s) = N(s), then Y(s) = R(s)/ 2 (38)

It is observed from the Eqn. 38 that the output trajectory has become half of the input. So if the input trajectory is chosen double of the required reference, there will be a perfect set-point tracking as the external noise is sufficiently removed. The proposed controller is shown in Fig. 22.

Fig 22 Modified IMC controller

Fuzzy Logic Controller

Control systems theory, or what is called modern control systems theory today, can be traced back to the age of World War II, or even earlier, when the design, analysis, and synthesis of servomechanisms were essential in the manufacturing of electromechanical systems. The development of control systems theory has since gone through an evolutionary process, starting from some basic, simplistic, frequency-domain analysis for single-input single output (SISO) linear control systems, and generalized to a mathematically sophisticated modern theory of multi-input multi-output (MIMO) linear or nonlinear systems described by differential and/or difference equations.

It is believed that the advances of space technology in the 1950s completely changed the spirit and orientation of the classical control systems theory: the challenges posed by the high accuracy and extreme complexity of the space systems, such as space vehicles and structures, stimulated and promoted the existing control theory very strongly, developing it to such a high mathematical level that can use many new concepts like state-space and optimal controls. The theory is still rapidly growing today; it employs many advanced mathematics such as differential geometry, operation theory, and functional analysis, and connects to many theoretical and applied sciences like artificial intelligence, computer science, and various types of engineering. This modern control systems theory, referred to as conventional or classical control systems theory, has been extensively developed. The theory is now relatively complete for linear control systems, and has taken the lead in modern technology and industrial applications where control and automation are fundamental. The theory has its solid foundation built on contemporary mathematical sciences and electrical engineering, as was just mentioned. As a result, it can

33

provide rigorous analysis and often perfect solutions when a system is defined in precise mathematical terms. In addition to these advances, adaptive and robust as well as nonlinear systems control theories have also seen very rapid development in the last two decades, which have significantly extended the potential power and applicable range of the linear control systems theory in practice.

Conventional mathematics and control theory exclude vagueness and contradictory

conditions. As a consequence, conventional control systems theory does not attempt to study any formulation, analysis, and control of what has been called fuzzy systems, which may be vague, incomplete, linguistically described, or even inconsistent. Fuzzy set theory and fuzzy logic play a central role in the investigation of controlling such systems. The main contribution of fuzzy control theory, a new alternative and branch of control systems theory that uses fuzzy logic, is its ability to handle many practical problems that cannot be adequately managed by conventional control techniques. At the same time, the results of fuzzy control theory are consistent with the existing classical ones when the system under control reduces from fuzzy to nonfuzzy. In other words, many well-known classical results can be extended in some natural way to the fuzzy setting. In the last three chapters, we have seen many such examples: the interval arithmetic is consistent with the classical arithmetic when an interval becomes a point; the fuzzy logic is consistent with the classical logic when the multi-valued inference becomes two-valued; and the fuzzy Lyapunov stability and fuzzy controllability (and observability) become the classical ones when the fuzzy control systems become nonfuzzy.

Basically, the aim of fuzzy control systems theory is to extend the existing successful

conventional control systems techniques and methods as much as possible, and to develop many new and special-purposed ones, for a much larger class of complex, complicated, and ill- modeled systems – fuzzy systems. This theory is developed for solving real-world problems. The fuzzy modeling techniques, fuzzy logic inference and decision-making, and fuzzy control methods to be studied in the following chapters, should all work for real-world problems – if they are developed correctly and appropriately. The real-world problems exist in the first place. Fuzzy logic, fuzzy set theory, fuzzy modeling, fuzzy control methods, etc. are all man-made and subjectively introduced to the scene. If this fuzzy interpretation is correct and if the fuzzy theory works, then one should be able to solve the real-world problems after the fuzzy operations have been completed in the fuzzy environment and then the entire process is finally returned to the original real world setting. This is what is called the “Fuzzification – fuzzy operation – defuzzification” routine in the fuzzy control systems theory.

uzzy Logic theory

Fuzzy logic is a logic. Logic refers to the study of methods and principles of human reasoning. Classical logic, as common practice, deals with propositions (e.g., conclusions or decisions) that are either true or false. Each proposition has an opposite. This classical logic,

34

therefore, deals with combinations of variables that represent propositions. As each variable stands for a hypothetical proposition, any combination of them eventually assumes a truth value (either true or false), but never is in between or both (i.e., is not true and false at the same time). The main content of classical logic is the study of rules that allow new logical variables to be produced as functions of certain existing variables. Suppose that n logical variables, x1, ..., xn , are given, say

x1 is true; x2 is false; xn is false.

Then a new logical variable, y, can be defined by a rule as a function of x1, ..., xn that has a particular truth value (again, either true or false). One example of a rule is the following:

Rule: IFx1 is true AND x2 is false AND ... AND xn is false THEN y is false.

Because one, and only one truth value (either true or false) is assumed by a logical function of a (finite) number of logical variables (hypothetical propositions), the classical logic is also called a two-valued logic. The fundamental assumption upon which the classical logic is based is that every proposition is either true or false. This principle has been questioned by many philosophers, ever since Aristotle (in his treatise On Interpretation). It is now well understood and well accepted that many propositions are both partially true and partially false. To describe such partial truth values by some new rules, in a way to extend and generalize the two-valued logic, multi valued logics were proposed and developed. As the first attempt, several three- valued logics have now been well established, with their own rationale. It is common in these logics to introduce a “neither” in between “true” and “false.” It has turned out that three-valued logics are successful both logically and mathematically. Motivated by the useful three-valued logics, n-valued logics were developed in the 1930s. In particular, the n-valued logic of Lukasiewicz even allows n = ∞. It has lately been understood that there exists an isomorphism between the two-valued logic and the crisp set theory, and, similarly, there is an isomorphism between the Lukasiewicz logic and the fuzzy set theory. In fact, the isomorphism for the former is the standard characteristic function

Y=XA(x) = 1 if x∈A =0 if x∉ A (39)

This can be interpreted as Y= true if x is true = false if x is false (40)

and the latter is a fuzzy membership function. uzzy Relations

Let S be a universe set, and A and B be subsets of S. Similar to the Cartesian products, A X B denotes a product set in the universe set S X S. A fuzzy relation is a relation between

elements of A and elements of B, described by a membership function ∈ B.

µ AXB (a,b), a ∈ A and b

35

Fig 23. The fuzzy relation “a is slightly larger than b” on [0,1]X[0,1].

A simple example of a fuzzy relation is the following. Let S = R and A = B = [0,1] ⊂R. Define a membership function µ AXB(a,b) for the relation “a is slightly larger than b” by

0 a ≤ b µ AXB (a, b) = −( a −b )

e a b

This is shown in Fig 23. Then, A, B, and µ AXB together define a fuzzy relation between a ∈A and b ∈ B.

Closed loop Set point Tracking System We consider the typical continuous-time, closed-loop, set-point tracking system shown in

Figure 23.

Fig 24 A typical closed loop set point tracking system

In this figure, we assume that the plant is a conventional (crisp) one, which is given but its mathematical model may not be known, and that all the signals (r, e, and y) are crisp. The

36

closed-loop set-point tracking control problem is to design the controller such that the output signal of the controlled plant, y, can track the given reference signal r.

e(t) := r(t) − y(t) → 0 (t →∞).

If the mathematical formula of the plant is unknown, for instance whether the system is

linear or non linear is not known (and, if it is linear, the order is unknown; if it is nonlinear, the kind of non linearity is not known), One may think of designing a conventional controller and try to answer this question at this point, to appreciate the ease of fuzzy logic controller design to be studied below.

First, the general structure of a fuzzy logic controller (FLC), or fuzzy controller (FC) for short, consists of three basic portions: the Fuzzification unit at the input terminal, the inference engine built on the fuzzy logic control rule base in the core, and the defuzzification unit at the output terminal, as shown in Figure 25.

Fig 25. General structure of a fuzzy logic controller.

