Question: A process has the transfer function, where K has a nominal-value of K = 1. PID controller settings are to be calculated using the Direct

A process has the transfer function, where K has a nominal-value of K = 1. PID controller settings are to be calculated using the Direct Synthesis approach with ?c = 5 min.Suppose that these controller constants are employed and that K changes unexpectedly from 1 to 1 + ?.(a) For what values of will the closed-loop system be stable?(b) Suppose that the PID controller constants are calculated using the nominal value of K = 1 but it is desired that the resulting closed-loop system be stable for |?| (c) What conclusions can be made concerning the effect that the choice of ?c has on the robustness of the closed-loop system to changes in steady-state gain K?

G(s) (10s + 1)(5s +1)

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