MATLAB Project
ENEE 3533 Classical Control System Design Spring 2021
Matlab Project
Compensator Design & Simulation
Objective
Your term project will be to design and simulate PI compensators for a control system using Matlab/Simulink
(using Octave is also accepted).
System Model
FYI, a possible block diagram of a speed control scheme for a hybrid electric vehicle driven by a dc motor is
With typical values of the parameters, the system can represented in a simpliÖed unity-feedback form as
follows:
where R(s) is the reference voltage, C(s) = KssV (s) is the output voltage of the speed sensor, and GSC (s)
denotes a controller (to be designed).
Assignment
Task 1. Proportional compensation
Assume GSC (s) is a proportional (P) controller, i.e., GSC (s) = KP .
(a) Find the closed-loop system transfer function and determine the range of KP > 0 for stability.
(b) For the uncompensated closed-loop system (i.e., with KP = KP1 = 1):
ñ Simulate and plot the system unit-step response c(t).
ñ Determine (from the plot) the P.O., peak time Tp, rise time Tr, settling time Ts, and steady-state
error estep(1) in % of the input.
ñ Find also eramp(1) =?
ñ Plot the Bode diagrams and indicate the bandwidth, and the phase and gain margins. Electrical Engineering homework help.
(c) Find KP = KP2
that yields a steady-state error estep(1) = 1%.
ñ Repeat part (b) with the found KP2
.
(d) Plot the RL for KP and determine KP = KP3
that yields critically damped closed-loop response.
ñ Repeat part (b) with the found KP3
.
(e) Compare the results from (b), (c) and (d), and make comments.
Task 2. PI compensation
Now assume GSC (s) is a PI controller, i.e.
GSC (s) = KP +
KI
s
=
KP (s + KI =KP )
s
(1)
(a) With KP = KP2
as determined in Task 1 (c), Önd KI2
that yields a steady-state error eramp(1) = 2:5%.
For this KI2
, Önd estep(1) =?
ñ Repeat the simulation of Task 1 (b) with GSC (s) = KP2 +
KI2
s
.
Compare this PI controller with the P controller KP2
from Task 1 (c).
(b) Now, assume in Eqn. (1) that KI =KP = 0:4, i.e., GSC (s) = KP (s+0:4)
s
.
ñ Plot the RL for KP and from the RL determine KP = KP4
that yields a closed-loop step response
with P.O. = 10%.
ñ Simulate and plot the unit-step system response c(t) and determine (from the plot) the actual P.O.,
peak time Tp, rise time Tr, settling time Ts, and steady state error estep(1) in % of the input.
Is the actual P.O. = 10%? Why? Electrical Engineering homework help.
ñ Plot also the Bode diagrams and indicate the bandwidth, and the phase and gain margins.
(c) Design a PI controller (choose both KP an KI ) such that the closed-loop system achieves the following
design objectives:
(i) P:O: 4:32%; (ii) Ts 4 sec; (iii) estep(1) = 0; (iv) eramp(1) 2%
ñ Simulate and plot the step and ramp responses of the compensated system to illustrate how your
design actually achieves the objectives.
ñ Plot also the Bode diagrams and indicate the bandwidth, and the phase and gain margins.
ñ Make comments on how the compensation was achieved, in terms of the frequency responses in
comparison with the previous (P and PI) compensators.
Task 3: Summary & Comparison.
Summarize your results from all tasks (except 1 (a)) in a table with the following format:
Task KP KI P.O. Tp Tr Ts estep(1) eramp(1) !B G.M. PM
1 (b)
1 (c)
1 (d)
2 (a)
2 (b)
2 (c)
Which one of your designs provides the best performance? Why?
2
Organization
For all students: everything (design, program code, report) must be individual.
Consultation with the instructor is available through email if you have some questions.
Report
As a minimum, you should include the following information in your Project Report (must be in PDF
format):
Cover Page: Title, author, date, course information.
Introduction: Concise description of the problem, project objectives and tasks, and content of the report.
Design and Simulation Results:
For each task give description of the performed work and obtained analytical and simulation results. Include:
design objectives, method used, details of your design, iterations performed, simulation results, your comments,
Öndings, etc.
Conclusions: Provide brief conclusions of your work.
References: List all references used.
Appendix: Matlab code
Deliverables (to be uploaded on Moodle under Project)
1. One PDF-Öle with the Report
2. One Zip-Öle including all program code Öles . Electrical Engineering homework help.