Question: A plasma etching batch process has a process gain of E A/min (but no dynamics). The manipulated variable is the etch time, so the controlled

A plasma etching batch process has a process gain of E Ȧ/min (but no dynamics). The manipulated variable is the etch time, so the controlled variable is the film thickness. There are no time constants that need to be included. Assume G_v = G_m= 1. Derive the closed-loop transfer function for a set-point change for two different controllers:

(a) G_c = K_c

(b) G_c = 1 / τ_Is

In both cases, analyze the effect of a unit step set-point change. Sketch the response and show whether there is offset or not.

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