The Fuzzification module transforms the physical values of the current process signal, the error signal in Figure 4.5 which is input to the fuzzy logic controller, into a normalized fuzzy subset consisting of a subset (interval) for the range of the input values and an associate membership function describing the degrees of the confidence of the input belonging to this range. The purpose of this Fuzzification step is to make the input physical signal compatible with the fuzzy control rule base in the core of the controller. Here, between the physical input signal and the fuzzy subset within the Fuzzification unit, a pre-processing unit mapping the physical signal to some point wise and crisp real values (that the fuzzy subset can accept) may be needed, depending on the nature of the underlying process. Generally speaking, a universal fuzzy logic controller for the closed-loop set-point tracking system shown in Figure 24 is unlikely possible. Hence, the fuzzy subset, both the subset and the membership function, has to be selected by the designer according to the particular application at hand. In other words, depending on the nature and characteristics of the given plant and reference signal, the FLC has to be designed to fit to the need, so as to make the closed-loop fuzzy control system work for that particular application. This situation is just like the design of a conventional controller for a specifically given system, where there is no universal controller in practical design.

The role of the inference engine in the FLC is key to make the controller work − and

work effectively. The job of the “engine” is to create the control actions, in fuzzy terms,

37

according to the information provided by the Fuzzification module and the set-point tracking requirement (and perhaps other control performance requirements as well).

A typical fuzzy logic IF-THEN rule base performing the inference is expressed in the

general form R1: IF controller input e1 is E11 AND ... AND

Controller input en is E1n THEN controller output u1 is U1.

M Rm: IF controller input e1 is Em1 AND ... AND

Controller input en is Emn THEN controller output um is Um.

The fuzzy subsets E11, ...,Em1 share the same subset E1 and the same membership

function μE1 defined on E1, and fuzzy subsets E1n, ..., Emn share the same subset En and the same membership function μEn defined on En. In general, m rules produce m controller outputs, u1, ..., um, belonging to m fuzzy subsets, U1, ..., Um, in which, of course, some of them may overlap. The establishment of this rule base depends heavily on the designer’s work experience, knowledge about the physical plant, analysis and design skills, etc., and is, hence, more or less subjective. Thus, a good design can make the controller work; a better design can make it work more effectively. This situation is just like conventional design: any specific design is not unique in general. Yet, there are some general criteria and some routine steps for the designer to follow in a real design, which will be discussed in more detail later. Here, basically, what have to be determined are the choices of the controller’s input and output variables and the IF-THEN rules.

The defuzzification module is the connection between the control rule base and the

physical plant to be controlled, which plays the role of a transformer mapping the controller outputs (generated by the control rule base in fuzzy terms) back to the crisp values that the plant can accept. Hence, in a sense the defuzzification module is the inverse of the Fuzzification module. The controller outputs u1, ..., um, generated by the rule base above, are fuzzy signals belonging to the fuzzy subsets U1, ..., Um, respectively. The job of the defuzzification module is to convert these fuzzy controller outputs to a point wise and crisp real signal, u, and then send it to the physical plant as a control action for tracking. Between the defuzzification step and the physical plant, a post-processing unit mapping the point wise signal u to a physical signal (that the plant can accept) may be needed, depending again on the nature of the underlying process. What has to be determined in this stage is essentially a defuzzification formula. There are several commonly used, logically meaningful, and practically effective defuzzification formulas available, which are by nature weighted average formulas in various forms.

The “Centre of Gravity” formula

38

Its continuous time form is

The “Centre of Sums” formula

Its continuous time form is

The “Mean of Maxima” formula

Its continuous time form is

(41)

(42)

(43)

(44)

(45)

(46) Design Principle of Fuzzy Logic Controllers

Fuzzification Module

It transforms the physical values (position, voltage, degree, etc.) of the process signal, the error signal shown in Figure 24 which is an input to the fuzzy logic controller, into a normalized

39

fuzzy subset consisting of a subset (interval) for the range of the input values and a normalized membership function describing the degree of confidence of the input belonging to this range.

In the context of controller of nano positioning system, the input variable is positional error (p) between desired and obtained trajectory and the output variable is control voltage (v) for the plant. The crisp set if input variable (p) is classified into 5 categories- 1. Positive large (PL), 2. Positive med (PM), 3. Zero (Z), 4.Negative med (NM), 5. Negative large (NL).

The membership function of the input variable is expressed as Fig 26.

Fig 26. Clustering and membership value of input variable

The membership function for the output variable i.e. controller voltage (v) is shown in Fig 27. The o/p variable can be classified into 5 groups such as 1. Positive (+ve), 2. Med positive (+med ve), 3. Zero (Z), 4. Med negative (-med ve), 5. Negative (-ve).

Fig 27. Clustering and membership value of output variable

Fuzzy Logic Rule Base

Designing a good fuzzy logic rule base is key to obtaining a satisfactory controller for a particular application. Classical analysis and control strategies should be incorporated in the establishment of a rule base. In this design the rule base is scripted as

IF ‘p’ is ‘NL’ ⇒ THEN ’v’ is ‘-ve’ IF ‘p’ is ‘NM’ ⇒THEN ‘v’ is ‘-med ve’ IF ‘p’ is ‘Z’ ⇒ THEN ‘v’ is ‘Z’

40

IF ‘p’ is ‘PM’ ⇒ THEN ‘v’ is ‘+med ve’ IF ‘p’ is ‘PL’ ⇒ THEN ‘v’ is ‘+ve’

Defuzzification Module

The defuzzification module is in a sense the reverse of the Fuzzification module: it

converts all the fuzzy terms created by the rule base of the controller to crisp terms (numerical values) and then sends them to the physical system (plant, process), so as to execute the control of the system. Here the “Centre of Gravity” formula of defuzzification has been used.

41

Chapter Four

Simulation using MATLAB/SIMULINK

42

These proposed controllers are simulated in MATLAB/SIMULINK platform and their performances are studied for the comparative study.

Input Reference Signal The effectiveness of the proposed control strategies are verified using a rectified sinusoidal signal of amplitude 100um and frequency 1Hz shown in fig 28.

MATLAB codes for the input

clc clear all t=0:.01:10 n=length(t) for i=0:n-1 y(i+1)= 100e-6*sin(2*pi*i/200); if (y(i+1)<0) y(i+1)=-y(i+1); end end for j=1:n ab1(j,1)=t(j); ab1(j,2)=y(j); end ab1 plot(t,y,'-'),grid on

Fig 28 Reference input trajectory

43

MATLAB model of the controllers Feedforward control

Fig29. Simulink model of Feedforward controller

Feedforward and Feedback control

Fig 30 Simulink model of closed loop control

Internal Model control

Fig 31 Simulink model of IMC

44

Two degree of freedom IMC

Fig 32 Simulink model of two degree freedom IMC

Modified IMC structure

Fig 33 Simulink model of modified IMC

45

4.2.6. Fuzzy logic controller Fig 34. Fuzzy controller model

Fig 35. FIS file structure Fig 36. FIS editor for i/p and o/p

Fig 37. Membership function editor for input and output variables

46

Fig 38 Fuzzy rule editor panel

Simulation Results

eresis Plots of the different controllers

In the following plot, the output voltage of the controller is plotted in the X axis and the output trajectory from the plant is plotted in Y axis. These curves indicate the non-linear behavior of the plant. The decrease in area under the hysteresis curve denotes the more amount of hysteresis is compensated.

Fig 39 Feedforward controller.

47

Fig 40 Feedforward+ feedback controller

Fig 41 Internal model controller

Fig 42 Modified IM

48

Tracking errors

Deviations between input and output trajectories Here the blur lines indicate the input trajectories and the green lines denote the output path.

Along Y axis position is plotted in meter and along X axis time is plotted in second.

Fig 43 Set point tracking of Feedforward controller

Fig 45 Set point tracking of conventional IMC

Fig 44 Set point tracking of Feedforward+ Feedback controller

49

Fig 46 Set point tracking of modified IMC structure

Set point errors

Fig 47 Set point tracking of Fuzzy control

Now the difference of the input and output trajectory is plotted. Here Positional difference is plotted in Y axis and time in second is plotted along X axis

Fig 48 Tracking error of Feedforward controller

50

Fig 49 Tracking error of Feedforward+ Feedback controller

Fig 50 Tracking error of Fuzzy controller

Fig 51 Tracking error of the conventional IMC

Fig 52 Tracking error of the modified IMC structure

51

Fuzzy control 13x10−7 5.82x10−7

1.3% 0.51%

2 degree of freedom IMC 15 x10 −8 5.82 x10 −8

0.15% 89%

The error values are tabulated in the form of peak to peak error and RMS error

Controllers Peak to peak value (m)

RMS value (m)

Percentage error(P-P)

Cumulative percentage error(rms value)

Feedforward control 20 x10 −7 6 x10 −7 2%

Feedforward with feedback control

15 x10 −7 5.85 x10 −7

1.5% 2.5%

Internal model control 12 x10 −7 5.8 x10 −7

1.2% 0.34%

Modified IMC

7 x10 −8

1.36 x10 −8

0.7% 76%

4.4 Variations of the plant parameters Now the uncertainty is introduced in the plant in the form of the plant parameter variation. Till

now we have considered that the nominal plant model Gm(s) and the plant model G(s) are exact. But in the practical situation, it is also to be considered that they may not be exact. Therefore the dynamic plant parameters like equivalent mass (M), damping factor (D) and the stiffness (K) are

varied for ± 2 % from the prescribed value. The performance of the controllers in the form of peak to peak error and the RMS error are tabulated for the comparison.

