Supervisor: Dr. Robert Morley
Electrical Engineering Department
Washington University in St. Louis
Abstract
In order to update a previously existing lab for ESE 102, Introduction
to Electrical Engineering, a new lab is developed. This new lab was
includes a Systems Engineering element so as to expose freshman
engineering students to both disciplines. The subject of the lab is DC
Motor Control using LabVIEW visual programming language and a Johnson
H.K. DC Motor. In addition to the development of a student GUI,
one hour of lecture notes, and two hours worth of lab exercises in
addition to analysis homework are created. The purpose of the lab is to
introduce a working knowledge of the theory and mathematics of Systems
Engineering and how it applies to the problem of angular velocity
control for a DC Motor. In doing so,
students are to derive the transfer function of the motor from a series
of equations, design a stable PID controller for the system to meet a
list of system specifications, reproduce basic the three basic system
reponses, and solve for the system parameters. The lecture takes
students from understanding the basic open-loop feedback system through
an introduction to the root locus for a controlled system. The lab
exercises guide students in tuning the controller gains to reach
desired responses while applying the theory and mathematics of the
lecture to the physical DC motor.
Specifications
The comprehensive list of specifications for this project are:
Literature research to find similar labs developed at other universities
Lecture notes for a one hour lecture
LabVIEW vi for students to use to interact with "CD Motor"
Lab instructions for students to use to wire up circuit, perform experiments and record and analyze results
Homework set covering lecture material
Report on design experience and theory of operation of the LabVIEW vi
LabVIEW vi
The DC motor circuitry only allows for an applied voltage of 0 to 5
volts. Saturation occurs at input values outside that range. Attached
to the motor is a CD with a black stripe drawn along the radius with a
duty cycle of approximately 10%. A Photodiode collects samples at 200
KHz, iterating every 0.5 seconds. A Boolean switch is installed to open
and close the loop. While the switch is off, the motor is driven by an
applied voltage and students may analyze open loop system properties in
order to solve for the system parameters later. While off, the closed
loop system is driven by a user-specified desired RPM. The controller
is PID whose gain coefficients can set in real-time. The design was
specified as an unity feedback loop, therefore no prior system
calibration is requried. Noise at the voltage source causes slight
fluctuations in applied voltage, therefore necessitating an average of
every 4 pulses to be fed back to the input. The output range is between
0 and 2200 RPM.
Lecture Notes
The following Systems Engineering topics were briefly covered at an introductory level:
Open loop system
Closed loop system
First and second order canonical forms
First and second order systems
PID controller transfer function
The effect of gain on each controller term
Common time-domain specifications:
Rise time
Peak time
Percent Overshoot
Settling time
Steady-state error
Derivation of the closed loop transfer function
Characteristic equation
Effects of measurement noise on the closed loop transfer function
Three basic types of system response:
Underdamped
Critically damped
Overdamped
Root locus
See the Appendix A for a copy of the Lecture Notes.
Laboratory Instructions
The lab begins with students noting the response to the motor when
given an outside disturbance (ie. applying a finger to the spinning
CD). Next students are asked to run a linear regression to translate
applied voltage to RPM. The loop is then closed and students experiment
with varous controller gain values, beginning with only proportional
gain and gradually adding in integral and derivative. All experiments
use a step input of 200 RPM beginning at 1000 RPM.
Students are then asked to recreate the three basic types of system
response and obtain a response given a set of specifications. Finally,
they are asked to apply a disturbance to their closed loop system and
compare the response to the open loop reponse. See Appendix B for the
Lab Instructions.
Laboratory Analysis
As post-lab analysis, a variety of questions are asked in order to
apply the theory from the lecture notes to the DC motor system. See
Appendix B for the Lab Analysis.
Operation
The initial operation of the feedback system worked as expected within
its input voltage boundaries. To get the motor to spin, the system had
to be set to open loop and have all but the proportional gain set to
zero. Once an input voltage was entered, the open loop system would
engage. With the motor operating, the loop could be closed and the
derivative and integral gains could be given nonzero values. While the
loop was closed, step inputs of amplitudes any greater than
approximately ±2V would cause the voltage to the actuator to exceed the
allowable range and freeze the program. In such cases, the motor would
either reach an RPM of around 2200 and stop responding, or would go to
zero RPM. The lab was initially designed so as to not exceed a step
input of 1V.
Conclusion
The specifications for this project were met, demonstrated by the above
report. The three basic system responses were replicated with this
design. All the information in the lecture notes is applicable to the
designed DC motor system and is required for completion of the
laboratory analysis.