A new measurement-based technique to design fixed structure controllers for unknown SISO systems, which does not require system identification, has been proposed. The fourth-order transfer function shown below and modified to have a unity steady state gain is used as an example (Khadraoui, 2013).

The interested reader is referred to the reference to explore this new technique. In this problem and its companion design problem in Chapter 11, however, we take a standard approach as covered in Chapters 10 and 11. Assuming that a cascade connected proportional controller, G_C(s) = K, is used, utilize MATLAB and frequency response techniques to obtain the Bode plots for this system and find:

a. The range of K for system stability 

b. The gain margin, phase margin, zero dB frequency, and 180° frequency, if K = 0.3.

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0.1111(4s2 +5s + 1) G(s) = %3D s4 + 3.1s + 0.85s? +0.87s + 0.1111