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The International Journal of Advanced Manufacturing Technology DOI 10.1007/s00170-008-1374-zOn-line identification and control of pneumatic servo drives via a mixed-reality environment

Saleem · Abdrabbo · Tutunji

Leah Mae Ariaga for SpringerE-mail: [email protected]: +1-703-5621873SPiSPi Building, Sac-sac Bacong,Oriental Negros 6216Philippines

AUTHOR'S PROOF!

Metadata of the article that will be visualized in OnlineFirst

1 Article Title On-line identification and control of pneumatic servo drives via a mixed-reality environment

2 Journal Name The International Journal of Advanced Manufacturing Technology

3

Corresponding

Author

Family Name Abdrabbo

4 Particle

5 Given Name S.

6 Suffix

7 Organization Philadelphia University

8 Division Mechatronics Department, Faculty of Engineering

9 Address Amman , Jordan

10 e-mail [email protected]

11

Author

Family Name Saleem

12 Particle

13 Given Name A.

14 Suffix





19

Author

Family Name Tutunji

20 Particle

21 Given Name T.

22 Suffix





27

Schedule

Received 27 May 2007

28 Revised

29 Accepted 3 January 2008

30 Abstract This paper presents a method to identify and control electro-pneumatic servo drives in a real-time environment. Acquiring the system’s transfer function accurately can be difficult for nonlinear systems. This causes a great difficulty in servo-pneumatic system modeling and control. In order to avoid the complexity associated with nonlinear system modeling, a mixed-reality environment (MRE) is employed to identify the transfer function of the system using a recursive least squares (RLS) algorithm based on the auto-regressive moving-average (ARMA) model. On-line system identification can be conducted effectively and efficiently using the proposed method. The advantages of the proposed method include high accuracy in the identified system, low cost, and time reduction in tuning the controller parameters. Furthermore, the proposed method allows for on-line system control using different control schemes. The results obtained

Page 1 of 2Testsite

1/19/2008file://C:\DDrive\Programs\Metadata\temp\hia81374.htm

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from the on-line experimental measured data are used to determine a discrete transfer function of the system. The best performance results are obtained using a fourth-order model with one-step prediction.

31 Keywords separated by ' - '

On-line identification - Auto-regressive moving-average - Pneumatic servo drive - Mixed-reality environment

32 Foot note information

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1

2

3 ORIGINAL ARTICLE

4 On-line identification and control of pneumatic servo drives5 via a mixed-reality environment

6 A. Saleem & S. Abdrabbo & T. Tutunji

7 Received: 27 May 2007 /Accepted: 3 January 20088 # Springer-Verlag London Limited 2008

11 Abstract This paper presents a method to identify and12 control electro-pneumatic servo drives in a real-time13 environment. Acquiring the system’s transfer function14 accurately can be difficult for nonlinear systems. This15 causes a great difficulty in servo-pneumatic system model-16 ing and control. In order to avoid the complexity associated17 with nonlinear system modeling, a mixed-reality environment18 (MRE) is employed to identify the transfer function of the19 system using a recursive least squares (RLS) algorithm based20 on the auto-regressive moving-average (ARMA) model. On-21 line system identification can be conducted effectively and22 efficiently using the proposed method. The advantages of the23 proposed method include high accuracy in the identified24 system, low cost, and time reduction in tuning the controller25 parameters. Furthermore, the proposed method allows for on-26 line system control using different control schemes. The27 results obtained from the on-line experimental measured data28 are used to determine a discrete transfer function of the29 system. The best performance results are obtained using a30 fourth-order model with one-step prediction.