Table 3 R.M.S error under parameter variation

Control strategies R.M.S error under parameter variation ( ±2%)(m)

Fuzzy control 4.67x10-7

Conventional Internal model control

4.056x10-7

Modified internal model control 7.17x10-7

Feedforward control 1.821x10-6

Feedforward+ Feedback control 1.79x10-6

51

D

Chapter Five 5. Hardware Modeling and Implementation

Feedforward Controller in TMS320C6713 DSK

ue to the simple structure and being open loop control system, the feedforward controller can be implemented in hardware platform. Based on the inverse Dahl model we have developed a hardware platform of the controller using Digital signal processor TMS320C6713 DSK board. The feedforward control is programmed in Code Composer Studio and then the control signal for the piezo

actuators is generated form DSK Board. The advantage of using DSK is to obtain faster processing speed, floating point operations and flexible programming.

verview of TMS320C6713 DSK The C6713™ DSK builds on TI's industry-leading line of low cost, easy-to-use

DSP Starter Kit (DSK) development boards. The high-performance board features the TMS320C6713 floating-point DSP Capable of performing 1350 million floating-point operations per second (MFLOPS), the C6713 DSP makes the C6713 DSK the most powerful DSK development board. The DSK is USB port interfaced platform that allows to efficiently develop and test applications for the C6713. The DSK consists of a C6713-based printed circuit board that will serve as a hardware reference design for TI’s customers’ products. With extensive host PC and target DSP software support, including bundled TI tools, the DSK provides ease-of-use and capabilities that are attractive to DSP engineers.

The C6713 DSK has a TMS320C6713 DSP onboard that allows full-speed verification of code with Code Composer Studio. The C6713 DSK provides: • A USB Interface • SDRAM and ROM • An analog interface circuit for Data conversion (AIC) • An I/O port • Embedded JTAG emulation support.

Connectors on the C6713 DSK provide DSP external memory interface (EMIF) and peripheral signals that enable its functionality to be expanded with custom or third party daughter boards. The DSK provides a C6713 hardware reference design that can assist you in the development of your own C6713-based products. In addition to providing a reference for interfacing the DSP to various types of memories and peripherals, the design also addresses power, clock, JTAG, and parallel peripheral interfaces.

The C6713 DSK includes a stereo codec. This analog interface circuit (AIC) has the following characteristics: High-Performance Stereo Codec

52

• 90-dB SNR Multibit Sigma-Delta ADC (A-weighted at 48 kHz) • 100-dB SNR Multibit Sigma-Delta DAC (A-weighted at48 kHz) • 1.42 V – 3.6 V Core Digital Supply: Compatible With TI C54x DSP Core Voltages • 2.7 V – 3.6 V Buffer and Analog Supply: Compatible Both TI C54x DSP Buffer

Voltages • 8-kHz – 96-kHz Sampling-Frequency Support

Software Control Via TI McBSP-Compatible Multiprotocol Serial Port • I 2 C-Compatible and SPI-Compatible Serial-Port Protocols • Glue less Interface to TI McBSP s •Audio-Data Input/ Output Via TI McBSP-Compatible Programmable Audio Interface • I 2 S-Compatible Interface Requiring Only One McBSP for both ADC and DAC • Standard I 2 S, MSB, or LSB Justified-Data Transfers • 16/20/24/32-Bit Word Lengths.

The C6713DSK has the following features: The 6713 DSK is a low-cost standalone development platform that enables customers to

evaluate and develop applications for the TI C67XX DSP family. The DSK also serves as a hardware reference design for the TMS320C6713 DSP. Schematics, logic equations and application notes are available to ease hardware development and reduce time to market. The DSK uses the 32-bit EMIF for the SDRAM (CE0) and daughter card expansion interface (CE2 and CE3). The Flash is attached to CE1 of the EMIF in 8-bit mode. An on-board AIC23 codec allows the DSP to transmit and receive analog signals. McBSP0 is used for the codec control interface and McBSP1 is used for data. Analog audio I/O is done through four 3.5mm audio jacks that correspond to microphone input, line input, line output and headphone output. The codec can select the microphone or the line input as the active input. The analog output is driven to both the line out (fixed gain) and headphone (adjustable gain) connectors. McBSP1can be re- routed to the expansion connectors in software.

A programmable logic device called a CPLD is used to implement glue logic that ties the board components together. The CPLD has a register based user interface that lets the user configure the board by reading and writing to the CPLD registers. The registers reside at the midpoint of CE1.

The DSK includes 4 LEDs and 4 DIP switches as a simple way to provide the user with interactive feedback. Both are accessed by reading and writing to the CPLD registers. An included 5V external power supply is used to power the board. On-board voltage regulators provide the 1.26V DSP core voltage, 3.3Vdigital and 3.3V analog voltages. A voltage supervisor monitors the internally generated voltage, and will hold the board in reset until the supplies are within operating specifications and the reset button is released. If desired, JP1 and JP2 can be used as power test points for the core and I/O power supplies.

Code Composer communicates with the DSK through an embedded JTAG emulator with a USB host interface. The DSK can also be used with an external emulator through the external JTAG connector.

53

S320C6713 DSP Features Highest-Performance Floating-Point Digital Signal Processor (DSP):

Eight 32-Bit Instructions/Cycle 32/64-Bit Data Word 300-, 225-, 200-MHz (GDP), and 225-, 200-, 167-MHz (PYP) Clock Rates 3.3-, 4.4-, 5-, 6-Instruction Cycle Times 2400/1800, 1800/1350, 1600/1200, and 1336/1000 MIPS/MFLOPS Rich Peripheral Set, Optimized for Audio Highly Optimized C/C++ Compiler Extended Temperature Devices Available.

Advanced Very Long Instruction Word (VLIW) TMS320C67x™ DSP Core Eight Independent Functional Units:

• Two ALUs (Fixed-Point) • Four ALUs (Floating- and Fixed-Point) • Two Multipliers (Floating- and Fixed-Point) • Load-Store Architecture With 32 32-Bit General-Purpose Registers

Instruction Packing Reduces Code Size All Instructions Conditional

Instruction Set Features Native Instructions for IEEE 754

• Single- and Double-Precision Byte-Addressable (8-, 16-, 32-Bit Data) 8-Bit Overflow Protection Saturation; Bit-Field Extract, Set, Clear; Bit-Counting; Normalization

Fig 53 Schematic diagram of the DSK Board

54

Composer Studio Code Composer is the DSP industry's first fully integrated development environment (IDE) with DSP specific functionality. With a familiar environment liked MS-based C++ TM, Code Composer lets you edit, build, debug, profile and manage projects from a single unified environment. Other unique features include graphical signal analysis, injection/extraction of data signals via file I/O, multi-processor debugging, automated testing and customization via a C-interpretive scripting language and much more.

CODE COMPOSER FEATURES INCLUDE:

• IDE • Debug IDE • Advanced watch windows • Integrated editor • File I/O, Probe Points, and graphical algorithm scope probes • Advanced graphical signal analysis • Interactive profiling • Automated testing and customization via scripting • Visual project management system • Compile in the background while editing and debugging • Multi-processor debugging • Help on the target DSP

Feedforward controller in Code composer studio

The following algorithm is followed to develop the controller

= −4 πt Desired trajectory equation xd is chosen. Here xd

10 .sin( ) 4

x d and xd are computed by numerical differentiation method. Here we use 5 point formula for numerical differentiation.

f '(x) = f (x − 2h) −8 f (x − h) + 8 f (x + h) − f (x + 2h) + O(h4 ) 12h (47)

f '' (x) = − f (x + 2h) +16 f (x + h) − 30 f (x) +16 f (x − h) − f (x − 2h) + O(h4 ) 12h2

(48)

O(h4 ) Denotes the truncation error proportional to h4 . So the smaller is h chosen, the error will be small as well.

the differential equations are solved for the intermediate state variables q1 and q 2

They can be expressed in the form:

55

2

dq1

dx = q2 ( x)

(49)

dq2 = −a q (x) − sgn(dx)a q (x) + u

dx 2 1 1 2 (50)

Now differentiating Eq.(49) with respect to x and substituting the value of dq2 we are getting dx

d q1 + a sgn(dx) dq1 + a q = u dx2 1 dx 2 1 (51)

The solution of q1(x) can be taken in the form

q1 ( x ) = e mx ( k1 . cos nx + k 2 .sin nx ) (52)

k1 and k 2 are the two arbitrary constants and m ± in respectively.

