16.10 The closed-loop transfer function for the Smith predic-

tor in Eq. 16-22 was derived assuming no model error.

(a) Derive a formula for Y/Y, when G‡ G. What is

the characteristic equation?

(b) Let G=2e-2s/(5s +1). A proportional controller with

Kc = 15 and a Smith predictor are used to control this process.

Simulate set-point changes for ±20% errors in process gain

(K), time constant (t), and time delay (six different cases).

Discuss the relative importance of each type of error.

(c) What controller gain would be satisfactory for ±50%

changes in all three model parameters?