31 Keywords On-line identification .

32 Auto-regressive moving-average . Pneumatic servo drive .

33 Mixed-reality environment

34NomenclatureAa 37Piston area of side a (m2)Ab 39Piston area of side b (m2)Cd 41Discharge coefficient (0.8)k 43Polytropic constant (1.4)Lo 45Half stroke length of cylinder+inactive lengthm 47Payload mass (kg)m�a 49Mass flow rate in chamber a (kg/s)

50m�b Mass flow rate in chamber b (kg/s)

m�1 53Leakage mass flow rate (kg/s)

Pa 55Pressure of chamber a (N/m2)Pb 57Pressure of chamber b (N/m2)Pe 59Exhaust pressure (N/m2)Ps 61Supply pressure (N/m2)R 63Universal gas constant (287 J/(kg.K))Ts 65Supply temperature (K)W 67Port width (m)V 69Piston velocity (m/s)X 71Piston position (m)Xa 73Valve spool displacement for chamber a as input (m)Xb 75Valve spool displacement for chamber b as input (m)Fr(X) 77Position-dependent resistance force (N)μd 79Dynamic friction coefficient (N.s/m)

811 Introduction

82Pneumatic servo drives play an important role in industrial83mechatronic systems. This is due to their cost-effectiveness,84easy maintenance, and clean operating conditions. Howev-85er, pneumatic actuators are characterized by high-order86time-variant dynamics, nonlinearities due to the compress-87ibility of air, internal and external disturbances, and payload88variations. In turn, it is difficult to build an accurate

Int J Adv Manuf TechnolDOI 10.1007/s00170-008-1374-z

A. Saleem : S. Abdrabbo (*) : T. TutunjiMechatronics Department, Faculty of Engineering,Philadelphia University,Amman, Jordane-mail: [email protected]

A. Saleeme-mail: [email protected]

T. Tutunjie-mail: [email protected]

JrnlID 170_ArtID 1374_Proof# 1 - 19/01/2008

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89 dynamic model for describing pneumatic servo-drive90 behavior. Therefore, in order to design controllers that are91 reliable and easy to understand in practice, simplified plant92 models are obtained by linearization around operating93 points [1–4].94 In practical applications, one often does not have95 available values for the model parameters and/or part of96 the model structure. Therefore, one tries to obtain these97 parameters and/or structural elements using experimental98 data from the real process. Researchers developed various99 parameter-identification methods and applied them to many100 engineering systems. Carducci et al. [5] presented the101 identification of viscous friction coefficients for a pneu-102 matic system model using optimization methods. Their103 work focused on developing a mathematical model of a104 pneumatic actuator driven by two on/off two-way valves105 based on the identified friction parameters. They reported106 that pneumatic systems are not only nonlinear, but also107 involve several tuning parameters. Daw et al. [6] employed108 a genetic algorithm in order to identify the dynamic friction109 parameters along the pneumatic cylinder. The evaluation110 function has been formed using the statistical expectation of111 the mean squared error (MSE). Further study has been112 conducted by Wang et al. [7] to improve the convergence113 rate and the accuracy of the algorithm. Their work114 concentrated on measuring the friction parameters of the115 cylinder rather than a complete system. Ziaei and Sepehri116 [8] discussed some practical issues concerning the identi-117 fication of electro-hydraulic actuators using discrete-time118 linear models. They considered a discrete-time linear model119 and estimated its unknown parameters. Other researchers120 used neural networks to identify system parameters.121 Angerer et al. [9] used a structured recurrent neural network122 to identify the physically relevant parameters and nonlinear123 characteristics of a nonlinear two-mass system with friction124 and backlash. None of the above researchers identified the125 transfer function of a servo-pneumatic system. Rather, they126 concentrated in their research on identifying certain127 nonlinear parameters within their plant model.128 In order to identify the transfer function of a plant,129 several researchers have employed auto-regressive moving-130 average (ARMA) models. ARMA models are based on131 difference equations that involve the system’s inputs and132 outputs. Söderström and Stoica [10] and Ljung [11] have133 worked on system-identification methods using ARMA134 models and recursive algorithms since the 1980s. Their135 work became a cornerstone in system identification. Many136 other researchers have employed ARMA models and137 recursive algorithms in their work. Yan et al. [12] used a138 recursive prediction error method based on an ARMA139 model to identify the transfer function of a CNC milling140 machine in order to apply combined self-tuning adaptive141 control and cross-coupling control to retrofit the machine

