AELE.3505 Control Theory 2 Class Test 1

AELE.3505 Control Theory 2Class Test

(10% of the final grade)All answers must be written in ink. Pencils may only be used for drawing, sketching or

graphical work.

Question 1

PSfrag replacementsK Plant

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Figure 1: The control system for Question 1.

A control system shown in Figure 1 has loop gain transfer function

G(s) =K(s + 7)

(s + 1)3

where 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, Sketch the form of the complete Nyquist plot for this system. Fromthe Nyquist plot determine the range of values of K for which the closed loop system isstable. Hint: The system has the phase crossover frequency of p =

5 rad/s.

(c) For the case of K = 0.4, determine the phase margin of the system. Hint: For this value ofK, the gain crossover frequency is c = 1 rad/s.

(d) For the case of K = 0.4, determine the gain margin of the system.

Please, turn over

8 September 2004

AELE.3505 Control Theory 2 Class Test 2

Question 2

PSfrag replacementsK G(s)

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Figure 2: The control system for Question 2.

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

G(s) =10(s + 0.4)

s(s + 1)2, 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.

8 September 2004