UNIVERSITY COLLEGE
THE UNIVERSITY OF NEW SOUTH WALES
AUSTRALIAN DEFENCE FORCE ACADEMY
Final Examination - 2002
Oct - Nov
 

Course No.:	AELE3505
Course Name:	Control Theory 2
Time Allowed:	TWO HOURS
No. of Questions on Paper:	FOUR
No. of Questions to be Answered:	ALL

 

All questions are of equal value.
This paper may be retained by the candidate.
All answers must be written in ink. Except where they are expressly required, pencils may only be used for drawing, sketching or graphical work.
 

Instructions to candidates:	Closed Book Exam
Examination materials:	Candidate may bring into room:
	1 sheet of A4 paper with written notes on both sides
	Provided by examination branch:
	Electronic calculators without stored memory
	(supplied by the School)

 

{\bf Question 1 }

Figure 1: Block Diagram: Question 1

A dynamical system is represented in the block diagram form as shown in Figure 1. The transfer function


G(s) =  1 s2+ 2s +1 .

[(a)]
1. Find y(t), t ³ 0 for the input r(t) = 2 Ö2 cosÖ2t, t ³ 0.
   
   
2. Find the steady-state error due to a unit-step input.
   
   
3. Plot the asymptotic Bode plot for G(s).
   
   






{\bf Question 2 }

Figure 2: Block Diagram: Question 2

[(a)]
1. For the system in Figure 2 test for the closed-loop stability by sketching Nyquist plots when:
   

   G(s) =  1 s(s+2)(s+8) .

   
   
   
2. Find the range of K for which the closed-loop system in Figure 2 is stable, where
   

   G(s) =  K s(s+2)(s+8) .

   
   
   









{\bf Question 3}

Figure 3: Block Diagram: Question 3

[(a)]
1. For the system in Figure 3 draw a root-locus diagram:
   

   G(s) =  s+1 (s2+2s+2)(s+2) .

   To draw the root-locus a clear derivation of the asymptotes, departure angles, and other relevant details must be shown.
   
   
2. For the system in Figure 3 draw a root-locus diagram:
   

   G(s) =  s-1 s2+2s+2 .

   To draw the root-locus a clear derivation of the asymptotes, departure angles, break-in points and other relevant details must be shown. From the root-locus obtain the values of gain K for which the closed-loop system will be stable.
   
   

{\bf Question 4}

Figure 4: Block Diagram: Question 4

The plant shown in Figure 4 has the transfer function:


104 s2 + 3s + 2 .

A feedback controller C(s) is to be designed with the configuration shown in Figure 4. The closed-loop system should satisfy the following specifications:
[(a)]
1. The system should have a zero steady-state error to a unit-step input.
   
   
2. The system should have a phase margin of greater than 30 degrees.
   
   
3. The cross-over frequency should be greater than 300 r/s.
   
   
Design a suitable controller C(s) to satisfy these specifications.

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