Control of HIV/AIDS. The linearized model for an HIV/AIDS

Chapter 10, Problem 52

(choose chapter or problem)

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).

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

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, GC(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 \(180^{\circ}\) frequency, if K = 0.3.