142with DC motors instead of stepper motors. Östring et al.143[13] identified the behavior of an industrial robot in order to144model its mechanical flexibilities, while Johansson et al.145[14] used a state-space model to identify the robot146manipulator dynamics. Tutunji et al. [15] and, later,147Abdrabbo and Tutunji [16] used a recursive least squares148(RLS) algorithm to identify gyroscopic system behavior149and examine a hydrostatic transmission system, respectively.150Their results showed that an RLS algorithm based on151ARMA models provides a reasonably accurate transfer152function of the systems under study.153In this work, ARMA models and RLS algorithms were154utilized within a mixed-reality environment (MRE) in order155to identify and control the servo-pneumatic system transfer156function on-line. Transfer function identification is considered157as one of the crucial issues that influence the control design158of pneumatic servo systems. MATLAB/Simulink is devised159to facilitate the realization of the proposed method in order160to identify the system model on-line. The developed plat-161form also provides an excellent environment to support162design, simulation, and emulation of servo-pneumatic control163systems.164The rest of the paper is organized as follows. Section 2165provides the nonlinear model of the pneumatic servo drive166system. ARMA models and the recursive estimation167algorithm is presented in Sect. 3. Section 4 introduces168the concept of a mixed-reality environment (MRE). The169experimental setup is provided in Sect. 5 and, finally, the170obtained results are discussed in Sect. 6.

1712 Nonlinear model of the pneumatic servo drive system

172The system under consideration consists of an electro-173pneumatic position control servo drive and a pneumatic174actuator with a load as shown in Fig. 1. The cylinder175(pneumatic actuator) represents a variable chamber which176contains a variable mass of gas. The present model was177established considering the following assumptions: the air178flow media is a perfect gas, pressure and temperature within179the system components are homogenous, and the process is180polytropic.

1812.1 Cylinder chamber model

182The governing equations of the pneumatic cylinder dynam-183ic behavior rely entirely on the study of the charging and184discharging processes of air to the controlled volume in the185cylinder chambers. The traditional approach on the analysis186is based on linearization, which makes the analysis valid187only for small perturbations about an operating point [17–18819]. Therefore, a nonlinear analysis was used in this189research. The following analysis refers to the double-acting

Int J Adv Manuf Technol


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190 asymmetric cylinder, which can be generalized to include191 symmetric cylinders (by assigning the bore diameter to192 zero). Figure 1 illustrates diagrammatically the relationship193 of the cylinder’s chambers and the inlet connections. The194 time derivative of the chamber pressure and flow rates can195 be written for the inlet side (a) and the outlet side (b) as:

dPa

dt¼ kRTs

Xao

m� a Pa; Ps; Pe; Xað ÞAa

��m� l Pa; Pbð Þ

Aa� Pa

RTsX�� ð1Þ

dPb

dt¼ kRTs

Xbo

m� b Pb; Ps; Pe; Xbð ÞAb

�

�m� l Pa; Pbð ÞAb

� Pb

RTsX�� ð2Þ

200 where:

Xao ¼ Lo þ X

Xbo ¼ Lo � X

Lo ¼ half stroke length þ inactive length

m� a ¼ CdWXa f Pa; Ps; Peð Þm� b ¼ CdWXb f Pb; Ps; Peð Þ

2032.2 Leakage mass flow rate

204The leakage mass flow rate between the cylinder chambers205is given by [1]:

m� l Pa; Pbð Þ ¼f Pb

Pa

� �Pa if Pa � Pb

f PaPb

� �Pb if Pa < Pb

8<: ð3Þ

2082.3 Payload

209For the payload, the inputs are the pressures in the210chambers (Pa and Pb) and the outputs are the piston’s211position and velocity, as shown in Fig. 1. Hence, the load212equation is given by the following expression:

mX� � ¼ PaAa � PbAb � md X

� �Fr Xð Þ ð4Þ

214where μd is the dynamic friction coefficient and Fr(X) is the215position-dependent resistance force. According to Eqs. 1–4,216the following states are defined:

