## Control System Engineering - May 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.

### Do as direct:

**1 (a) (i)** State the advantages and disadvantages of closed loop system.(1 marks)
**1 (a) (ii)** What is steady-state error?(1 marks)
**1 (a) (iii)** What is PID controller?(1 marks)
**1 (a) (iv)** What is transient and steady state response?(1 marks)
**1 (a) (v)** What is polar plot?(1 marks)
**1 (a) (vi)** When lag compensation is employed in feedback control system?(1 marks)
**1 (a) (vii)** Define BIBO stability?(1 marks)
**1 (b)** Using suitable diagram derive the transfer function of liquid level system with interaction.(7 marks)
**2 (a)** For the given mechanical translation system as shown in Fig. 1. Write down differential equations, represents in Force-Voltage analogy, and find out X_{1}(s)/F(s).
(7 marks)

### Answer any one question from Q2 (b) & Q2 (c)

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

### Answer any two question from Q3 (a), (b) & Q3 (c), (d)

**3 (a)** A unity feedback closed loop control system is given by differential equation $$ \dfrac {d^2 y(t)}{dt^2} + 4 \dfrac {dy(t)}{dt} + 8y(t)=8x(t); $$ where y(t)=output and x(t)=input.

(a) Draw the block diagram for closed loop system.

(b) What is the characteristics equation of the system?

(c) Find out damping ratio and natural frequency of oscillation?

(d) Discuss the nature of the system.

(e) Determine and sketch the transient response for unit step input.

(f) Find out the time domain specifications: rise time, peak time, settling time, Maximum overshoot.(7 marks)
**3 (b)** Discuss the various performance indices.(7 marks)
**3 (c)** Define Routh's stability criterion. Construct Routh array and determine the stability of the system whose characteristics equation is s^{6}+2s^{5}+8s^{4}+12s^{3}+20s^{2}+16s+16=0.(7 marks)
**3 (d)** He maximum overshoot for a unity feedback control system having its forward path transfer function $$G(s) = \dfrac {K} {s(sT+1)} $$ is to be reduced 60% to 20%. The system input is unit step. Determine the factor by which K should reduce to achieve aforesaid reduction.(7 marks)

### Answer any two question from Q4 (a), (b) & Q4 (c), (b)

**4 (a)** The open-loop transfer function of a unity feedback system is given as $$ G(s) = \dfrac {1}{s(s+1)(2s+1)}$$ Sketch the polar plot and determine the gain margin. Comment on system stability.(7 marks)
**4 (b)** A unity feedback control system has an open-loop transfer function $$ G(s) H(s) = \dfrac {K} {s(s^2+2s+2)} $$ Sketch the root locus and determine the limiting value of K for stability.(7 marks)
**4 (c)** Define and explain following terms with respect to root locus

(i) Centroid

(ii) Asymptote

(iii) Dominant pole

(iv) Breakaway point

(v) Breaking point

(vi) Angle of departure

(vii) Angle of arrival.(7 marks)
**4 (d)** The open-loop transfer function of a unity feedback control system is given as $$ G(s) H(s) = \dfrac {(s+2)}{(s+1)(s-1)} $$ Determine the closed-loop system stability by applying Nyquist criterion.(7 marks)

### Answer any two question from Q5(a), (b) & Q5 (c), (d)

**5 (a)** Define and explain Gain Margin and Phase Margin with respect to (i) Bode Plot (Frequency Response Plot) and (ii) Nyquist Plot.(7 marks)
**5 (b)** Design suitable lag compensator for a system with unity feedback and having open-loop transfer function. $$ G(s)= \dfrac {K}{s(s+2)(s+8)} $$ to meet the following specifications:

(i) percentage overshoot ≤16% for unit step input

(ii) Steady state error ≤ 0.125 for unit ramp input.(7 marks)
**5 (c)** Obtain the state model and determine the state transition matrix for a system whose transfer function is given as, $$ \dfrac {C(s)} {R(s)} = \dfrac {s+3}{s^2+3s+2} $$(7 marks)
**5 (d)** The open loop transfer function of a control system is $$ G(s) = \dfrac {4}{s(2s+1)} $$ i) Determine the gain cross over frequency, phase cross over frequency, phase margin and gain margin.

ii) if a lead compensator with transfer function as shown below is inserted in the forward path. $$ G_s(s)= \dfrac {1+0.9s} {1+0.36s} $$ Determine the new gain cross over frequency, phase cross over frequency, phase margin, and gain margin.(7 marks)