SPPU Electrical Engineering (Semester 6)
Control System I
December 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


Solve any one question fromQ.1(a,b,c) and Q.2(a,b,c)
1(a) Distinguish between
i) Open loop and closed loop system.
ii) Feedback and feedforward system
6 M
1(b) Write a short note an tachogenerator.
6 M
1(c) A unity feedback system characterised by the open loop transfer function. \( G(s)=\frac{1}{s\left ( 0.5s+1 \right )\left ( 0.2s+1 \right )}\)/ Determine the steady state errors for unit step, unit ramp and unit acceleration inputs.
8 M

2(a) Draw mechanical equvalent network of a guven system and als draw the electrical analogous circuit using F-V analogy.
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8 M
2(b) State and explain Mason's Gain Formula.
5 M
2(c) Define and explain time domain specification.
7 M

Solve any one question fromQ.3(a,b) and Q.4(a,b)
3(a) State and explain Routh Hurwitz stability criterion.
6 M
3(b) A unity feedback control system has an open loop transfer function. \(G(s)=\frac{K}{s\left (s^2+4s+13 \right )} \)/
System the root locus pot of the system by detemining the following:
) Centroid, number and angle of asymptotes.
ii) Angle of departure of root loci from the poles.
iii)Breakaway point if any
iv) The value of K and the frequency at which the root loci cross the jω-axis.
10 M

4(a) Sketch the root locus for the open-loop transfer function of a unity feedback control system given below and determine
i) The value of K for ξ=0.5
ii) the value of K for marginal stability.\( G(s)=\frac{K}{s\left ( s+1 \right )\left ( s+3 \right )} \)/
9 M
4(b) The open-loop transfer function of a unity feedback system is given by \( G(s)=\frac{K}{s\left ( s+2 \right )\left ( s+4 \right )\left ( s^2+6s+25 \right )} \)/
By applying the Routh Criterion discuss the stability of the closed loop system as a function of K. Determine the value of K which will cause sustained oscillation in the closed loop system. What are the corresponding oscillation frequencies?
7 M

Solve any one question fromQ.5(a,b) and Q.6(a,b)
5(a) Explain the terms gain margin, phase margin, Gain cross over frequency, phase cross over frequency.
8 M
5(b) Sketch the bode plot of the transfer function and determine PM and GM from the plot. \[G(s)H(s)=\frac{30}{s\left ( 1+0.5s \right )\left ( 1+0.08s \right )}\]
10 M

6(a) Explain Nyquist stability criteria.
8 M
6(b) A control system with closed loop transfer function \( G(s)H(s)=\frac{K\left ( s-1 \right )}{s\left ( s+1 \right )} \)/ Plot Nyquist plot and comment on stability.
10 M

Solve any one question fromQ.7(a,b) and Q.8(a,b)
7(a) Draw block diagram of PID controller and discuss the effect of increasing Kp, K1, KD on rise time overshoot andstability.
8 M
7(b) The system given below is so design to have damping ratio 0.707. Determine the required value of Kp for the given damping ratio.
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8 M

8(a) Explain Ziegler Nichols method of tuning PID controller.
8 M
8(b) An open loop test of a temperature control system yields the reaction curve shown below The system open loop transfer function is given by \( G(s)=\frac{1}{\left (20 s+1 \right )\left ( 50s+1 \right )}\)/
Use Ziegler Nichols method to determine Kp, K1, KD? For a quarter step response PID control system.
!mage
8 M



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