X1 ¼ XX2 ¼ VX3 ¼ Pa

X4 ¼ Pb

Pneumatic Actuator

bbb mTP•

,,aaa mTP•

,,

Chamber A Chamber B Displacement Transducer

Pneumatic Servo-Valve

DAQ Card

Pa, Ta, Va

Fig. 1 Schematic of the pneu-matic test setup



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219 If the valve displacements are given by U1=Xa and220 U2=Xb, then the system nonlinear model in the state221 equations form can be written as:

X�1 ¼ X2 ð5Þ

X�2 ¼ 1

mAaX3 � AbX4 � μdX2 � Fr X1ð Þ½ � ð6Þ

X�3 ¼ kRTs

Lo þ X�f

X4

X3

� �X3

Aa� X2X3

RTs

�

þ CdW

Aaf X3; Ps; Peð ÞU1

� ð7Þ

X�4 ¼ kRTs

Lo � Xf

X4

X3

� �X4

Abþ X2X4

RTs

�

þ CdW

Abf X4; Ps; Peð ÞU2

� ð8Þ

233 Obviously, it is not easy to accurately derive and234 simulate the mathematical model of a nonlinear system.235 Furthermore, it is extremely difficult to acquire the system236 parameters, such as component dimensions, dynamic237 friction parameters, and internal leakage coefficients,238 accurately once the servo system is assembled. This causes239 a great difficulty in system modeling and control. Therefore,240 many researchers adopted system-identification methods in241 order to approximate the desired system model using input/242 output measurements [8]. The basic concept of the proposed243 method is to deal with the physical system as a “black box,”244 where the input and output variables can be measured in a245 series of experiments on the system. The following section246 will explain the ARMA model-identification algorithm247 which was employed in this research.

248 3 ARMA models and recursive estimation algorithms

249 System identification is the field of modeling dynamic250 systems from measured data using mathematical algorithms.251 These algorithms use a “black box” model and assume no252 prior knowledge of the system physics [10].253 Discrete-time signals are resulted from A/D sampling254 and are represented as y(nTs)=y(n). Here, Ts is the sampling255 time and n is an integer value that represents the sample

256number. The model structure used to identify the system257dynamics for a single-input-single-output is given by:

by nð Þ ¼ g u nð Þ . . . u n� pð Þ; y n� 1ð Þ . . . y n� qð Þ;ða1; . . . ; aq; b0; . . . ; bp

� ð9Þ

259Equation 9 shows that the estimated output sample by nð Þ is a260function of the present input u(n), past inputs u(n−p), past261outputs y(n−q), and parameters aj, bi.262For linear models, the function g becomes a linear263multiplier and, therefore, the output can be represented as264an ARMA model [20]:

by nð Þ ¼Xqj¼1

ajy n� jð Þ þXpi¼0

biu n� ið Þ ð10Þ

267The goal is to find a linear system model that gives an268output by equal to the real output y. The least square error269between the actual and the modeled output is given by:

error ¼ 1

2

XNn¼1

by nð Þ � y nð Þð Þ2 ð11Þ

272Input–output patterns (u, y) are available. They are used273in Eq. 10 to calculate by: The parameters aj and bi are274updated to minimize the least square error, as shown in275Fig. 2.276In vector format, the following vectors are defined:

6T nð Þ ¼ y n� 1ð Þ � � � y n� qð Þ u nð Þ � � � u n� pð Þ½ �θT ¼ a1 � � � aq b0 � � � bp½ �

