Question Paper: Control System Engineering : Question Paper May 2016 - Electronics & Telecomm (Semester 4) | Gujarat Technological University (GTU)
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## Control System Engineering - May 2016

### 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.

### Do as directed (short questions)

1(a) List out the features of negative feedback in a closed loop system.(1 marks) 1(b) What is steady-state error?(1 marks) 1(c) Define pole, zero and order of a control system.(1 marks) 1(d) What are the advantages of state space analysis?(1 marks) 1(e) Draw the block diagram/signal flow graph representation of the system described by the state model $\begin{bmatrix} x_1\\\\ x_2\\\\ x_3 \end{bmatrix}=\begin{bmatrix} a_1 & a_2 & 0\\\\ 1 & 0 & 1\\\\ 0 & 1 & 0 \end{bmatrix}\begin{bmatrix} x_1\\\\ x_2\\\\ x_3 \end{bmatrix}+\begin{bmatrix} 1\\\\ 0\\\\ 0 \end{bmatrix}u\ \text{and}\ y=x_3.$(1 marks) 1(f) The closed loop transfer function of a second order system is given by $\dfrac{200}{s^2+20s+200}$. Determine the damping ratio and natural frequency of oscillation.(1 marks) 1(g) What is polar plot? Draw the polar plot of G(s) = 1/(1 + sT).(1 marks) 1(h) With graphical representation, explain How the roots of characteristic equation are related to stability?(1 marks) 1(i) What is Nyquist stability criterion?(1 marks) 1(j) How will you find the gain K at a point on root locus?(1 marks) 1(k) Sketch the frequency response (bode) plot of G(s) = 1/(1 + sT).(1 marks) 1(l) What is the effect on system performance, when a proportional controller is introduced in a system?(1 marks) 1(m) State the transfer function of lead compensator and draw its pole-zero plot.(1 marks) 1(n) What is PD-Controller and what are its effect on system performance?(1 marks) 2(a) For the given mechanical translation system as shown in Fig. 1. Write down differential equations, represents in Force-Voltage analogy.

(3 marks) 2(b) Obtain the state space representation of armature controlled DC motor with load. Consider armature current ia , the angular displacement of shaft θ , and the speed dθ/dt as state variables, and θ as output variable.(4 marks)

### Solve any one question from Q.2(c) & Q.2(d)

2(c) A linear feedback control system has the block diagram shown in Fig. 2. Using block diagram reduction rules, obtain overall transfer function C(s)/R(s) .

(7 marks) 2(d) For the signal flow graph shown in Fig. 3, using Masson's gain formula determine the overall transmission C/R.

(7 marks)

### Solve any three question from Q.3(a), Q.3(b), Q.3(c) & Q.3(d), Q.3(e), Q.3(f)

3(a) Define thermal resistance and thermal capacitance. Also derive the transfer function of Thermometer placed in water bath as a Thermal system.(3 marks) 3(b) Find the position, velocity and acceleration error constants, for a unity feedback control system has the open loop transfer function G(s) = 10(s+2)/s2(s+1).(4 marks) 3(c) Obtain the state model and give block diagram representation for a system whose closed-loop transfer function is given as, $$\dfrac{Y(s)}{U(s)}=\dfrac{10(s+4)}{s(s+1)(s+3)}$$(7 marks) 3(d) Using suitable diagram derive the transfer function of liquid level system with interaction.(3 marks) 3(e) A unity feedback system has a open loop transfer function of $G(s)=\dfrac{20(s+5)}{s(s+0.1)(s+3)}$. Determine the steady-state error for parabolic input.(4 marks) 3(f) The open-loop transfer function of a unity feedback system is given by G(s) = K/s (sT+1). where K and T are positive constant. By what factor should the amplifier gain K be reduced, so that the peak overshoot of unit step response of the system is reduced from 75% to 25%.(7 marks)

### Solve any three question from Q.4(a), Q.4(b), Q.4(c) & Q.4(d), Q.4(e), Q.4(f)

4(a) State advantages and limitations of Routh's stability criterion.(3 marks) 4(b) Using R-H criterion determine the relation between K and T so that unity feedback control system whose open-loop transfer function given is stable $G(s)=\dfrac{K}{s[s(s+10)+T]}.$(4 marks) 4(c) Investigate the stability of a closed-loop system whose open-loop transfer function is $G(s)H(s)=\dfrac{5}{s(1+5s)}$ using Nyquist stability criterion.(7 marks) 4(d) What do you understand by absolute stability and relative stability? Which method indicates what type of stability?(3 marks) 4(e) Explain, How the gain and phase margin are obtained from Nyquist Plots?(4 marks) 4(f) Draw the Bode plot for a system having $G(s)H(s)=\dfrac{100}{s(s+1)(s+2)}.$ Find out Gain margin, Phase margin, Gain crossover frequency and phase cross over frequency.(7 marks)

### Solve any three question from Q.5(a), Q.5(b), Q.5(c) & Q.5(d), Q.5(e), Q.5(f)

5(a) What is breakaway and breakin point? How to determine them?(3 marks) 5(b) Determine the relation between the phase margin and damping ratio for an underdamped second-order system.(4 marks) 5(c) Sketch the root locus of the system whose open-loop transfer function is $G(s)=\dfrac{K}{s(s+2)(s+4)}.$ Find the values of K so that the damping ratio of the closed-loop system is 0.5.(7 marks) 5(d) How will you obtain the transfer function from Bode magnitude plot?(3 marks) 5(e) What is lag compensator? With respect to the electrical equivalent phase-lag compensator state the transfer function, draw its pole-zero plot, and the bode plot of lag compensator.(4 marks) 5(f) Design suitable lead compensator for a system with unity feedback and having open-loop transfer function $$G(s)=\dfrac{K}{s(s+8)}.$$
to meet the following specifications:
(i) Percentage peak overshoot = 9.5%
(ii) Natural frequency of oscillation, ωn = 12 rad / sec
(iii) Velocity error constant, Kv ≥ 10.
(7 marks)