Download GTU BE/B.Tech 2018 Winter 8th Sem New 2181705 Advance Control Theory Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VIII (NEW) EXAMINATION — WINTER 2018

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Instructions:

1. Attempt all questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Introduce terms positive definite, negative definite and indefinite function. 03

(b) Discuss about mapping between s and z domain. 04

(c) Describe fuzzification and defuzzification in detail. 07

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Q.2 (a) Discuss about zero-order hold. 03

(b) Discuss error dynamics of full order state observer. 04

(c) Consider the system x(k +1) = Gx(k)+ Hu(k) where G = 0 1 0.16 0 and H = 0 1. Determine a suitable state feedback gain matrix K such that the system will have the closed loop poles at z=0.5;0.5. 07

OR

(c) Discuss stability in the sense of Lyapunov and state Lyapunov theorem on stability. 07

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Q.3 (a) Give difference between full order observer and minimum order observer. 03

(b) Obtain discrete time pulse transfer function by taking z transform when the sampling period T=1 of the following continuous time system

G(s) = 1 / s(s+2) 04

(c) Describe about digital implementation of PID controller. 07

OR

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Q.3 (a) State and briefly explain sampling theorem. 03

(b) Write about interaction and decoupling in multivariable systems. 04

(c) Obtain discrete time state and output equations when the sampling period T=1 of the following continuous time system

G(s)= 1 / s(s+2) 07

Q.4 (a) Comment on describing function analysis for nonlinear systems. 03

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(b) Brief about phase plane analysis. 04

(c) Explain any four type of common nonlinearities in instruments. 07

OR

Q.4 (a) Comment on stability of nonlinear systems. 03

(b) Write a note on phase trajectories. 04

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(c) Discuss two degree of freedom controller design with example. 07

Q.5 (a) Give introduction about relative gain array for multivariable systems. 03

(b) Explain jump resonance in non-linear system. 04

(c) With sketch explain terms stability, asymptotic stability and Instability. 07

OR

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(a) Explain adaptive control and discuss model reference adaptive system(MRAS) 07

(b) Discuss fuzzy logic applications in control systems. 07

(c) Draw root locus diagrams in the z plane for the system shown in Fig. for the sampling period T=2 sec and G_h0(z) = Z(G_h0G(s)) = K * (z+0.717) / (z-1)(z-0.135)

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