279RLS, in vector format, gives the following equations280[10]:

θ ¼ θ� Qe

e ¼ 6Tθ� y

Q ¼ P6

P ¼P�P66TPlþ6TP6

n ol

ð12Þ

282where P is a positive definite matrix initialized to be cI (I is283the identity matrix, 100<c<10,000) and l is the forgetting284factor (0.95<l<0.99). The equations in Eq. 12 are used in a

U(Input)

Y^ (Model Output)

Error

Y (Output)PhysicalSystem

ARMAModel

+

-

Fig. 2 Block diagram of the auto-regressive moving-average(ARMA) identification model



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285 recursive algorithm, where the parameter vector θ is286 updated at every iteration until convergence.287 Once the parameters are identified, the Z-transform of288 the ARMA ( p, q) model is calculated to yield the estimated289 transfer function of the model, which is given by:

Z y nð Þ �Xqj¼1

ajy n� jð Þ( )

¼ ZXpi¼0

biu n� ið Þ( )

) H zð Þ ¼ Y zð ÞU zð Þ ¼

b0 þ b1z�1 þ . . .þ bpz�p

1� a1z�1 � . . .� aqz�q

ð13Þ

292 The disadvantage of off-line system identification is the293 need to acquire a sufficient set of experimental test data of294 the system, which may require a long time and large efforts.295 Furthermore, this approach cannot be adopted as a general296 analysis or configuration for modular servo-pneumatic

297systems, since the model is created for a particular actuator298with certain dimensions. Therefore, a new data collection299and training procedure should be conducted if any300modification on the system is applied. This was the main301motivation to develop a new method in order to identify the302system on-line. MRE was employed in order to facilitate303system identification and control on-line control. On-line304identification saves time in data collection and improves the305model accuracy and reliability. Moreover, any change in the306system structure and/or components will be reflected on307the system model without the need to data recollection.

3084 The concept of a mixed-reality environment

309Generally, mechatronic systems comprise of a controller,310actuators, and sensors. The controller generates an output

Pneumatic actuator Displacement transducer

Pneumatic Servo-valve

DAQ Card Terminal;

Fig. 4 Photograph of thepneumatic test setup

Position

SpeedAcc.

Controller

Sensors

Actuator

Simulation EnvironmentReal System

DAQ Card

Matlab/Simulink

Fig. 3 Mixed-reality environ-ment (MRE) structure for controlscheme implementation



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311 according to the feedback signal from the sensors and sends312 it to the actuator, which performs a certain task. According313 to the above situation, some of the hardware components,314 such as the controller, can be substituted by its model and315 simulated in real time. The simulated component(s) can be316 run in conjunction with real components under the same317 environment. This environment can be regarded as an318 MRE. Figure 3 shows the concept of the proposed319 environment.320 The MRE is an environment whereby virtual compo-321 nents can be applied on real systems’ components. From322 the control perspective, working with an MRE should323 include control system synthesis off-line (or under a324 simulation environment) and then apply the simulated325 model on the real system under the MRE. Off-line326 simulation will normally take place before moving onto

327the real system, where the system should be tested and the328controller should be tuned or optimized. Then, the329optimized virtual controller will be applied on the real330system.331This environment should allow the system to be332controlled with different control schemes by simply replac-333ing the “controller” component according to the application334requirements. Furthermore, the MRE gives the capability to335monitor the system’s behavior by observing the output336signals, such as speed and position signals. These signals337can be utilized to identify the real system using one of the338system-identification methods. In the context of this339research work, the ARMA model was employed for on-340line system identification using the MRE. The following341sections give an overview of the experimental setup of the342system.

