Question Paper: Control Systems : Question Paper Dec 2015 - Electronics & Telecom Engineering (Semester 4) | Pune University (PU)
0

## Control Systems - Dec 2015

### Electronics & Telecom Engineering (Semester 4)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.

### Solve any one question from Q1 and Q2

1 (a) Consider the R-L-C network shown in Fig. 1:
i) Obtain transfer function if Vi and Vo are input and output voltage respectively.
ii) Find the location of poles in terms of R, L and C.
iii) If R=1 MΩ, C=1 μF, L=1 mH. Is the location of poles of transfer function given in (i) are real? If yes, find the location.

(6 marks) 1 (b) If $G(s)= \dfrac {K}{s(s+64)}$ with H(s)=1, determine value of K so that damping factor is 0.5. For this value of 'K' determine:
i) Rise time, and
ii) Settling time.
Assume unit step input.
(6 marks)
2 (a) Find $\dfrac {C(s)}{R(s)}$ for the system shown in Fig. 2 using Block diagram rules.

(6 marks) 2 (b) The open loop transfer function of unity feedback system is:
$G(s) = \dfrac {K}{s(\tau s+1)}, K, \tau > 0$ with a given value of K, the peak overshoot was found to be 80%. Suppose peak overshoot is decreased to 20% by decreasing gain K. Find the new value of K (say K2) in terms of the old value.
(6 marks)

### Solve any one question from Q3 and Q4

3 (a) Comment on stability of a system using Routh's criteria, if characteristics equation is D(s)=s4+5s3+s2+10+1. How many poles lies in Right of s-plane?(4 marks) 3 (b) Construct Bode Plot and calculate GM, PM, Wgc and Wpc if $G(s) = \dfrac {200(s+20)}{s(2s+1)(s+40)}$ and H(s)=1.(8 marks) 4 (a) Open loop transfer function of unity feedback system is $G(s) = \dfrac {K}{s(s+2)(s+10)}.$ Sketch the complete root locus and comment on stability of system.(8 marks) 4 (b) For unity feedback system with $G(s) = \dfrac {100}{s(s+5)}$.
Determine:
i) Resonance peak
ii) Resonance frequency.
(4 marks)

### Solve any one question from Q5 and Q6

5 (a) Enlist any two advantages of state space approach over transfer function. Obtain a state space representation in controllable and observable canonical form for the system $G(s) = \dfrac {s+3}{s^2 + 3s +2}$(6 marks) 5 (b) Obtain the state space representation of system whose differential equation is: $$\dfrac {d^2 y}{dt^3}+ 2 \dfrac {d^2 y}{dt^2}+ 3 \dfrac {dy}{dt}+ 6y = \dfrac {d^2u}{dt^2} - \dfrac {du}{dt}+ 2u.$$ Also find controllability and observability of the system. Assume zero initial conditions.(7 marks) 6 (a) Obtain state transition matrix if: $$i) \ \dfrac {dx}{dt} = \begin{bmatrix} 0 &1 \\-1 &0 \end{bmatrix}x \\ ii) \ \dfrac {dx}{dt} = \begin{bmatrix} 0 &1 \\0 &0 \end{bmatrix} x$$ using Laplace transformation.(6 marks) 6 (b) Write a short note on 'state transition matrix and its properties'.(4 marks)

### Solve any one question from Q7 and Q8

7 (a) Advantage of digital control system over analog control systems.(4 marks) 7 (b) Application of PLC (Programmable Logic Controller) in Elevator/List.(4 marks) 7 (c) PID controllers and its operational characteristics.(5 marks) 8 (a) Obtain pulse transfer function of the system shown in Fig. 3 with a=1.

(6 marks) 8 (b) Obtain pulse transfer function of system shown in Fig. 4

(7 marks)