1.    Consider a field controlled d.c. motor whose transfer function is:

G(s) =          50         

s(s+1)(s +10)

It is to be driven by harmonic input u(t) = cos Φ t .

(a)  By writing u(t) as a sum of two complex exponential signals or otherwise show:

U(s) =             s            

(s - jΦ )(s +jΦ) [5 marks]

(b)  Plot the pole-zero pattern for the output X(s) = G(s)U(s) on a complex plane. [5 marks]

(c)  Do the partial fraction expansion for the output signal X(s) . If any of the signal amplitudes are complex, convert them into polar form. [15 marks]

2.    An open loop system comprises the coupled water tanks shown in Figure 2.1. The input to the system is flow  qin , the  output is flow  q out ,  and the system variables are the heights of the water in the two tanks, h 1  and  h2 . The flow in the pipe between the tanks is laminar and the outflow is also laminar. The system equations for a particular geometry of the tanks are:

dh 1                                              dh 2

dt  = -3h1 + 3h2 + qin ,      dt   = 3h1 - 5h2 ,   qout  = 2h2

(a)  Explain briefly what physical features of the water system cause the system equations to

take the above form. Your answer should explain the significance of the fact that the flows are laminar and explain qualitatively how the positive or negative sign of each term arises. [5 marks]

(b)  Based on the system equations, draw an s-plane block diagram representing the system. [10 marks]

(c)  Convert the three system equations into the state-space form given below:

dh

dt  = Ah + bqin ,  qout = ch

( h1 )

with h = ||（h 2 )|| , A a 2×2 matrix, b  a 2×1 vector and c  a 1×2 vector of constants. [10 marks]

Tank 1                             Tank 2

Figure 2.1. Open loop system comprising two interconnected water tanks.

3. (a)  Figure 3.1 shows the Nichols plots of four different transfer functions. State what features of a system are represented by a curve on a Nichols plot. Explain what the grid is used for in the Nichols plot. [5 marks]

(b)  Copy the table below into your answer book. Complete the table by matching the Nichols plots to the open loop transfer functions given in the table. Explain all the reasons for your selections. If there is more than one feature leading you to your decision then every such feature should be mentioned. [10 marks]

(c)   Sketch the form of the time trend expected for the closed loop response to a unit step for:

(i)   The system whose Nichols plot is shown by curve B in Figure 3.1.

(ii)  The system whose Nichols plot is shown by curve D in Figure 3.1.

Hints: Consider the system class and its implications for steady state errors, and also the overshoot and damping of the closed loop response. [10 marks]

100

10

1

0.1

0.01

D

                                                                                                                                                                                         -40 d

-270                          -180                           -90

open loop phase/degrees

Figure 3.1. Nichols plots of four transfer functions: A, B, C and D.

SECTION 2 - Programming: Answer any TWO questions out of THREE from this section

4. (a)      What is an abstract class and what is an interface in Java? [5 marks]

(b)        Explain why making instance variables public is not a good practice in object-oriented software engineering. Which is the alternative approach to making such variables public and what does it achieve? [8 marks]

(c)       Write the constructor and toString methods of class Point which extends the abstract class Shape, then of class Circle which extends class Point and then of class Cylinder which extends class Circle. You should demonstrate and explain how you achieve reusability by re-using the methods of the respective superclass. [12 marks]

5.  (a)       Explain the concepts of inheritance and composition and discuss the benefits they bring

to object-oriented software engineering. [7 marks]

(b)     Write  a  merge  method  of an  OrderedList  class  which  takes  as  argument  an  external ordered list and merges it with the ordered list instance variable, keeping it ordered. OrderedList inherits from List, which includes methods such as removeFromFront and removeFromBack, and adds an insert method which inserts an Object argument in the right position to the list. [10 marks]

(c)      What  is a queue data  structure?  Show how a Queue class can be easily implemented through inheritance from a List class. [8 marks]