Fig. 5 MRE Simulink block

Fig. 6 Variation of the on-lineactual output, third-orderpredicted model with one-stepprediction, and the error versestime



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343 5 Experimental setup

344 Figures 1 and 4 show the schematic and a photograph,345 respectively, of the experimental setup used to validate the346 proposed method. The main feature of the test rig is to347 perform integrated components of mechanical, electronics,348 and computer interface structure, with high computational

349capacity and good software programmability. It is also350designed to resemble the basic pneumatic circuit of various351applications. The pneumatic unit consists of a pneumatic352power supply, which includes a compressor with an air353conditioning unit, lubricating unit, and manifold.354The servo-pneumatic valve was an 1/8-inch port and had355an operating voltage from zero to 10 V, while the pneumatic

Fig. 7 Variation of the on-lineactual output, fourth-orderpredicted model with one-stepprediction, and the error versestime

Fig. 8 Variation of the on-lineactual output, fifth-orderpredicted model with one-stepprediction, and the error versestime



AUTHOR'S PROOF!

UNCORRECTEDPROOF356 actuator had a piston diameter of 27 mm, rod diameter of

357 8 mm, and stroke length of 100 mm. A rotary potentiometer358 has a resistance range from 2 to 12 kΩ, with a voltage359 source of 10 V, and is fixed on the cylinder, which is used360 for measuring the position of the piston and providing the361 position feedback. All signals were sent to a computer via a362 National Instruments (NI) DAQ card 1036E through an363 A/D converter terminal. The DAQ card had 16 analog364 inputs, two analog outputs, a sampling rate of 200 kS/s, and365 a input voltage range of ±10 V. The final signals were used366 to activate an analog input block in MATLAB’s real-time367 windows target (rtwt).368 The input signal of the valve was the controlled voltage369 from the analog output block of MATLAB (rtwt) to the D/A370 converter of the DAQ card and, finally, to the servo valve.

371The change of input voltage from zero to 5 V produces the372change of air flow through the valve to control the motion373of the piston of pneumatic actuator.

3746 Results and discussion

375In order to examine the plant characteristics and obtain its376model, a group of experiments were performed on the test377rig outlined in the previous section. First, on-line identifi-378cation using the ARMA model was obtained using the379impulse response of the real system. Figure 5 shows the380Simulink block diagram of on-line system identification381that was interfaced to the real system through the DAQ382card. The input signal was applied to the servo drive via an

t1.1 Table 1 Comparison of the statistical error analysis of different orders with one-step prediction

Transfer function order Signal Statistical criteriat1.2

Min. Max. Square error Standard deviationt1.3

Third order Actual output 0 4.958 7.09e−5 0.4231t1.4Predicted model output 0 5.007 0.423t1.5Error −0.2923 0.1987 0.008468t1.6

Fourth order Actual output 0 5.036 3.22e−5 0.4351t1.7Predicted model output 0 5.08 0.435t1.8Error −0.2052 0.1147 0.00571t1.9

Fifth order Actual output 0 5.2 3.397e−5 0.456t1.10Predicted model output 0 5.251 0.456t1.11Error −0.1818 0.1089 0.005861t1.12

Fig. 9 Variation of the on-lineactual output, fourth-orderpredicted model with five-stepprediction, and the error versestime



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383 analog output block (DAQ output). The response of the384 pneumatic actuator (piston displacement) was measured385 and sent back to the computer through the analog input386 block (DAQ input).387 To find the proper model structure, different prediction388 strategies were performed with a 6-bar supply pressure, 2-389 bar back pressure (load), and 1-ms sampling time.

