ZITE 3203 Control Theory 2 Class Test 1

ZITE 3203 Control Theory 2Class Test

(10% of the final grade)

All answers must be written in ink. Pencils may only be used for drawing, sketching orgraphical work.

Question 1

PSfrag replacementsK G(s)

+

Figure 1: The control system for Question 1.

In the control system shown in Figure 1,

G(s) =1

(s + 3)3

and K > 0 is a gain parameter.

(a) For the case of K = 1, determine the steady state error for this control system when theinput is

(i) a unit step;

(ii) a unit ramp.

(b) For the case of K = 1, determine the phase margin and gain margin of the system.

(c) For the case of K = 1000, determine whether the closed look system is stable.

Please, turn over

20 September 2006

ZITE 3203 Control Theory 2 Class Test 2

Question 2

PSfrag replacementsK G(s)

+

Figure 2: The control system for Question 2.

(a) For the system in Figure 2 draw a root-locus diagram if

G(s) =(5s + 1)

s2(s + 1), K > 0.

A clear derivation of the asymptotes, departure angles, and other relevant details must beshown.

(b) Determine, whether the closed loop system is stable for all K > 0.

20 September 2006