a. Design an observer for the dc-dc converter of 36. The
Chapter 12, Problem 35(choose chapter or problem)
Figure P12.6 shows a continuous stirred tank reactor in which an aqueous solution of sodium acetate \(\left(\mathrm{CH}_3 \mathrm{COONa}\right)\) is neutralized in the mixing tank with hydrochloric acid (HCl) to maintain a particular pH in the mixing tank.
The amount of acid in the mix is controlled by varying the rotational speed of a feeding peristaltic pump. A nominal linearized transfer function from HCl flow rate to pH has been shown to be (Tadeo, 2000)
G(s) = \(\frac{-0.9580 \times 10^{-4} s-0.01197 \times 10^{-4}}{s^3+0.5250 s^2+0.01265 s+0.000078}\)
a. Write the system in state-space phase-variable form.
b. Use state-feedback methods to design a matrix K that will yield an overdamped output pH response with a settling time of \(T_s \approx 5 \mathrm{~min}\) for a step input change in pH.
c. Simulate the step response of MATLAB the resulting closed-loop ML system using MATLAB.
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