Implementation

are the roots of complementary equation

Fig. 54 Code composer studio window

56

Fig 55 Feedforward controller on DSK platform

Operating PI piezo-electric stages with LABVIEW

dware Description Piezo Actuator Model no. PI-P-840 · P-841

The P-840 and P-841 series translators are high-resolution linear actuators for static and dynamic applications. They provide sub-millisecond response and sub nanometer resolution.

Design: These translators are equipped with highly reliable multilayer piezo ceramic stacks protected by a non-magnetic stainless steel case with internal spring preload. The preload makes them ideal for dynamic applications and for tensile loads as well.

Ceramic insulated piezo actuators: The highest possible reliability is assured by employing the award-winning PICMA® multilayer piezo actuators. PICMA® actuators are the only actuators on the market with a ceramic insulation which makes them resistant to ambient humidity and leakage current failures. They are thus far superior to conventional actuators in liability and lifetime.

57

Optimum UHV compatibility: the lack of polymer insulation and high Curie temperature make for optimal ultra high vacuum compatibility (no out gassing/ high beak out temperature, up to 150 o c)

Mounting: Mounting is at the foot, with push/pull forces of less than 5 N, the actuator can be held by clamping the case. The versions with ball tip decouple torque and off-center forces from the piezoceramic to provide magnetic coupling, the P-176.20 magnetic adapter can be screwed into the top piece (only for versions without ball tip.

High Accuracy in Closed-Loop Operation: the standard model P-840 is designed for open-loop positioning. Version P-841 with integrated high-resolution strain gauge position sensors provides high precision for closed loop operation.

Piezo amplifier module Model no. PI-E 505.00 The E-505 piezo amplifier module is designed to work in the E-500 Controller system. It

features a low-noise, high-power amplifier for low voltage piezo actuators and positioners, that can output and sink a peak current of up to 2000 mA in the -30 to 130 V voltage range. The E- 505 units are designed to provide high-resolution operation of piezo actuators and positioning systems in voltage-controlled mode (open-loop) and optionally in position-controlled mode (closed loop). For switching applications the E-505.10 version provides a peak outputcurrentofupto10A.Technical data (Appendix I)

Piezo servo controller module Model no. E 509.S1 The E-509 module is both a signal conditioner for high-resolution capacitive and SGS

displacement sensors and a servo controller for closed-loop piezo nanopositioning mechanics. It Compensates for the drift and hysteresis inherent in PZT materials and quickly adjusts the operating voltage on the PZT as soon as a change in force or load occurs. Single and multi- channel versions for strain gauge and capacitive sensors are available. for piezo operation. Both P and I parameters as well as the control bandwidth can be set internally. The integrated notch filters (adjustable for each axis) improve the stability and allow high-bandwidth operation closer to the piezomechanics' resonant frequency. Closed-loop piezo mechanics from PI can provide positioning accuracy and repeatability down to the nanometer range and below. Technical data (Appendix I)

Digital Piezo Controller Operation Module Model no. PI-E-517.I3 The E-517 is a microprocessor controlled interface and display module for the E-500

piezo controller system (see p. 2-142). It is equipped with low-noise, 24-bit D/A converters and can be controlled through four digital interfaces: TCP/IP, USB, RS-232 and IEEE 488 (GPIB).

58

Alternatively, stand-alone operation is possible by uploading macro command sequences to the internal non-volatile memory. For manual control a trackball interface is provided. An LCD display indicates position or operating voltages of the individual channels / axes. The integrated wave generator can output periodic motion profiles. In addition to sine and triangle waves, arbitrary, user defined motion profiles can be created and stored. (Appendix I)

Piezo actuation stage Model no. PI M-014 M-014 ultra-high-precision magnetically coupled stages use the force of integrated

magnets to preload the bearing. This magnetic preload result in extremely uniform and smooth motion with minimum friction. Unlike conventional stages, where two bearings with limited parallelism guide the carriage (inducing run out and rotational errors) in M-014 stages, only one of the two linear bearings has a guiding function (V-groove) while the second bearing is for support only (U-groove).

For both the manual and motorized version, closed-loop and open-loop PZT drives are available. They provide 5 nm minimum incremental motion over a travel range of 45 µm and allow for dynamic operation such as scanning and tracking. The closed-loop PZT drive provides repeatability of 90 nm. All stages can be cross stacked and combined with the M-053.10 (manual versions) and M-053.20 (motorized versions) Z-axis mounting bracket to provide multi-axis motion. Vertical use of the M-014 is only permitted with loads less than 0.5 kg. For vertical positioning with loads in excess of 0.5 kg we recommend M-126 stages and the 125.90 Z-axis mounting bracket.

roller design in LabVIEW

Fig 56. Feedforward control in LabVIEW

59

Fig 57. Dahl hysteresis model in LabVIEW

dware interface with LabVIEW

NI- CompactRIO Architecture: CompactRIO is a rugged, reconfigurable embedded system containing

three components: a processor running a real-time operating system (RTOS), a reconfigurable FPGA, and interchangeable industrial I/O modules. The real-time processor offers reliable, predictable behavior and excels at floating-point math and analysis, while the FPGA excels at smaller tasks that require high-speed logic and precise timing. Often CompactRIO applications incorporate a human machine interface (HMI), which provides the operator with a graphical user interface (GUI) for monitoring the system’s state and setting operating parameters.

LabVIEW: LabVIEW is a graphical programming environment used by thousands of engineers and scientists to develop sophisticated control systems using graphical icons and wires that resemble a flowchart. It offers integration with thousands of hardwaredevices and provides hundreds of built-in libraries for advanced control, analysis, and data visualization—all for creating user-defined systems more quickly. The LabVIEW platform is scalable across multiple targets and OSs, and, in the case of CompactRIO

60

Fig 58. Reconfigurable embedded system architecture

LabVIEW can be used to access and integrate all of the components of the LabVIEW

reconfigurable I/O (RIO) architecture. Real time controller: The real-time controller contains a processor that reliably and

deterministically executes LabVIEW Real-Time applications and offers multi rate control, execution tracing, onboard data logging, and communication with peripherals. Additional options include redundant 9 VDC to 30 VDC supply inputs, a real-time clock, hardware watchdog timers, dual Ethernet ports, up to 2 GB of data storage, and built-in USB and RS232 support. An RTOS is able to reliably execute programs with specific timing requirements, which is important for many science and engineering projects.

Reconfigurable I/O FPGA: The reconfigurable I/O FPGA chassis is the center of

the embedded system architecture. It is directly connected to the I/O for high- performance access to the I/O circuitry of each module and timing, triggering, and synchronization. Because each module is connected directly to the FPGA rather than through a bus, you experience almost no control latency for system response compared to other controller architectures. By default, this FPGA automatically communicates with I/O modules and provides deterministic I/O to the real-time processor. Out of the box, the FPGA enables programs on the real-time controller to access I/O with less than 500 ns of jitter between loops. You can also directly program this FPGA to further customize the system. Because of the FPGA speed, this chassis is frequently used to create controller systems that incorporate high-speed buffered I/O, fast control loops, or custom signal filtering. For instance, using the FPGA, a single chassis can execute more than 20 analog proportional integral derivative (PID) control loops simultaneously at a rate of 100 kHz.

61

Additionally, because the FPGA runs all code in hardware, it provides the highest reliability and determinism, which is ideal for hardware-based interlocks, custom timing and triggering, or the elimination of custom circuitry normally required with nonstandard sensors and buses.

