Question Paper: Principles of Control Systems : Question Paper Dec 2014 - Electronics Engineering (Semester 4) | Mumbai University (MU)
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## Principles of Control Systems - Dec 2014

### Electronics Engineering (Semester 4)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.

### Attempt any five

1 (a) Differentiate between open loop and closed loop control system.(4 marks) 1 (b) Explain the Mason's Gain formula with reference to signal Flow Graph Technique.(4 marks) 1 (c) Define and state the condition for controllability and observability for nth order MIMO system.(4 marks) 1 (d) The characteristic equation for certain feedback control system is given below. Determine the range of value of K for the system to be stable.
S3+2ks2+ (k+2)s+4=0
(4 marks)
1 (e) Define gain and phase margin. Draw approximate Bode plot for a stable system showing gain and phase margin.(4 marks) 1 (f) Compare between Lead and Lay compensator.(4 marks) 2 (a) Derive the output response for second order under-damped control system subjected to unit step input.(10 marks) 2 (b) Find the transfer function C(S)/R(S) using Block diagram reduction Technique. (10 marks) 3 (a) Find the Transfer function for the system show below. (4 marks) 3 (b) What are the properties of state transition matrix?(4 marks) 3 (c) For the system shown below, chose V1(t) and V2(t) as state variales and write down the state equations satisfied by them. Bring these equations in the vector-matrix form (12 marks) 4 (a) Examine the observability of the system given below using kalman's test. $$\begin{bmatrix}x_1\\x_2 \\x_3 \end{bmatrix} = \begin{bmatrix}0 &1 &0 \\0 &0 &1 \\0 &-2 &-3 \end{bmatrix} \begin{bmatrix}x_1\\x_2 \\x_3 \end{bmatrix} = \begin{bmatrix}0\\0 \\1 \end{bmatrix} u = Ax+ Bu$$(8 marks) 4 (b) Derive the expression for Peak resonant of a standard second order control system.(8 marks) 4 (c) Explain the concept of ON/OFF controller.(4 marks) 5 (a) For a unit feedback system the open loop transfer function is given by $$G(S) = \dfrac {K}{S(S+2) (S^2+6S+25)}$$ Sketch the root locus and find the value of K at which the system becomes unstable.(10 marks) 5 (b) Explain Robust control and Adaptive control system.(10 marks) 6 (a) Find polar plot for the transfer function given below $$G(S) = \dfrac {1}{(1+S)(1+4S)}$$(5 marks) 6 (b) Write a short note on PID controller.(5 marks) 6 (c) Determine the stability of a system shown by following open loop transfer function using Nyquist criterion $$G(s) \ H(s) = \dfrac {(4s+1)} {s^2 (s+1) (2s+1)}$$(10 marks)