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2003 Course Advanced Control System (Elective I)

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Total No. of Questions : 12] P1007 [Total No. of Pages : 4 [3664]-249 B.E. (Instrumentation & Control) ADVANCED CONTROL SYSTEM (Elective - I) 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) Neat diagrams must be drawn wherever necessary. 4) Figures to the right indicate full marks. 5) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, if necessary. 7) All questions are compulsory. SECTION - I Q1) a) Explain the concept of Jump resonance with the help of soft and hard spring. [6] b) Find the Describing Function for the Nonlinear system having characteristic as shown in figure 1. [12] OR Q2) a) Distinguish between linear and non-linear systems. [4] b) Explain the procedure to construct phase plane. [4] c) Find Frequency and Amplitude of Limit Cycle(s) for the system as shown in figure 2. [10] P.T.O. Q3) An amplifier as shown in figure 3 drives a Two Phase Servomotor. The transfer function of the motor is Ke 0.2 s G ( s) = s (0.2 s + 1) Investigate the stability of the system for K=0.2. What is the largest value of K for no limit cycle to exist? [16] OR Q4) Consider a System as shown in figure 4. Find the amplitude and frequency of limit cycles. Also Comment on nature of limit cycle(s) and Stability of system. [16] Q5) a) Explain MIT rule for adaptive systems. [8] b) What are the different components of Model reference adaptive systems? Explain each in short. [8] OR Q6) a) Consider the Dynamics of Mass-Spring-damper system given by d2y dy M 2 + B + Ky = u dt dt where M = B = K = 2, y = output u = input [3664]-249 -2- Design Model Reference Adaptive Control (MRAC) system to follow the response of reference model given by [10] d 2 ym dy + 15.14 m + ym = r 2 dt dt select r = 1 b) Explain Lyapunov approach for stability analysis of continuous non linear time system. [6] SECTION - II Q7) a) In Self-Tuning Regulator (STR) following input output data has been obtained from real plant Time(t) Input data [u(t)] Output data [y(t)] 1 1.0 0.0 2 0.5 0.5 3 1.0 0.5 4 1.0 1.25 5 0.0 0.35 Use any regression method to fit a model with the structure [10] y(t)+ay(t 1)=bu(t 1)+e(t) where e(t) is error signal b) Derive Least Squares (LS) as a real time parameter estimator. OR Q8) Write short note on following: a) Indirect self tuning regulator b) Continuous time self tuners c) Linear Quadratic self tuning regulator [8] [18] Q9) a) Explain any two industrial products, which incorporate adaptive control techniques. [8] b) Explain feed control of a distillation column using adaptive control technique. [8] OR Q10) Explain following industrial adaptive controllers with reference to parameter estimation, control design, prior information and industrial experiences.[16] a) EXACT: The Foxboro adaptive controller b) DPR 900 [3664]-249 -3- Q11) a) Obtain the control law that minimizes the performance index J = (x12 + u 2 )dt 0 for the system dx1 dt 0 dx = 2 0 dt 0 .1 x1 0 + u 0 .1 x2 1 using reduced matrix Riccati equation. [8] b) Consider the feedback system shown in figure 5. The output required to track unit step. Find the value of alpha ( ) that minimizes integral square error. [8] OR Q12) Consider the plant dx1 0 x1 1 dt 1 + u dx = 1 0.2 x 0 2 2 dt a) Is the given system stable? b) Is the given system controllable? c) Select the values for matrices Q and R with the constraint that they are positive definite and design a controller for the plant so as to minimize 1 T J = ( x Qx + u T Ru )dt 20 Check that the resulting overall system is stable. [3664]-249 -4- [16]

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