Fig 59. Reconfigurable FPGA chassis

I/O Modules: I/O modules contain isolation, conversion circuitry, signal conditioning,

and built-in connectivity for direct connection to industrial sensors/actuators. By offering a variety of wiring options and integrating the connector junction box into the modules, the CompactRIO system significantly reduces space requirements and field-wiring costs. You can choose from more than 70 NI C Series I/O modules for CompactRIO to connect to almost any sensor or actuator. Module types include thermocouple inputs; ±10 V simultaneous sampling, 24-bit analog I/O; 24 V industrial digital I/O with up to 1 A current drive; differential/TTL digital inputs; 24-bit IEPE accelerometer inputs; strain measurements; RTD measurements; analog outputs; power measurements; controller area network (CAN) connectivity; and secure digital (SD) cards for logging. Additionally, you can build your own modules or purchase modules from third-party vendors. With the NI cRIO-9951 CompactRIO Module Development Kit, you can develop custom modules to meet applicationspecific needs. The kit provides access to the low-level electrical CompactRIO embedded system architecture for designing specialized I/O, communication, and control modules. It includes LabVIEW FPGA libraries to interface with the custom module circuitry. In this current research, two I/O modules are being employed, they are NI-9205 32 channel 16 bit analog input modules and NI-9263 4 channel 16 bit analog voltage output modules.

NI-9205: It 32 single-ended or 16 differential analog input channels, 1 digital input channel, and 1 digital output channel. ADC resolution is 16 bit, analog bandwidth is 370 kHz and CMRR (DC to 60 Hz) is 100dB.

62

NI-9263: Number of channels are 4 analog output channels, DAC resolution is 16 bits, Type of DAC is String type, Power-on output state Channels off, Startup voltage is 0 V and Power-down voltage is 0 V.

System configuration: The simplest embedded system consists of a single controller running in a “headless” configuration. This configuration is used in applications that do not need an HMI except for maintenance or diagnostic purposes. However, most control and monitoring applications require an HMI to display data to the operator or allow the operator to send commands to the embedded system. A common configuration is 1:1, or 1 host to 1 target, as shown in Figure 49. The HMI communicates to the CompactRIO hardware over Ethernet through either a direct connection, hub, or wireless router.

Fig 60 Host to target configuration

63

Fig 61 CRIO with I/O modules

LabVIEW FPGA interface

With the LabVIEW FPGA Interface mode, you can unlock the real power of CompactRIO by customizing the FPGA personality in addition to programming the real-time processor. This helps you achieve performance that typically requires custom hardware. Using LabVIEW FPGA, you can implement custom timing and triggering, offload signal processing and analysis, create custom protocols, and access I/O at its maximum rate. When communicating data between an FPGA VI and Real-Time VI, you have the option to stream data at very high rates using DMA FIFOs, or to communicate single-point data using controls and indicators.

The advantages of using FPGA interface mode:

Maximum Performance and Reliability: When control application is compiled for an FPGA device, the result is a highly optimized silicon implementation that provides true parallel processing with the performance and reliability benefits of dedicated hardware circuitry. Because there is no OS on the FPGA chip, the code is implemented in a way that ensures maximum performance and reliability.

High-Speed Waveform Acquisition/Generation (>500 Hz): The RIO Scan Interface is optimized for control loops running at less than 500 Hz, but many C Series I/O modules are capable of acquiring and generating at much higher rates. If you need to take full advantage of these module features and acquire or generate at speeds higher than 500 Hz, you can use LabVIEW FPGA to acquire at a user-defined rate tailored to your application.

64

Custom Triggering/Timing/Synchronization: With the reconfigurable FPGA, simple, advanced, or otherwise custom implementations of triggers, timing schemes can be created, and I/O or chassis synchronization. These can be as elaborate as triggering a custom CAN message based on the rise of an analog acquisition exceeding a threshold or as simple as acquiring input values on the rising edge of an external clock source.

Highest Performance Control: Not only the FPGA can be used for high-speed acquisition and generation, but many control algorithms can be implemented on the FPGA. You can use single-point I/O with multichannel, tunable PID or other control algorithms to implement deterministic control with loop rates beyond 1 MHz. For example, the PID control algorithm that is included with the LabVIEW FPGA Module executes in just 300 ns (0.000000300 seconds).

Hardware-Based Analysis/Generation and Co-processing: Many sensors output more data than can be reasonably processed on the real-time processor alone. You can use the FPGA as a valuable coprocessor to analyze or generate complex signals while freeing the processor for other critical threads. This type of FPGA-based co- processing is commonly used in applications such as, encoding/decoding sensors, signal processing and analysis, sensor simulation and hardware-in-loop simulation.

Fig 62. Selection of programming mode

Fig 63. Analysis from LabVIEW platform

65

Proposed work flowchart

The proposed work plan consists of the following phases as mentioned above. The controller is designed in LabVIEW. The desired trajectory is fed to the Feedforward controller and it produces the output voltage based on this (Fig 63). The C-RIO module is connected with the host system running LabVIEW via FPGA scan interface which operates from the output taken from the A/O module of C-RIO. This control output after feeding through the servo controller system is applied to piezo amplifier module. The piezo actuator operates from the output of the amplifier. The feedback from the sensor can be analyzed which in case of the feedback controller needs be fed to the servo controller.

The schematic of the proposed hardware setup is shown in Fig 64.

ontroller designed in LabVIEW

Interfacing CRIO with FPGA interface module

Control effort from CRIO fed to Piezo servo controller

The control signal is fed to Piezo amplifier.

The amplifier output is fed to Piezoactuator and the movement is observed from the sensor output data

66

Fig 64. Complete hardware setup

67

Chapter Six 6. Conclusion and Future Scopes

Contribution of the present work

The present research deals with nano positioning using Piezo-electric actuators. It is

chosen due to its high blocking force, large stiffness constant etc. The most important difficulty working with piezoelectric material is its hysteretic property which attenuates the positional precision. Our focus has been concentrated on compensating the hysteresis by the design of suitable control strategies. The mathematical model of the plant is developed incorporating the hysteresis in it. Dahl hysteresis model is considered as one of the most effective approach to describe hysteresis. Basic feedforward control, feedback control and finally some novel control like Internal model control and Fuzzy logic controller has been developed as a part of the controller design segment. The effectiveness of these algorithms have been verified by rigorous simulations Matlab/Simulink platform involving some model uncertainty and external disturbance. Finally some of the controllers have been realized on hardware platform. The Feedforward model has been built on TMS320C6713 DSK platform initially. Consequently the control algorithms have to be ported for actual hardware implementation with PI based piezo actuator stage and our proposed methodology includes the further workflow to cascade the PI actuator system with LabVIEW running over PC where our controller would be placed.

Future Scopes

This work can extended by designing Kalman filter based Linear Gaussian Regulator

(LQG) which is a good Adaptive method for precise set point tracking. H ∞ Optimal control can be also an efficient set point tracking control for piezo actuator. Sliding mode control can be incorporated with feedforward compensation for better

positional accuracy. Controller with perturbation estimation strategies also can be done where no specific

hysteresis model is required. For model less control, neural network control can be developed for compensating

hysteresis of piezo electric actuator.

68

Bibliography 1. J Lee, D Lee, S Won. “Precise tracking control of Piezo actuator using sliding mode

control with feedforward compensation” SICE Annual Conference 2010 August 18-21, 2010, The Grand Hotel, Taipei, Taiwan.

2. Qingsong Xu and Yangmin Li. ‘Sliding Mode Control of a Piezo-Driven Micropositioning System Using Extended Kalman Filter’ Proceedings of the 2010 IEEE International Conference on Automation and Logistics August 16-20 2010, Hong Kong and Macau.

3. Jin Li , Liu Yang. ‘Adaptive PI-Based Sliding Mode Control for Nanopositioning of Piezoelectric Actuators’ Hindawi Publishing.

4. S K Shome, M Prakash, A Mukherjee, U Datta, “Dither Control For Dahl Model Based Hysteresis Compensation” IEEE International Conference on Signal Processing, Computing and Control, 2013.

5. S K Shome, S Pradhan, A Mukherjee, U Datta, “Dither Based Precise Position Control of Piezo Actuated Micro-Nano Manipulator” proceedings of 39th Annual Conference of IEEE Industrial Electronics Society, Austria, 2013

6. J Peng, X Chen. ‘H2-optimal Digital Control of Piezoelectric Actuators’ Proceeding of the 8th World Congress on Intelligent control and Automation july2010, Jinan China.

7. K. Kuhnen, H. Janocha, ‘Adaptive inverse control of piezoelectric actuators with hysteresis operators’ University of Saarland, Im Stadtwald, Geb. 13 D-66123 Saarbrücken, Germany.