390 6.1 Effect of prediction orders

391 Based on the mathematical model presented in Sect. 2 and392 the state equations presented in Eqs. 5–8, the servo-393 pneumatic system under study has four state variables,394 namely, load position, load velocity, and pressures in both395 chambers. Therefore, it was predicted that it can be best396 modeled by a fourth-order ARMA model. Consequently, a397 set of experiments using third, fourth, and fifth orders were398 conducted to show the effect of the identification orders399 with a one-step prediction strategy. Figure 6 shows the on-400 line actual output and third-order predicted model with one-401 step prediction. The square error was 7.09e−5 cm, with a402 standard deviation of 0.008468 cm. Referring to the ARMA

403model detailed in Sect. 3, the identified system parameters404vector (θ) was 1:3857 �0:073178�0:320960:0082979�½4050:0154160:020473�T; and, therefore, the resulting transfer406function is:

Gp ¼ 0:0082979� 0:015416z�1 þ 0:020473z�2

1� 1:3857z�1 þ 0:073178z�2 þ 0:32096z�3ð14Þ

409Figure 7 represents the on-line actual output and the410fourth-order predicted model with one-step prediction. The411square error was 3.22e−5 cm with a standard deviation of4120.00571 cm and θ ¼ 1:9827 �1:2989 0:43504�0:12436½4130:0070699 �0:017738 0:019649 0:00027783�T: The corre-414sponding transfer function is depicted as:

Gp ¼ 0:0070699� 0:017738z�1 þ 0:019649z�2 þ 0:00027783z�3

1� 1:9827z�3 þ 1:2989z�2 � 0:43504z�3 þ 0:12436z�4

ð15Þ

Fig. 10 Variation of the on-lineactual output, fourth-order pre-dicted model with ten-step pre-diction, and the error verses time

Table 2 Effects ofindependent proportional-integral-derivative (PID) tuning

Closed-loop response Rise time Overshoot Steady-state error t2.1

Increasing Kp Decrease Small increase Decrease t2.2Increasing Ki Small decrease Increase Large decrease t2.3Increasing Kd Small decrease Decrease Minor changes t2.4



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Figure 8 shows the results of the on-line actual output and418 the fifth-order model with the same conditions. The square419 error was 3.397e−5 cm with a standard deviation of

4200.005861 cm. The identified corresponding transfer function421was:

Gp ¼ 0:0075351� 0:017093z�1 þ 0:013851z�2 þ 0:012393z�3 � 0:0075649z�4

1� 1:9622z�1 þ 1:2423z�2 � 0:2243z�3 � 0:22505z�4 þ 0:17458z�5ð16Þ

429 Table 1 shows a comparison of the statistical analysis of430 the ARMA predicted output with different orders and one-431 step prediction. As expected, the fourth-order model432 resulted in the minimum square error and, therefore, was433 adopted as the system model for the controller design. It is434 worth noting that, since the ARMA model converges to a435 local minimum, the identified transfer functions in Eqs. 14–436 16 are not unique.

4376.2 Effect of step predictions

438To explain the effect of step size prediction, a number of439experiments were performed using the fourth-order model440and different step size predictions. Figures 7, 9, and 10)441show the on-line actual output and predicted model outputs442with different prediction step sizes (one step, five steps, and443ten steps, respectively). It can be observed that the best

Fig. 13 Variation of the simulated and demand positions (cm) versestime (ms)

Fig. 12 Variation of the simulated and demand speed profiles (cm/ms) verses time (ms)

Fig. 11 Simulink block for the real feedback system



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444 result was the one-step prediction. This is because, in445 pneumatic systems, which are highly nonlinear systems,446 one-step prediction succeeded in tracking the changes in the447 system behavior, while five- and ten-step predictions448 introduced delay in the samples, which prevented the449 model from following the transient system response450 accurately.

451 6.3 Implementation of a PID control scheme

452 A desired speed profile was prepared to be used as a453 reference input signal for both simulated and real systems.454 The software block of a proportional-integral-derivative

455(PID) servo controller was designed to control the position456and speed of the pneumatic actuator. The challenge in PID457controller design is to tune the values of the proportional458gain Kp, integral gain Ki, and derivative gain Kd. Tuning459work is usually performed manually by trying out different460tuning parameter combinations on-line until satisfactory or,461at least, acceptable results are achieved. This method is462laborious, time-consuming, unsafe, and does not always463give the best possible solution. The effects of varying the464PID controller parameters are shown Table 2 [21].465This was the motivation to tune the controller parameters466under a simulation environment (off-line tuning) using an467established tuning technique, such as the Ziegler-Nicholas

