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2003 Course Control Systems - II

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Total No. of Questions : 12] P1157 [Total No. of Pages : 4 [3664]-181 B.E. (Electrical) CONTROL SYSTEMS - II (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answer 3 questions from Section-I and 3 questions from Section-II. 2) Answers to the two sections should be written in separate books. 3) Figures to the right indicate full marks. 4) Neat diagrams must be drawn wherever necessary. 5) Use of logarithmic tables, slide rule, non-programmable electronic pocket calculator is allowed. 6) Assume suitable data, if necessary. SECTION - I Q1) a) Compare the state space technique with the transfer function methods. [8] b) Obtain the state model in Jordan s canonical form of a system whose transfer function is [8] Y (s) 2s 2 + 6s + 5 =3 U ( s ) s + 4 s 2 + 5s + 2 OR Q2) a) Define following terms: [8] i) Physical Variables ii) Phase Variables iii) Canonical Variables b) For the system shown in Fig. 1, obtain the state model choosing V1(t) and V2(t) as the state variables. U(t) is the input and Y(t) is the output. [8] P.T.O. Q3) a) Explain the concept of diagonalization and discuss how this is achieved. [8] b) Obtain the state transition matrix of the following system using Caley Hamilton theorem. [8] & x1 0 3 x1 = x 2 1 x 2 &2 OR Q4) a) Define and explain the state transition matrix. State and prove the properties of state transition matrix. [8] b) Obtain the state transition matrix of the following system. [8] & 3 x1 x1 0 = x 2 5 x 2 &2 Q5) a) Define Controllability and observability of a system. Give the necessary and sufficient conditions for complete state controllability and complete observability of a system represented by [9] & x = Ax + Bu y = Cx b) A system is represented by the state equation & 1 0 x1 0 x1 0 x = 0 & 0 1 x2 + 0 u 2 x3 1 2 3 x3 1 & x1 y = [1 2 0] x2 x3 Find the controllability and observability of the system. [3664]-181 -2- [9] OR Q6) a) Explain the principle of Duality, due to Kalman. Using duality principle find the relation between state observer gain matrix Ke and state feedback gain matrix K. [9] b) A regulator system has the plant [9] 1 0 0 0 0 x + 0 u & x= 0 1 6 11 6 1 y = [1 0 0] x Design a state feedback controller which will place the closed loop poles at 2 j3.464, 5. SECTION - II Q7) a) Classify the different types of non linearities generally encountered in the feedback control system. Give example of each. [6] b) In a unity feedback control system, an ideal relay with output equal to 1 unit is connected in cascade with linear transfer function [10] G (s) = 10 s ( s + 1) ( s + 2) Construct G(jw) and 1/kN(x, w) plots. Determine the amplitude and the frequency of the limit cycle if it exists. OR Q8) a) What is limit cycle? How the existence of a limit cycle and it s type is determined for Non linear control systems using Describing function method? [6] b) Determine the stability of the system as shown in Fig.2. [3664]-181 -3- [10] Q9) a) Discuss the different types of singular points that occur in phase plane method. [6] b) A linear second order servo is described by the equation && & E + 2 wn E + wn2 E = 0 where wn = 1, = 0.15, & E(0) = 1.0, E (0) = 0 Construct phase trajectory using method of isocline. [10] OR Q10) a) Explain the direct method of Liapunov to determine the stability of a nonlinear control systems. [7] b) Classify the following scalar functions with justifications. [9] i) ii) V(x) = 10x12 + 4x22 + x32 + 2x1x2 2x2x3 4x1x3 V( x) = 2 x1 2 2 x2 2 1 + x2 iii) V(x) = x1x2 + x22 Q11) Write detailed notes on the following. a) Performance Index as used in optimal control theory. [6] b) Various factors considered while designing optimal controller. [6] c) Calculus of variation method as used for optimal control design. [6] OR Q12) Write detailed notes on the following. a) Switches and relays as control system components. b) Proximity sensors. c) Various types of actuators. [3664]-181 -4- [6] [6] [6]

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