The process described by the transfer function GP(S)

Kp (T₁S+1) e-TDS

(T₂S + 1)(T3S + 1)

Gp(s) =

is controlled by a P controller with an arbitrary gain of Kc.

a) If Kc = 2; Kp = 5; T₁ = 2; Td = 1; T₂ = 2; T3 = 3 determine whether the

closed-loop response will be stable using frequency response

techniques.

What is the limiting value of the controller gain to ensure stability?

b) For the following scenarios, generate the Bode plots for the open-

loop behavior using Excel. Comment on the effect of the

parameter changes on plots 2, 3 and 4 using plot 1 as the

reference.

1.

2.

3.

4.

Kc = 2; Kp = 5; t₁ = 0; TD = 0; T₂ = 2; T3 = 3

Kc = 2; Kp = 5; t₁ = 0; TD = 5; T2 = 2; T3 = 3

Kc = 4; Kp = 5; T₁ = 0; TD = 0; T₂ = 2; T3 = 3

Kc = 2; Kp = 5; T₁ = 0; TD = 10; T₂ = 2; T3 = 3

c) Using the same general transfer function, plot the Nyquist plots

using Excel for the following parameters. Comment on the behavior.

1. Kc = 2; Kp = 5; T₁ = 1; TD = 0; T₂ = 2; T3 = 3

2.

Kc = 2; Kp = 5; T₁ = 3; TD = 0; T2 = 2; T3 = 3