EG4311 
All candidates 
January Examinations 2015
DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE
CHIEF INVIGILATOR
Department  ENGINEERING 
Module Code  EG4311 
Module Title  Robust Control (Semester 1) 
Exam Duration  Two Hours 
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Number of Pages  5 
Number of Questions  4 
Instructions to Candidates  Answers are expected to three questions. Answers to only three questions will be marked. Attempted solutions which you do not wish to submit should be crossed out. If you do attempt more than three questions, and do not identify which three you want to be marked, only the first three in the answer book will be marked. For each question, the distribution of marks out of 20 is indicated in brackets. 
For this exam you are allowed to use the following  
Calculators  Casio FX83 or Casio FX85 (any variant) 
Books/Statutes  Engineering Data book 
Additional Stationary  Not required 
Page 1 of 5
EG4311 
All candidates 
1. i. Give two dailylife or engineering device/process examples to explain what is meant
by an openloop control system and by a closedloop system, respectively.
[6 marks]
ii. Further, using your example, compare the advantages and possible disadvantages
between the open and closedloop system structures.  [6 marks] 
iii. What is meant by a control system being robust? Why is the closedloop structure essential to robust control? What kind of uncertainties are usually considered in 

robust control? Please use your example to illustrate your viewpoints.  [8 marks] 
Page 2 of 5
EG4311 
All candidates 
2. a. i. What is meant by BoundedInputBoundedOuput (BIBO) stability?
[3 marks]
ii. A control system is modelled by a transfer function matrix G(s). How do you find
out if G(s) is BIBO stable? [3 marks]
iii. Consider the feedback system depicted in Figure 1, where G(s) represents the
plant to be controlled and K(s) the controller to be designed. r is the reference
input signal, y the system output, u the control signal, d the disturbance at the
system output and n the sensor noise. Please define what is meant by internal
stability, using this feedback system. b. Consider the feedback system depicted in Figure 1. 
[5 marks] 
i. In the case that G(s) = (s+2s)(1s+3), one at first trial chooses a controller K(s) =
s+2
s1. Derive the transfer function Tyr(s) that describes the relationship between
r and y, and further determine the stability of Tyr(s). ii. Can such a controller K(s) be used in practice? Give your reasons. 
[4 marks] 
[5 marks]
K(s) G(s)
r
u
y
+
–
d +
+
+
+
n
Figure 1:
Page 3 of 5
EG4311 
All candidates 
3. a. Gain and phase margins are commonly used measures of robust stability in classical
control theory.
i. How are gain and phase margins defined?  [3 marks] 
ii. State the major limitation of these robustness measures. Draw a Nyquist plot to  
show that they are not always reliable measures.  [3 marks] 
b. The Small Gain Theorem is a much more powerful tool in robust control than the gain
and phase margins.
i. With the aid of a block diagram, state the Small Gain Theorem. [4 marks]
ii. Why can the Small Gain Theorem sometimes give conservative results? Describe a circumstance in which the Small Gain Theorem would be a necessary
condition as well, i.e. it is not conservative at all in that circumstance.
[5 marks]
iii. Consider the closedloop system depicted in Figure 2, where the plant dynamics
is represented by the nominal dynamics G(s) and an unstructured, multiplicative
perturbations D(s) at the (plant) input end. Use the Small Gain Theorem to
derive a condition for the design of K(s) to achieve robust stability. [5 marks]
r + e K(s) u G(s) y
–
+
+
v
∆
Figure 2:
Page 4 of 5
EG4311 
All candidates 
4. Consider the H¥ Mixed Sensitivity control system design problem shown in Figure 3.
i. Define the various signals labelled in Figure 3, i.e. r; d; e; u; y; z1; z2. [3 marks]
ii. Derive the relationship between z1 and d and between z2 and r, respectively.
[6 marks]
iii. Derive the generalised interconnection plant P for the feedback system considered,
as in Figure 4.  [4 marks] 
iv. Use the (lower) Linear Fractional Transformation (LFT) to derive a cost function for the H¥ optimal control problem for minimum disturbance rejection and limited control 

effort.  [4 marks] 
v. Does the cost function formulated in (iv) also consider reference tracking? Give your  
reasons.  [3 marks] 
d
P
u
G
K
+
+
–
+
W1
W2
r
z1
z2
e
y
Figure 3:
P(s)
K(s)
dr
u e
z z1 2
Figure 4:
END OF EXAMINATION
Page 5 of 5
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