Question: A dissolved oxygen analyzer in a bioreactor is used to provide composition measurements at each sampling time in a feedback control loop. The open-loop transfer

A dissolved oxygen analyzer in a bioreactor is used to provide composition measurements at each sampling time in a feedback control loop. The open-loop transfer function is given by

Got - G.G 10 12s +1 Ge

(a) Suppose that a sampling period of ?t = 1 min is selected. Derive Gc(z) using a backward-difference approximation of Gc(s).

(b) If a unit step change in the controller error signal e(t) is made, calculate the sampled open-loop response ym(k?t) using MATLAB with a zero-order hold after the controller Gc and before the process G in the block diagram constructed via Simulink.

Got - G.G 10 12s +1 Ge

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