8. Q.Xu,Y.Li, “Dahl Model-Based Hysteresis Compensation and Precise Positioning Control of an XY Parallel Micromanipulator With Piezoelectric Actuation.” journal of dynamic system, measurement and control, ASME, 2010.

9. Ge, P., and Jouaneh,M., 1995 “Modeling Hysteresis in Piezoceramic Actuators,” Precis. Eng., 17(3) ,pp.211-221

10. Weibel, F., Michellod, Y., Mullhaupt, P., and Gillet, D.,2008,”Real time compensation of hysteresis in a Piezoelectric-stack actuator tracking a Stochastic Reference,”Proceeding of the American Control Conference, pp.

11. Goldfarb, M., and Celanovic, N.,1997 “Modeling piezoelectric stack actuators for control of micromanipulation”.IEEE trans.control syst.technol.17(3).pp 69-79.

12. Stepanenko, Y and su, C-Y.,1998 “Intelligent control of peizoelectric actuators” proceeding to the international conference on descision and control,pp 4234-4239.

13. Bashash, S., and Jalili, N., 2007 “Robust Multiple Frequncy Trajectory Tracking Control of Piezoelectrically driven Micro-nano positioning System,” IEEE Trans. Control syst. Technol., 15(5) pp. 867-878

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14. Ha,J.L,Kung, Y-S., Fung,R-F., and Hsien,S-C., 2006 “A comparison of fitnes function for the identification of a piezoelectric hysteresis actuators based on the real-coded generic algorithm”.sens.actuators.

15. A Bhakta, S K Shome, A mukherjee, U Datta. ‘Hysteresis Compensation using Modified Internal Model Control for Precise Nano Positioning’ IESA 2014 NIT Durgapur.

16. A Bhakta, S K Shome, A mukherjee, S Sen. “Dahl model based Feedforward control for Precise Positioning of Nano Actuators using TMS320C6713” proceeding to IEEE International Conference on Control, Instrumentation, Energy & Communication, CIEC 14,Kolkata.

17. Basem M. Badr and Wahied. G. Ali ‘Nanopositioning Fuzzy Control for Piezoelectric Actuators’ International Journal of Engineering & Technology IJET -IJENS Vol: 10 No:01

18. Q Xu, M Jia, ‘Model Reference Adaptive Control With Perturbation Estimation for a Micropositioning System’. IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 1, JANUARY 2014.

19. Han Yao, Jun Fu, Wen-Fang Xie. ‘Neural Network Based Adaptive Control of Piezoelectric Actuator with Unknown Hysteresis’ Proceedings of the 2007 American Control Conference Marriott Marquis Hotel at Times Square N.Y city, USA JULY 2007.

20. Santosh Devasia, Evangelos Eleftheriou, Reza Moheimani “A Survey of Control Issues in Nanopositioning” IEEE Transactions on Control Systems Technology, VOL. 15, NO. 5, September 2007.

21. Shen, J.-C., Jywe, W.-Y., Chiang, H.-K., and Shu, Y.-L., 2008,”Precision Tracking Control of Piezoelcetric-Actuated System,” Precis. Eng.,32(2),pp 71-78.

22. Choi,G. S., Lim, Y. A., and Choi, G. H., 2002, “Tracking Position Control of Piezoelectric Actuators for Periodic Reference Inputs,” Mechatronics,12(5),pp. 669-684.

23. Theory and Applications of Piezo Actuators and PZT NanoPositioning Systems. Physik Instumente (PI) material.

24. Daniel Helmick and William Messner, Department of Mechanical Engineering “Higher Order Modeling of Hysteresis in Disk Drive Actuators” 42nd IEEE conference on Decision and Control, Macau Hawaii USA dec’03.

25. Hoi-Wai Chow and Norbert C. Cheung, “Disturbance and Response Time Improvement of Submicrometer Precision Linear Motion System by Using Modified Disturbance Compensator and Internal Model Reference Control” IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 1, JANUARY2013.

26. DSP Applications Using C and the TMS320C6x D, Rulph Chassaing Copyright © 2002 John Wiley & Sons, Inc. ISBNs: 0-471-20754-3 (Hardback); 0-471-22112-0 (Electronic).

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27. TMS320C6713 DSK USER MANUAL, Cranes Software International Limited(TI- Solutions).

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Appendix I

15 µm Travel Range

Piezo • Nano • Positioning

P-840 · P-841 Preloaded Piezo Actuators Optional with Integrated Position Sensor

Preloaded Piezo Actuator, 1000/50 N

0 No Sensor

1 SGS Sensor

P-84 . (V)

1

2 30 µm Travel Range

3 45 µm Travel Range

4 60 µm Travel Range

6 90 µm Travel Range

V: Vacuum Compatible to 10-6 hPa

0 without Ball Tip

B with Ball Tip

• Outstanding Lifetime Due to PICMA® Piezo Ceramic Stacks • Travel Range to 90 µm • Compact Case • Pushing Forces to 1000 N • Pulling Forces to 50 N • Sub-Millisecond Response, Sub-Nanometer Resolution

• Versions: with Ball Tip, Vacuum Versions

Optimum UHV Compatibility – Minimum Outgassing

The lack of polymer insulation and the high Curie temperature make for optimal ultra-high- vacuum compatibility (no out- gassing / high bakeout tem- peratures, up to 150 °C).

Mounting

Mounting is at the foot, with push/pull forces of less than 5 N, the actuator can be held by

Read details in Mounting and Handling Guidelines (p. 1-67).

High Accuracy in Closed-Loop Operation

The standard model P-840 is designed for open-loop posi- tioning. Version P-841 with inte- grated high-resolution strain gauge position sensors pro- vides high precision for closed- loop operation (further details see p. 2-199).

The P-840 and P-841 series translators are high-resolution linear actuators for static and dynamic applications. They provide sub-millisecond res- ponse and sub-nanometer res- olution.

Design These translators are equipped with highly reliable multilayer piezo ceramic stacks protected by a non-magnetic stainless steel case with internal spring preload. The preload makes them ideal for dynamic applica- tions and for tensile loads as well.

Ceramic Insulated Piezo Actu- ators Provide Long Lifetime

The highest possible reliability is assured by employing the award-winning PICMA® multi- layer piezo actuators. PICMA®

actuators are the only actuators on the market with a ceramic- only insulation, which makes them resistant to ambient hu- midity and leakage-current fail- ures. They are thus far superior to conventional actuators in re- liability and lifetime.

clamping the case. The ver- sions with ball tip decouple torque and off-center forces from the piezoceramic. To provide magnetic coupling, the P-176.20 magnetic adapter can be screwed into the top piece (only for versions without ball tip).

Piezo Drivers, Controllers & Amplifiers

High-resolution amplifiers and servo-control electronics, both digital and analog, are de- scribed in the “Piezo Drivers / Servo Controllers” (see p. 2-99) section.

Ordering Information

Application Examples • Static and dynamic

Precision positioning

• Disc-drive-testing

• Adaptronics

• Smart structures

• Active vibration control

• Switches

• Laser tuning

• Patch-Clamp

• Nanotechnology

P-840, P-841 piezo translators (DIP switch for size comparison)

P-840, P-841 dimensions in mm. Length L: See table

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Linear Actuators & Motors

Response of a P-841.10 to a 3 nm peak-to- peak square wave control input signal, measured with servo-control bandwidth set to 240 Hz and 2 msec setting time.

Nanopositioning/ Piezoelectrics

Nanometrology

Micropositioning

Piezo • Nano • Positioning

PiezoWalk® Motors / Actuators

PILine® Ultrasonic Motors

DC-Servo & Stepper Actuators

Piezo Actuators & Components

Guided / Preloaded Actuators Unpackaged Stack Actuators

Patches / Benders/ Tubes / Shear..

