UESTC4003 - Control
Computer Lab Exercise 3
MATLAB for Control Engineering
1.0 Objectives
The primary aim of this class is to use MATLAB to:
• Represent state-space systems
• Convert a system to state space form and other forms
• Pole Placement for plants in phase-variable form.
• Discrete-time transfer function analysis
2.0 State space representation of a transfer function (Exercise 3A)
Consider the below system.
2.1 Find the state-space representation of the transfer function using manual techniques.
2.2 Define A,B, C and D matrices in MATLAB and create state-space object.
2.3 Convert the transfer function directly to state space (controller canonical form) using MATLAB.
2.4 Now convert the controller canonical form. to phase-variable form. and, compare with the manual calculations in part 2.1. (To obtain phase-variable form, perform Ap=inv(P)*A*P;Bp=inv(P)*B;Cp=C*P,Dp=D; assume phase variable form. matrices areAp, Bp, Cp and Dp and P=[0 0 1;0 1 0;1 0 0]).
2.5 Convert the controller canonical state space object (obtained in part 2.3) into parallel form.
2.6 Convert the transfer function to the observer canonical state-space representation.
2.7 Repeat part 2.6 using manual techniques and verify the answers.
3.0 State space representation to transfer function
Consider the below state space representation of a system.
where U(s) is the input and Y(s) is the output.
3.1 Define A,B, C and D matrices in MATLAB and create a state-space object in MATLAB.
3.2 Now convert state-space object into a transfer function.
3.3 Assume that it is desired to have closed-loop poles at −2 ± j4 and −10. Determine the corresponding state feedback-gain matrix for the design.
4.0 Discrete-time transfer function analysis (Exercise 3B)
Consider the below control system which is used to regulate ventilation rate of an environment chamber by adjusting fan voltage.
4.1 Create the system shown above in MATLAB Simulink environment assuming aproportional controller (with a gain of 0.1) and a first order discrete-time transfer function of:
Assume desired ventilation rate as 300 m3/hour.
4.2 Run the simulation and examine the results using the Scope in MATLAB Simulink (i.e. ventilation rate output and controller output).
4.3 Adjust the controller gain using trial and error. What is the effect on the steady state error and the speed of response? What happens if you keep increasing the value of the proportional controller gain to reduce the steady state error?
4.4 Modify your above simulation by replacing the proportional controller with an integral control. Note that the control algorithm is another Discrete Filter block with a discrete-time transfer function of:
with an integral gain (kI) of 0.1.
4.5 Run the simulation and examine the results using the Scope block. Investigate different values of kI and find the maximum value of kI (approximately) that does not yield an overshoot.
4.6 How does this response compare with the equivalent proportional control case?
The laboratory exercises will be assessed according to the below criteria:
|
Assessment of Laboratory Exercises
Laboratory exercises will be assessed according to the accuracy of the answers and
designs provided. You will be required to include your results for the following parts:
• Computer Lab 1 - Exercises 1A and 1B
• Computer Lab 2 - Exercises 2A and 2B
• Computer Lab 3 - Exercises 3A and 3B
You will be assessed against the correctness of your answers: models, designs and results, and the correctness of your interpretation of these results. You should create a single word (pdf) file and copy your MATLAB answers, plots, and diagrams corresponding to the parts in each lab exercise mentioned earlier. Also, make sure to include annotations/discussions relating to your results where necessary. You must submit this report (as a word or pdf file) to Moodlevia the assessment link and failure to submit this will result in a mark of zero for computer-based tutorials.
The deadline for the report submission is the 6th of December 2024 (Beijing time) and late submissions will not be accepted.
|
References
Gene F. Franklin, J. Da Powell, Abbas Emami-Naeini, Feedback Control of Dynamic Systems, 7th Edition.
Katsuhiko Ogata, Modern Control Engineering, 5th Edition.
Norman S. Nise, Control Systems Engineering, 7th Edition.