(Submit your properly commented MATLAB source code along with a report that includes
the output images/plots, and your analysis/comments on the results in a zip via Blackboard.)
In this homework, you will use both Matlab and Simulink environment, and you will design a
digital controller in C(z) for an analog plant P(s) . The structure of the overall feedback
control system, where r(t) is the reference input, and o (t ) is the output signal is shown below.
In your work, you may use “tf”, “zpk”, “rlocus”, “step”, “stepinfo”, “pid”, “c2d”, “d2c”, “pade”, and “feedback” commands on MATLAB. Also you may use “transfer function”, “zero-order hold”, “scope”, and “step” blocks in Simulink.
First, create a continuous-time model of the plant. Then transform the transfer function into zero-pole-gain model. Plot the root-locus of the plant transfer function. What can you say about the stability of the plant itself?
You will now design an analog controller with the transfer function C(s)= 500s+50 100 s 2 +s in Simulink. Then plot step response of the closed-loop system.
Now, convert analog controller into a discrete-time controller with sampling period Ts = 0.2 in Matlab using bilinear mapping. Find the transfer function of the digital controller.
In Simulink, design digital controller with the transfer function you have found above. Note
that you should insert zero-order hold block to convert its output to analog signal. After all,
plot the step response of closed-loop system. What kind of differences did you observe in
fully analog system’s step response and hybrid system’s step response. Discuss your