Question: (a) Using the process, sensor, and valve transfer functions in Exercise 11.21, find the ultimate controller gain K cu using a Bode plot. Using simulation,

(a) Using the process, sensor, and valve transfer functions in Exercise 11.21, find the ultimate controller gain K_cuusing a Bode plot. Using simulation, verify that values of K_c> K_cucause instability.

(b) Next fit a FOPTD model to G and tune a PI controller for a set-point change. What is the gain margin for the controller?

Function From Exercise 11.21,

2e-1.5s G,(6) = (60s + 1)(5s + 1) 0.5e-0.3s G,(s) = 3s +1 Зе-0.25 G„(8): 2s + 1 G_(s) = K.

2e-1.5s G,(6) = (60s + 1)(5s + 1) 0.5e-0.3s G,(s) = 3s +1 -0.25 G(8): 2s + 1 G_(s) = K.

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