in Chapter 10 mentioned a measurementbased technique to

Chapter 11, Problem 31

(choose chapter or problem)

Problem 52 in Chapter 10 mentioned a measurement based technique to design fixed-structure controllers, which does not require system identification. In that problem, we assumed a plant transfer function of (Khadraoui, 2013)

G(s) = \(\frac{0.1111\left(4 s^2+5 s+1\right)}{s^4+3.1 s^3+0.85 s^2+0.87 s+0.1111}\)

Again, the interested reader is directed to the reference for further study. In this problem, however, we use the design and analysis techniques developed in this and the previous chapters.

Use MATLAB and Bode plots to design a PID controller, Gc(s), to yield zero steady-state error for a step input, an overshoot of 10 to 20%, and a settling time of 20 to 50 seconds. Start your design assuming an overshoot of 10% and a settling time of 50 seconds. Consider the design acceptable if the PID-controlled response satisfies the above requirements.