Question Paper: Control System Engineering : Question Paper Dec 2015 - Electronics & Telecomm (Semester 4) | Gujarat Technological University (GTU)
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## Control System Engineering - Dec 2015

### Electronics and Comm. Engg. (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.
1(a) Write short notes on open loop control systems and closed loop control systems. Discuss their advantages and disadvantages.(7 marks) 1(b) Obtain system transfer function C(s)/R(s) using block diagram reduction technique for the system shown in figure 1.(7 marks) 2(a) Derive Correlation Between Transfer Functions and State-Space Equations.(4 marks)

### Solved any one question from Q.2(b) & Q.2(c)

2(b) Explain Mason's gain formula.(3 marks) 2(c) Determine the state space model of the system shown in figure 2.(7 marks)

### Solved any one question from Q.3 & Q.4

2(d) Define transfer function. Obtain the transfer of the system defined by $$\begin{bmatrix} \dot{x_1}\\ \dot{x_2}\\ \dot{x_3} \end{bmatrix}=\begin{bmatrix} -1 & 1 & 0\\ 0 & -1 & 1\\ 0 & 0 & -2 \end{bmatrix}\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}+\begin{bmatrix} 0\\ 0\\ 1 \end{bmatrix}u\ \ \ \ \ y=\begin{bmatrix} 1 & 0 & 0 \end{bmatrix}\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}$$(7 marks) 3(a) Define steady state error and derive the expressions for error constants K p , K v and K a corresponding to step, ramp and parabolic input respectively.(7 marks) 3(b) Obtain the values of delay time t d , rise time t r , peak time t p , settling time t s and peak overshoot M p for the given open loop transfer function of a unity feedback control system G(s)=16/s (s+6)(7 marks) 4(a) Derive the expressions Of Rise time, Peak time and Peak overshoot for the system having close loop transfer function $$T(s)=\dfrac{C(s)}{R(s)}=\dfrac{{\omega _{n}}^{2}}{s62+2\xi \omega _ns+{\omega _{n}}^{2}}.$$(7 marks)

### Solved any one question from Q.5 & Q.6

4(b) The open loop transfer function of a unity feedback system is given by $$G(s)=\dfrac{k}{s(1+Ts)}$$ where k and T are constants. By what factor should the amplifier gain be reduced so that the peak overshoot of the system is reduced from 60% to 15% ?(7 marks) 5(a) Using Routh's criterion check the stability of a system whose characteristic equation is given by s 6 +2s 5 +8s 4 +12s 3 +20s 2 +16s+16=0(7 marks) 5(b) What is Root locus? Sketch the Root locus plot for the unity feedback system having $$G(s)=\dfrac{K}{s(s+1)(s+3)(s+4)}$$(7 marks) 6(a) Determine range of k for system stability, for the given characteristic equation of Feedback control system s 4 +2s 3 +(4+k)s 2 +9s+25=0(7 marks)

### Solved any one question from Q.7 & Q.8

6(b) Sketch the Root locus plot for the unity feedback system having an open loop transfer function $$G(s)=\dfrac{K}{s(s+3)(s^2+2s+2)}$$.(7 marks) 7(a) State and explain compensator? Explain Phase-Lead compensator in detail.(7 marks) 7(b) The feed forward transfer function of a close loop system is G(s)=1/s(s+1) and feedback transfer function is H(s) =1/(s+2).
(i) Draw the polar plot of G(s)H(s).
(ii) Find ? corresponding to $$\angle G(j\omega )H(j\omega )=180^{\circ}.$$
(iii) Find $$| G(j\omega )H(j\omega )|$$ corresponding to frequency obtain in (ii).
(7 marks)
8(a) Draw the Nyquist plot for G(s)=1/s(s-1) and comment on system stability.(7 marks) 8(b) Determine gain margin and phase margin using bode plot for the system having transfer function $$G(s)H(s)=\dfrac{1}{s(1+s)(1+0.1s)}$$ and comment on stability.(7 marks)