Subject Code: 2161707
GUJARAT TECHNOLOGICAL UNIVERSITY
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BE - SEMESTER-VI (NEW) EXAMINATION - WINTER 2018
Subject Name: Control System Design
Time: 02:30 PM TO 05:00 PM
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1
(a) Consider a linear system described by differential equation V+2y+y=u+u. Test the controllability of the system by Kalman’s test. [03]
(b) Explain basic electrical lead-lag compensator. [04]
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(c) With suitable example, explain the robust PID Controller. [07]
Q.2
(a) Discuss about the advantages of state space method over conventional method. [03]
(b) Write steps to design a lag compensator for a given system in frequency domain. [04]
(c) Obtain state model of field-controlled DC servomotor. Choose 6, 6 and ir as state variables. [07]
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OR
(c) Design a lag compensator using root-locus method for a system whose open-loop transfer function is given by G(s) = K / (s(s+1)(s+5)). The system is to be compensated for following specifications: Damping ratio = 0.5, settling time = 10 sec, velocity error constant > 5 sec-1. [07]
Q.3
(a) Give the properties of state transition matrix. [03]
(b) Give the design steps of lead compensator in frequency domain. [04]
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(c) Design a phase lead compensation network in frequency domain for a system having open-loop transfer function G(s) = K / (s(1+0.05s)). The system have acceleration error co-efficient=100 sec-2 for the phase margin of 20°. [07]
OR
(a) Obtain the state-space equation and output equation for the system described by differential equation given by Y''' + 4y'' + 5y' + 2y = 2u''' + u'' + u' + 2u. [03]
(b) Explain dead beat response with suitable example. [04]
(c) Explain robustness of the system with reference to system sensitivity. [07]
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Q.4
(a) Explain Internal Model Design. [03]
(b) Explain the following terms for robust control system. [04]
- sensitivity function
- complementary sensitivity function
- additive perturbation
- multiplicative perturbation
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(c) Explain the control of uncertain parameter in robust control system. [07]
OR
Q.4 (a) Determine the transfer function from the following data. A=[-3 1; -2 0], B=[1; 0], C=[1 1], D=0 [03]
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(b) Discuss the Full state Controller and Observer with associated block diagram. [04]
(c) State and derive Ackermann’s formula for determination of the state feedback gain matrix K. [07]
Q.5
(a) Explain Ricatti Equation. [03]
(b) Explain Liapnov’s stability criterion theorem. [04]
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(c) Determine the state transition matrix and solution of the system described by the vector-differential equation x' = [0 1; -5 -2]x + [0; 1]u(t) Where u(t)=1, t>0 and u(t)=0, t<0. Assume the system to be initially relaxed. [07]
OR
Q.5 (a) Explain performance index of optimal control system. [03]
(b) Explain positive definite and positive semidefinite function. [04]
(c) Explain Linear Quadratic Regulator. [07]
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Date: 16/11/2018
Total Marks: 70
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