ENGR 058 (Control Theory) Laboratory
Rigorous motor control
In this lab you will build on your work from last week, and use some of the
theory we've discussed in class.
You will need a PC with data acquisition card a "Universal Power Module" and
a
"Srv02 Plant." The Power modules has two purposes: 1) it takes signals
from the motor set up and converts them to appropriate levels for the computer,
and 2) it takes low power signals from the computer and sends much higher power
signals to the motor. The "Plant" is just Control Theory jargon for the
system being controlled.
These are all in 310. Please put away any equipment you use when you are
done. There are only two sets of apparatus, so you may need to schedule
with other groups to avoid conflicts.
The lab
Task 1
 Connect "S3" on the "Univeral
Power Module" to the unlabelled connector between "ENCODER" and "MOTOR"
on the back of "SRV02." Connect channel 3 (red) of "To A/D" from "Universal Power
Module" to "ADIN2" of "NI ESeries Terminal Board." This
connection is for measurement of the speed of the output motor. Measure the voltage as you turn the motor
slowly. .
 Now connect the "DAC0" output from the terminal board to the "From D/A"
input on the Power Module. Connect the "To Load" output from the Power
Module to the "MOTOR" input of the plant. Now, you can turn the motor by
applying a voltage from the computer.
 Turn on the "Universal Power Module" (the tall black box with connectors
on the top of the front panel).
Task 2: System Identification
 Load the model "E58Lab5Template.mdl" into Simulink
and compile and run it. Note  this only runs for 2 seconds. Make sure
all of your programs for this lab run until equilibrium is achieved.
 This will find the step response of the system (but not the unit step,
because the input is multiplied by 5).
 Use the data to find the transfer function of the motor in the form:
To do this, find the step response due to H_{m}(s) and use the final
value and the time constant of your response to find t_{m} and K_{m}.
Don't forget to compensate for the fact that the input is 5 volts instead of
a unit step.
I used the following MatLab code to isolate the interesting part of the data
(for curve fitting):>> y=y(find((t>=1) & (t<1.4)));
>> t=t(find((t>=1) & (t<1.4)));
>> t=tt(1);
>> plot(t,y)
As a quick check, I got K_{m}≈1.7 and t_{m}≈0.02.
Your numbers will be somewhat different, but in the same ballpark.
Note: in this equation Ω_{v}(s) is the voltage from the output of the tachometer that measures motor speed
(it is not the motor speed itself).
V_{i}(s) is the input voltage to the power amplifier (from the D/A convertor).
Task 3: Proportional Control
 Put your system in a a loop with a proportional controller. A Simulink
model is shown below. To do the experiment you will need to send the output of
the controller to the D/A output that controls the motor (don't forget a
saturation block to limit the range of the output to less than ±10V), and read the speed of
the motor in from the A/D convertor and feed that back to the summing block. Make sure your sampling time is
0.001 S (the easiest thing is probably to save the model from Task 2 under a
different name, and modify it). The step should be a unit step (1 V).
 Measure the output with K_{p}=2, 10, and 50. For each value
of K_{p} find the time constant and steady state error.
Task 4: Integral Control
 Put your system in a a loop with an integral controller.
 Present data for 3 values of K_{i} corresponding to heavily overdamped
(ζ≥2), heavily underdamped (ζ≤0.2) and near "optimal" (ζ≈1/√2).
For your report
Present at least the following:

Task 2: Your H_{m}(s), and data that supports it. (20 pts)

Task 3: Responses for the three values of K_{p},
along with
comparisons with theoretical. Think carefully about how best to do
this  these comparisons are critical to the purpose of this lab (and
to technical writing in general). (35 pts)

Task 4: Responses for the three values of K_{i}, and
comparisons with theoretical. How did you choose them? Again 
consider the presentation of data/theory/discussion carefully to make your
case strongly and succinctly. (35 pts)

Extras  up to 10 pts.
Make sure:
 Writing is clear and concise.
 Considerable thought is given to presentation of data to make them easy
to understand.
 Direct comparison of theory and experiment easy for the reader.
This should be done in graphs and tables, and not just in the text.
 Graphs and tables are labeled and discussed in the text.
 Any expressions for theoretical results should have their derivations
clearly explained in the text.
 Small amounts of code (if any) are in body of text. Larger
amounts can be in an appendix.