Distributed Laboratories: Control System Experiments with LabVIEW and the LEGO NXT

Platform

Greg Droge, Dr. Bonnie Heck Ferri, Jill Auerbach

Outline

• Motivation and Background• Experimental Setup• Control Projects

– Velocity Control– Position Control

• Assessment

Motivation and Background

• Control Theory can be a highly abstract subject

• Distributed Laboratories:– Experiments can be done in various locations such as homes,

classrooms, and dorm rooms– Labs utilize inexpensive equipment– Well-suited for inclusion into lecture-based classes to be done at the

desks in the class room or to be taken home as a project

• New pedagogical model: more complete integration of theory and laboratory experience

Goal: Introduce lab experience into early courses through Distributed

Laboratories

Motivation and Background

• Distributed Lab Features– Fully support or demonstrate a fundamental principle that is hard to

understand from theory alone– Experiments should not require faculty to change their standard

evaluation methods– Should contain supplemental material including a tutorial

• Logistical Considerations– Each experimental module should be made as accessible as possible

to as wide a range of instructors as possible– Designed primarily for faculty who do not have resources for high-end

experiments – Must be easy for students to use

Experimental Setup

• NXT and motor– Includes encoder for position

measurement– Only integer arithmetic

• Experimental Block Diagram– Velocity Control:

– Position Control:

Reference

Filtered Derivative

Motor

Sensor

ControllerPosition+

-

Velocity

ReferenceMotor

Sensor

ControllerPosition+

-

Position

Experimental Setup

• LABVIEW NXT Toolkit– NXT toolkit free with access to LABVIEW– Students can use floating point arithmetic since the conversion to

integer arithmetic is done automatically at a lower level of abstraction– Program controlled with graphical user interfaces

Experimental Setup

• LABVIEW is based on data-flow: similar to Control Theory block diagrams

Reference

Filtered Derivative

Motor

Sensor

ControllerPosition+

-

Velocity

Velocity Control

Fundamental concepts– PID Control– Zeigler-Nichols tuning rules– Steady-state error– Sinusoidal tracking– System performance with different controllers– Frequency response– Controller bandwidth– Resonance– System identification

Velocity Control (In-Class Component)

In-Class Component: Zeigler-Nichols tuning rules (performed in 50 minutes)

• Students given proportional gain which is stable with large steady state error

• Students follow rules for Zeigler-Nichols PID tuning– Bring system to steady state oscillation

– Use rules for PID gains

Velocity Control (In-Class Component)

Velocity Control (At-Home Component)

System modeling using sinusoid inputs with different frequencies– Students measure output amplitudes and phase differences– Done using the plotting tools in LABVIEW

• Open Loop Transfer Function:

• Example magnitude and phase plots:

)30s)(bs(

A30

)s(U

)s(V

From Velocity Filter

Open Loop PI Control

Position Control

• Fundamental Concepts– Time domain specifications– System identification– Lead control– Root locus– Discretization– Difference equation implementation– Robustness

Position Control

Procedure– Modify motor velocity controller to replace velocity feedback with

motor position feedback• Step-by-step instructions allow the students to become familiar

with LABVIEW dataflow

– Obtain model from step response• Given closed loop step response, students can determine open-

loop system parameters• Students can compare results obtained from Velocity experiment

Position Control

Procedure– Design lead compensator to achieve a settling time of about .3

seconds (Requires implementing digital control in LABVIEW)

– Plot frequency response of closed loop system and compare with expected results

Assessment

• Data collected from six classes

• Two assessment tools were used1. Concepts Inventory

• Pre and post tests administered to assess students understanding

2. Surveys: administered before students took class and one semester afterward• Students were surveyed on their perceived understanding of

different topics

Requiring students to use Bode plots and root locus in the experiment forced them to

understand the concepts on a much deeper level

Assessment (Concepts Inventory)

Systems and Controls Concepts Inventory Test% correct comparison / experimental & control classes

Concept Inventory Questions Directly Related to LabBrief Description of Question % correct

experimental N=30

% correctcontrolN=28

difference

Q A: identify a difference equation corresponding to a transfer function

63.0% 57.1% +5.9

Q B: select the z-domain pole-zero plots corresponding to a discretized system

11.1% 10.7% +.4

Q C: determine the transfer function of a digital filter corresponding to a discrete time system

63.0% 46.4% +16.6

Q D: identify the purpose of a PD controller

74.1% 57.1% +17.0

Q E: identify the purpose of a PI controller

81.5% 53.6% +27.9

Assessment (Concepts Inventory)Systems and Controls Concepts Inventory Test

% change pre- post- tests / experimental & control classesConcept Inventory Questions Directly Related to Lab

Questions % change experimental

% changecontrol

QA: identify a difference equation corresponding to a transfer function

+28.6% +17.1%

Q B: select the z-domain pole-zero plots corresponding to a discretized system

+11.1% -2.6%

Q C: determine the transfer function of a digital filter corresponding to a discrete time system

+41.1% +16.4%

Q D: identify the purpose of a PD controller

+58.5% +43.8%

Q E: identify the purpose of a PI controller

+69.0% +36.9%

Assessment (Follow-up Survey)

• Students who took follow-up systems and control class– Control:21% – Experimental: 33%

• Students who said their interest in applications of control engineering had increased– Control:29% – Experimental: 62%

Assessment (Follow-up Survey)

Follow-Up Survey for System and Controls Students from Previous Semester Percentage of Students That Rated “Solid Understanding” for 11 Topics Covered in the Course

Control ExperimentalImplementation of digital filters 29% 48%Transient response of 1st and 2nd order systems 71 67Steady state response of systems 71 71Root locus methods 36 52Frequency response methods 43 48Routh-Hurwitz stability criterion* 36 38Nyquist stability criterion* 36 10PID controllers 29 43Lead and lag controllers 36 38Discretization of continuous-time systems 14 62Discrete time control systems 14 43

Conclusion

• Distributed experiments that are integrated into lecture-based courses have a large potential for improving student learning of theoretical material

• The LabVIEW interface allows the experiment to be abstracted to the point of letting the students see the structure of the system through the graphical programming

• The position control experiment requires students to modify the code in such a way that they gain practical experience in the implementation of a control system

• Web support was designed with the goal of lowering the threshold for instructors to adopt these experiments