Index

*Closed-loop models can attain linearity up to 0.15 % and are shipped with performance reports. **Resolution of piezo actuators is not limited by stiction or friction. Value given is noise equivalent motion with E-503 amplifier. (p. 2-146)

***Dynamic small-signal stiffness is ~ 30 % higher. Voltage connection: LEMO FFA.00.250. Coaxial cable, RG 178, 1 m. Sensor connector: LEMO FFA.0S.304. Coaxial cable, 1 m. Recommended amplifiers / controllers Single-channel: E-610 servo-controller / amplifier (p. 2-110), E-625 servo-controller, bench-top (p. 2-114), E-621 controller module (p. 2-160) Modular piezo controller system E-500 (p. 2-142) with amplifier module E-505 (high-power) (p. 2-147) and E-509 controller (p. 2-152) (optional) Multi-channel: modular piezo controller system E-500 (p. 2-142) with amplifier module E-503 (three channels) (p. 2-146) or E-505 (1 per axis, high-power) (p. 2-147) and E-509 controller (p. 2-152) (optional)

Technical Data

Model P-841.1 P-840.1

P-841.2 P-840.2

P-841.3 P-840.3

P-841.4 P-840.4

P-841.6 P-840.6

Units

Open-loop travel @ 0 to 100 V 15 30 45 60 90 µm ±20 % Closed-loop travel 15 / – 30 / – 45 / – 60 / – 90 / – µm

Integrated feedback sensor* SGS / – SGS / – SGS / – SGS / – SGS / – Closed-loop / open-loop resolution** 0.3 / 0.15 0.6 / 0.3 0.9 / 0.45 1.2 / 0.6 1.8 / 0.9 nm

Static large-signal stiffness*** 57 27 19 15 10 N/µm ±20 % Pushing forces to 1000 N 1000 1000 1000 1000 1000 N

Pulling forces to 50 N 50 50 50 50 50 N Max. torque limit (on tip) 0.35 0.35 0.35 0.35 0.35 Nm

Electrical capacitance 1.5 3.0 4.5 6.0 9.0 µF ±20 % Dynamic operating current coefficient (DOCC) 12.5 12.5 12.5 12.5 12.5 µA / (Hz • µm)

Unloaded resonant frequency fo 18 14 10 8.5 6 kHz ±20 % Operating temperature -20 to +80 -20 to +80 -20 to +80 -20 to +80 -20 to +80 °C

Mass without cables 20 28 46 54 62 g ±5 % Material: case, end pieces N-S N-S N-S N-S N-S Length L 32 50 68 86 122 mm ±0.3

Piezo • Nano • Positioning

E-505 Piezo Amplifier Module High Power, E-500 Piezo Controller System

tors and positioning systems in voltage-controlled mode (open-loop) and optionally in po- sition-controlled mode (closed- loop). For switching applications the E-505.10 version provides a peak output current of up to 10 A.

For frequency response with selected capacitive loads, see graph below.

• Up to 10 A Peak Current

• Output Voltage Range -30 to 130 V

• Module for E-500 Piezo Controller Rack

• Prepared for Position Servo-Control Upgrade (optional)

• Prepared for Interfaces / Display Modules (optional)

The E-505 piezo amplifier mod- ule is designed to work in the E-500 Controller system (see p. 2-142). It features a low-noise, high-power amplifier for low- voltage piezo actuators and po-

sitioners, that can output and sink a peak current of up to 2000 mA in the -30 to 130 V volt- age range. The E-505 units are designed to provide high-reso- lution operation of piezo actua-

Technical Data

Model E-505.00 E-505.10 E-505.00S

Function Power amplifier Power Amplifier for Offset Voltage Supply Switching Applications* for Tip/Tilt Systems

Channels 1 1 1

Modular Design for Flexibility: Optional Servo Controller Upgrade

Up to three E-505 amplifier mod-

Amplifier

Control input voltage range

-2 to +12 V

-2 to +12 V

– ules can be installed in one E-500 chassis. The flexible, mod-

Output voltage -30 to +130 V -30 to +130 V 100 V ular design of the E-500 piezo Peak current 2 A (<3 ms) 10 A (<200 µs) 2 A (<5 ms) servo-controller system allows Average current 215 mA 215 mA 300 mA easy installation of an optional Current limitation Short-circuit-proof Short-circuit-proof Short-circuit-proof E.509 sensor- / servo-controller Noise, 0 to 100 kHz 0.6 mVrms 1.0 mVrms <0.7 mVrms module for closed-loop opera- Voltage gain 10 ±0.1 10 ±0.1 – tion. The output voltage is then Input impedance 1 MΩ / 1 nF 1 MΩ / 1 nF – set by the servo-control loop. Interfaces and operation Closed-loop piezo mechanics Piezo connector LEMO ERA.00.250.CTL LEMO ERA.00.250.CTL LEMO ERA.00.250.CTL from PI can provide positioning Analog input BNC BNC – accuracy and repeatability down

DC-Offset 10-turn pot., adds 0 to 10 V to Control In

10-turn pot., adds 0 to 10 V to Control In

– to the nanometer range and below.

Miscellaneous Operating temperature range +5 to +50 °C +5 to +50 °C +5 to +50 °C Overheat protection Deactivation at +85 °C Deactivation at +85 °C Deactivation at +85 °C Dimensions 14HP/3U 14HP/3U 14HP/3U Mass 0.9 kg 0.9 kg 0.9 kg Operating Voltage E-500 System E-500 System E-500 System Max. power consumption 55 W 55 W 55 W

* For piezo actuators with special high-current layout

E-505.00 is a high- performance amplifier

module for the piezo servo-controller system E-500

Ordering Information

E-505.00 Piezo Amplifier Module, 2 A, -30 to 130 V, 1 Channel

E-505.10 Piezo Amplifier Module for Switching Applications, 10 A, -30 to 130 V, 1 Channel

E-505.00S Offset Voltage Supply for Tip/Tilt Systems, One Fixed Voltage of +100 V

E-505: operating limits with various PZT loads (open-loop), capaci- tance is measured in µF

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Piezo • Nano • Positioning

E-509 Signal Conditioner / Piezo Servo Module 3-Channel Servo-Controller Module for E-500 Piezo Controller System

• Position Servo-Control for Piezo Mechanics with SGS or Capacitive Sensors • 1-, 2- and 3-Channel Versions • Improves Linearity • Eliminates Drift and Hysteresis • Notch Filter for Higher Bandwidth • Increases Piezo Stiffness • ILS Circuitry Maximizes Capacitive Sensor Linearity • Plug-In Module for E-500 System

• Prepared for Interfaces / Display Modules (optional)

tance sensors provide direct and non-contact position feed- back (direct metrology). Strain gauge sensors (SGS) are avail- able for cost-effective appli- cations.

For PISeca™ single-plate high- resolution capacitive sensors (see p. 3-8), the E-509.E3 or E-509.E03 versions are avail- able (see p. 3-12).

2-152

The E-509 module is both a sig- nal conditioner for high-resolu- tion capacitive and SGS dis- placement sensors and a servo- controller for closed-loop piezo nanopositioning mechanics. It compensates for the drift and hysteresis inherent in PZT materials and quickly adjusts the operating voltage on the PZT as soon as a change in force or load occurs. Single- and multi-channel versions for strain gauge and capacitive sensors are available.

Nanometer-Precise Piezo Positioning

The proportional-integral (P-I) algorithm used by the E-509 servo-controller is optimized

for piezo operation. Both P and I parameters as well as the con- trol bandwidth can be set inter- nally. The integrated notch fil- ters (adjustable for each axis) improve the stability and allow high-bandwidth operation clos- er to the piezomechanics' reso- nant frequency. Closed-loop piezo mechanics from PI can provide positioning accuracy and repeatability down to the nanometer range and below.

Two Types of Sensors

PI employs proprietary position sensors for fast response and optimum positioning reso- lution and stability in the nano- meter range and below. For high-end applications, capaci-

Ordering Information

E-509.C1A Sensor / Piezo Servo-Control Module, Capacitive Sensor, 1 Channel

E-509.C2A Sensor / Piezo Servo-Control Module, Capacitive Sensors, 2 Channels

E-509.C3A Sensor / Piezo Servo-Control Module, Capacitive Sensors, 3 Channels

E-509.S1 Sensor / Piezo Servo-Control Module, SGS Sensor, 1 Channel

E-509.S3 Sensor / Piezo Servo-Control Module, SGS-Sensors, 3 Channels

Ask about custom designs!