Fig. 17 Variation of the simulated and demand multiple positionprofiles (cm) verses time (ms)

Fig. 16 Variation of the simulated and demand multiple speedprofiles (cm/ms) verses time (ms)

Fig. 15 Variation of the real and demand displacements verses time atKp=14, Ki=0, and Kd=0.2

Fig. 14 Variation of the real and demand displacements verses time atKp=14, Ki=6, and Kd=0.2



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468 method, to avoid the drawbacks of a manual tuning method.469 The practical steps used to tune the virtual PID controller470 are:

471 Step 1: The tuning was started by applying a small value472 to the proportional gain (Kp) and then increasing473 Kp until the system oscillated. Fifteen percent474 (15%) of the total value of Kp was decreased.475 Step 2: Once the proportional gain (Kp) was set, the476 integral gain (Ki) was increased by a small value477 until the minimum error was achieved. Twenty-478 five percent (25%) of the total values of Ki and479 Kp was decreased.480 Step 3: After increasing the integral gain Ki, Kp was481 increased until the system oscillated again to482 enhance the stability of the system. Then, 15% of483 the total value of Kp was decreased.484 Step 4: Steps 1 to 3 were repeated, adjusting each gain value485 carefully to achieve better system performance

486 After achieving satisfactory results from off-line tuning,487 the optimized controller(s) was applied to the real system488 through the proposed MRE. Figure 11 shows the proposed489 MRE for real system control. Basically, the system under490 the MRE consists of hardware and software components.491 The hardware components (cylinder, valve, and encoder)492 are located in the “Real System” block. The software493 components are the PID controller, profile generator,494 integrator, and the scopes.495 Figure 12 shows the variations of the desired speed496 profile and the resulting simulated speed response at the497 shown tuning parameters. The results ensure much closer

498tracking of the speed profile, together with good time-499response characteristics.500Figure 13 represents the variations of the demand and501the obtained simulated position. The simulated position502succeeded in matching the demand position with minimum503error. Figure 14 shows the variations of the demand504position and the on-line real displacement at the same505tuning parameters that have been obtained from the506simulation environment. The results show good tracking507with small sustained oscillation around the demand position508due to pneumatic compressibility. However, the steady-state509error is apparent. In order to decrease the steady-state error,510the integral gain was introduced. The system response is511shown in Fig. 15, where the steady-state error was512decreased.513Multiple profiles with different widths were prepared to514check the proposed system reliability. Figure 16 shows that515the simulated system succeeded in tracking the proposed516speed profile. Figures 17 and 18 show the results of the517accumulated displacements of the simulated and on-line518real system, respectively, due to multiple profiles. The519pneumatic system succeeded in tracking the desired520position and showed minimum sustained oscillations.

5217 Conclusions

522In this research, a method to identify and control electro-523pneumatic servo drives in a real-time environment was524proposed and implemented. In order to avoid the great525difficulty associated with servo-pneumatic system modeling526and control, a mixed-reality environment (MRE) was527employed to identify the system using the recursive least528squares (RLS) algorithm based on the auto-regressive529moving-average (ARMA) model. On-line system identifi-530cation was performed effectively and efficiently using the531proposed method. The advantages of the proposed method532include high accuracy in the identified system, low cost,533and reduction in the tuning time required of the controller534parameters.535The results showed a reasonably good match between536the simulated and real system behaviors. This implies that537the accuracy of the system model obtained through on-line538identification is high and that the developed MRE is539appropriate for different virtual control scheme applications540on real systems. Furthermore, the proposed method used to541control the pneumatic system showed good performance in542tracking the demand positions of multiple profiles with543different widths.

Fig. 18 Variation of the real and demand positions (cm) verses time(ms)



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544 References

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