The closed-loop transfer function for the Smith predictor in Eq. 16-22 was derived assuming no model error.

(a) Derive a formula for Y/Ysp when Gp ≠ Gp. What is the characteristic equation?

(b) Let Gp = 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 (Kp), Lime constant (τ), and lime 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?

(d) For Kc = 15, how large a change in either Kp, τ or θ can be tolerated before the loop goes unstable?