E-509 3-channel servo-controller module for nanopositioning systems with strain gauge sensors

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Piezo • Nano • Positioning

Linear Actuators & Motors

Nanopositioning / Piezoelectrics

Piezo Flexure Stages / High-Speed Scanning Systems

Linear Vertical & Tip/Tilt 2- and 3-Axis 6-Axis

Fast Steering Mirrors / Active Optics

Piezo Drivers / Servo Controllers

Single-Channel Multi-Channel Modular Accessories

Nanometrology

Micropositioning

Index

2-153

Piezoelectrics in Positioning

The E-509 controller module installed in an E-501 9½-inch chassis together with E-516 digital interface and E-503 three-channel amplifier modules

Technical Data

Model E-509.C1A/E-509.C2A/E-509.C3A E-509.S1/E-509.S3 Function Signal conditioner & servo-controller

for piezo mechanics Signal conditioner & servo-controller for piezo mechanics

Channels 1/2/3 1/3

Sensor Servo characteristics P-I (analog), notch filter P-I (analog), notch filter

Sensor type Capacitive SGS Sensor channels 1 / 2 /3 1 / 3

Sensor bandwidth 0.3 to 3 kHz (selectable with jumper); up to 10 kHz on request

0.3; 1; 3 kHz

Noise factor 0.115 ppm/Hz½ Thermal drift <0.3 mV / C° <3 mV / C° Linearity <0.05 % <0.2 %

Interfaces and operation Sensor connection LEMO EPL.00.250.NTD LEMO ERA.0S.304.CLL

Sensor monitor output 0–10 V 0–10 V Sensor monitor socket LEMO 6-pin FGG.0B.306.CLAD56 BNC (1-ch.) / 3-pin. LEMO (3-ch.)

Supported functionality ILS (Integrated Linearization System) ILS (Integrated Linearization System) Display Overflow LED Overflow LED

Miscellaneous Operating temperature range +5 to +50 °C +5 to +50 °C

Dimensions 7HP/3U 7HP/3U Mass 0.35 kg 0.35 kg

Operating Voltage E-500 System E-500 System Max. power consumption 4 to 8 W 4 to 8 W

Piezo • Nano • Positioning

E-517 Digital Piezo Controller Operation Module Wave Generator, Data Recorder, Display, Multiple Interfaces, for E-500 System

• Low-Noise 24-bit D/A Converter • Sample Rate 25 kHz • TCP/IP, USB, IEEE 488 and RS-232 Interfaces • 6-Digit Display for Voltage and Position • 1- & 3-Channel Versions • Wave Generator with Programmable Trigger-I/O

• Module for E-500 Piezo Controller Rack

macro command sequences to the internal non-volatile memo- ry. For manual control a track- ball interface is provided. An LCD display indicates position or operating voltages of the individual channels / axes.

Wave Generator

The integrated wave generator can output periodic motion profiles. In addition to sine and triangle waves, arbitrary, user- defined motion profiles can be created and stored.

The E-517 is a microprocessor controlled interface and display module for the E-500 piezo con- troller system (see p. 2-142). It is equipped with low-noise, 24- bit D/A converters and can be

controlled through four digital interfaces: TCP/IP, USB, RS-232 and IEEE 488 (GPIB).

Alternatively, stand-alone oper- ation is possible by uploading

Extensive Software Support The controllers are delivered with Windows operating soft- ware. Comprehensive DLLs and LabVIEW drivers are available for automated control.

2-156

Ordering Information

E-517.i1 Interface / Display Module, 24 Bit D/A, TCP/IP, USB, RS-232, Single Channel

E-517.i3 Interface / Display Module, 24 Bit D/A, TCP/IP, USB, RS-232, 3 Channels

Ask about custom designs!

The E-517 piezo display and D/A converter module, provides USB and

TCP/IP connectivity

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Piezo • Nano • Positioning

Technical Data

Linear Actuators & Motors

Function Digital operation module Digital operation module Channels 1 3

Processor DSP 60 MHz DSP 60 MHz Sampling rate, sensor 25 kHz, 8-times oversampling 25 kHz, 8-times oversampling

Thermal drift Stability: 0.2 mV Stability: 0.2 mV Linearity @ nominal range 0.01 % 0.01 %

Resolution DAC: 24 bit, ±12 V DAC: 24 bit, ±12 V ADC: 18 bit, sampling ADC: 18 bit, sampling

Nanopositioning / Piezoelectrics

Interfaces/communication Ethernet (TCP/IP), USB, RS-232, IEEE 488 Ethernet (TCP/IP), USB, RS-232, IEEE 488 I/O ports 1 trigger input 3 trigger inputs

1 trigger output 3 trigger outputs 5 V 5 V MDR14 connector MDR14 connector

Command set PI General Command Set (GCS) PI General Command Set (GCS) User software PIMikroMove™ PIMikroMove™

Software drivers Lab VIEW drivers, Lab VIEW drivers, Windows and Linux Libraries (DLL) Windows and Linux Libraries (DLL)

Supported functionality Wave generator, data recorder, Wave generator, data recorder, macro programming macro programming

Display LCD display for monitor signals LCD display for monitor signals (position and voltage), (position and voltage), states and trackball menus states and trackball menus

Manual control Operation via trackball Operation via trackball

Miscellaneous Operating temperature range +5 to +50° C +5 to +50° C

Dimensions 21HP / 3U 21HP / 3U Mass 0.37 kg 0.37 kg

Operating voltage E-500 system E-500 system

Nanometrology

Micropositioning

Index

2-157

Piezoelectrics in Positioning

Interfaces and operation

Model E-517.i1 E-517.i3

Piezo Flexure Stages / High-Speed Scanning Systems

Linear Vertical & Tip/Tilt 2- and 3-Axis 6-Axis

Fast Steering Mirrors / Active Optics

Piezo Drivers / Servo Controllers

Single-Channel Multi-Channel Modular Accessories

Appendix II

SPECIFICATIONS of NI 9205

32-Channel, ±200 mV to ±10 V, 16-Bit Analog Input Module

Fig 65. NI 9205 Terminal and Pin Assignments

Fig 66. Input Circuitry for One Analog Channel on the NI 9205

This module supports a low-power sleep mode. Support for sleep mode at the system level depends on the chassis that the module is plugged into. Refer to the chassis manual for information about support for sleep mode. If the chassis supports sleep mode, refer to the software help for information about enabling sleep mode.

Specifications

The following specifications are typical for the range -40 to 70 °C unless otherwise noted. All voltages are relative to COM unless otherwise noted.

Analog Input Characteristics

Number of channels.......................... 32 single-ended or 16 differential analog input channels, 1 digital input channel, and 1 digital output channel

ADC resolution.................................16 bits

DNL .................................................. No missing codes guaranteed.

Conversion time

R Series Expansion chassis ........ 4.50 µs (222 kS/s)

All other chassis ......................... 4.00 µs (250 kS/s)

Input coupling...................................DC

Nominal input ranges........................±10 V, ±5 V, ±1 V, ±0.2 V

Minimum over range

(for 10 V range) ................................ 4%

Maximum working voltage for analog inputs

(signal + common mode) .................. Each channel must remain within ±10.4 V of common.

Power Requirements

Power consumption from chassis

Active mode ...............................625 mW max

Sleep mode .................................15 mW

Thermal dissipation (at 70 °C)

Active mode ...............................625 mW max

Sleep mode .................................15 mW

Fig 67. Typica! AI+ to AI- CMRR graph

SPECIFICATIONS of NI 9263

4-Channel, ±10 V, 16-Bit Analog Voltage Output Module

Fig 68. NI 9263 Termina! Assignments

Fig 69. Output Circuitry for One Channe! of the NI 9263

This module supports a low-power sleep mode. Support for sleep mode at the system level depends on the chassis that the module is plugged into. Refer to the chassis manual for information about support for sleep mode. If the chassis supports sleep mode, refer to the software help for information about enabling sleep mode.

Fig 70. Connecting load with NI 9263

Specifications

The following specifications are typical for the range -40 to 70 °C unless otherwise noted. All voltages are relative to COM unless otherwise noted.

Output Characteristics

Number of channels.......................... 4 analog output channels

DAC resolution .................................16 bits

Type of DAC..................................... String

Power-on output state ....................... Channels off

Startup voltage .................................. 0 V

Power-down voltage ......................... 0 V

Output voltage range

Nominal...................................... ±10 V

Minimum.................................... ±10.4 V

Typical........................................ ±10.7 V

Maximum ...................................±11 V

Current drive ..................................... ±1 mA per channel max

Output impedance ............................ 20.

Power Requirements

Power consumption from chassis

Active mode (at -40 °C).............500 mW max

Sleep mode .................................25µW max

Thermal dissipation (at 70 °C)

Active mode ............................... 750 mW max

Sleep mode .................................25µW max

Stability

Gain drift .................................... 14 ppm/°C

Offset drift .................................. 110µV/°C