Question Paper: Control Systems : Question Paper Dec 2013 - Electronics & Telecomm (Semester 4) | Visveswaraya Technological University (VTU)
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## Control Systems - Dec 2013

### Electronics & Communication (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.
1 (a) Define a control system. Explain with examples, open loop and closed loop control systems. List the merits and demerits of open loop and closed loop control system.(10 marks) 1 (b) For the mechanical system shown in Fig. Q1(b).
i) Draw the mechanical network
ii) Write the differential equations description the system.
iii) Draw the F-V analogous electrical circuit after writing the corresponding electrical equations.
(10 marks)
2 (a) For the circuit shown in Fig Q2(a). Draw the block diagram and determine the transfer function $$\dfrac {V_p(S)}{V_1(S)}$$ using block diagram rules. (10 marks) 2 (b) For the system represented by the following equations, find the transfer function X(s)/U(s) by signal flow graph techniques
$$x=x_1+\alpha_3 U \\ x_1=-\beta_1x_1+x_2+\alpha_2U \\ x_2=-\beta_2x_1+\alpha_1U$$
(10 marks)
3 (a) Explain the following time domain specification of a second order systems, with neat sketch i) Peak time ii) Delay time iii) Rise time iv) Maximum over shoot
v) Settling time.
(6 marks)
3 (b) A system description by $$\dfrac {d^2 y}{dt^2}+ \dfrac {8dy}{dt}+ 25y(t)=50x(t)$$ Evaluate the response and maximum output for a step of 2.5 units.(8 marks) 3 (c) In the block shown in Fig. Q3(c) G(s)=A/S2 and H(s)=(ms+n). For A=10, determine the values of m and n for a step input with a time constant 0.1 sec; which give a peak over shoot of 30%. (6 marks) 4 (a) What are the difficulties encountered while assessing Routh-Hurwitz criteria and how do you eliminate these difficulties, explain with examples.(6 marks) 4 (b) The open loop transfer function of a feedback control system is given by $$G(s)H(s)= \dfrac {k}{S(s+4)(s^2+2s+2)}$$
i) Using R-H criterion determine the range of K" for which the system will be stable
ii) If a zero at S=-4 is added to the forward transfer function
(8 marks)
4 (c) Using R-H criterion, find the stability of a unity feedback system having closed loop transfer function $$G(s)= \dfrac {e^{-s1}}{S(s+2)}$$(6 marks) 5 (a) State the different rules for the construction of root locus.(8 marks) 5 (b) A feedback control system has open loop transfer function: $$G(S)H(S)= \dfrac {k}{S(s+4)(s^2+4s+20)}$$ Plot the root locus for K=0 to ? indicate all point on it.(12 marks) 6 (a) Explain co-relation between time domain and frequency domain for second order systems.(6 marks) 6 (b) The open loop transfer function of unity feedback control system is given by $$G(s)H(s)= \dfrac {k}{s(1+0.00 ls)(1+0.25s)(1+0.1s)}$$ Determine the value of K, so that the system will have a phase margin of 40°, what will be the gain margin. Use code plot.(14 marks) 7 (a) State and explain Nyquist stability criterion.(6 marks) 7 (b) Using Nyquist stability criterion, find the range of K for closed-loop stability $$G(s)H(s)= \dfrac{K}{S(s^2+2s+2)}K>0$$(14 marks) 8 (a) Explain properties and significance of state transition matrix.(10 marks) 8 (b) A linear time invariant system is characterized by the homogeneous state equation: $$\begin{bmatrix} \dot{x_1} \\ \dot{x_2} \end{bmatrix} = \begin{bmatrix} 1 &0 \\1 &1 \end{bmatrix} \begin{bmatrix}x_1\\x_2\end{bmatrix}$$ Compare the solution of homogeneous equation assume the initial state vector.(10 marks)