Control Engg - Jun 2015

Mechanical Engg. (Semester 8)

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) Distinguish between open loop and closed loop control system, with suitable examples.(4 marks) 1 (b) What are the ideal requirements of control system?(6 marks) 1 (c) What is Control Action? Briefly explain proportional, proportional plus derivative and proportional plus derivative plus integral controllers, with the help of block diagrams.(10 marks) 2 (a) Obtain the differential equation for the mechanical system shown in fig. Q2(a) and draw the equivalent mechanical system, also draw the analogous electrical network based on i) Force - voltage analogy ii) Force - current analogy. (10 marks) 2 (b) Derive the transfer function of an armature controlled DC motor. The field current is maintained constant during operation. Assume that the armature coil has back emf $$ e_b = k_b \dfrac {d\theta} {dt} $$ and the coil current produces a torque T=K_mI on the rotor, K_b and K_m are the back emf constant and motor torque constant respectively.(10 marks) 3 (a) Reduce the block diagram shown in fig Q3(a) to its simplest possible form and find its closed loop transfer function. (10 marks) 3 (b) Using Mason's gain formula, find the gain of the following system shown in fig. Q3(b). (10 marks) 4 (a) Derive an expression for the unit step response of first order system.(8 marks) 4 (b) A unity feedback system is characterized by an open loop transfer function $ G(s) = \dfrac {K} {s(s+10)} $ . Determine the gain K, so that the system will have a damping ratio of 0.5. For this value of k determine peak time, setting time and peak overshoot for a unit step input.(8 marks) 4 (c) Ascertain the stability of the system given by the characteristics equation S⁵+4S⁴+12S³+20S²+30S+100=0, using R-H criteria.(4 marks) 5 (a) Sketch the polar plot for the transfer function. $$ G(s) = \dfrac {10} {s(s+1)(s+2)} .$$(10 marks) 5 (b) Apply Nyquist stability criterion to the system wit transfer function. $$ G(s) H(s) = \dfrac {4s+1} {s^2 (1+s)(1+2s) } $$ and ascertain its stability.(10 marks) 6 Sketch the Bode plot for $$ G(s) H(s) = \dfrac {2} {s(s+1)(1+0.2s) }.$$ Also obtain gain margin and phase margin and crossover frequencies.(20 marks) 7 Sketch the root locus plot for $$ G(s) H(s) = \dfrac {K} {s(s+2)(s+4)(s+6) } .$$ For what values of K the system becomes unstable?(20 marks) 8 (a) Explain the following: i) Lead compensator ii) Lag compensaor.(12 marks) 8 (b) Determine the state controllability and observability of the system described by $$ \dot x= \begin{bmatrix} -3 &1 &1 \\-1 &0 &1 \\0 &0 &1 \end{bmatrix}x+ \begin{bmatrix} 0 &1 \\0 &0 \\2 &1 \end{bmatrix} u \\ Y=\begin{bmatrix} 0 &0 &1 \\1 &1 &0 \end{bmatrix}x .$$(8 marks)