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2003 Course Advanced Control System (Elective I)

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Total No. of Questions : 12] [Total No. of Pages : 5 P1118 [3864]-287 B.E. (Instrumentation and Control) ADVANCED CONTROL SYSTEM (2003 Course) (406264) (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) Use of logarithmic tables slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 5) Assume suitable data, if necessary. SECTION - I Q1) a) b) Find describing function for combine deadzone & saturation characteristics as shown in figure 1. [12] What are the characteristics of phase plane method. [6] OR P.T.O. Q2) a) b) What mean by Jump Resonance ? Explain it with the help of soft & hard spring technique. [6] Find frequency & Gain (K) of limit cycle for the system shown in the figure. 2. [12] Q3) Consider the system shown in fig. 3. Find the amplitude and frequency of limit cycle. Also comment on nature of limit cycle (s) and stability of system. [16] OR Q4) The nonlinear system described the nonlinear element as u = g(e) = e3 and the system is described by differential equation [16] e + e = Ke3; K > 0 Find stability region of nonlinear system as shown in fig. 4. (Note : - The equilibrium point lies at the origin) [3864]-287 2 Q5) a) b) Explain different elements of Model Reference Adaptive Control (MRAC) system with the help of neat block diagram. [8] Consider Dynamics of Mass-Spring-Damper system given by [8] d2y dy + ky = u; y = output M 2 +B dt dt u = Input where M = 1kg = 1N/ms K = 1 N/m design MRAC system response follows the reference model given by d 2 y m 15.14 dy m + ym = r select r(t) = 2 + dt dt 2 OR Q6) a) Explain MIT Rule for continuous time Model Reference Adaptive Control (MRAC) scheme with reference to 1st order system. [8] b) Explain Model Reference Adaptive Control using Lyapunov approach for stability analysis of continuous time system. [8] SECTION - II Q7) a) In Self-Tuning Regulator (STR) following input output data has been obtained from real plant. [12] Time (t) Output data [y(t)] 1 2.0 0.0 2 1.0 4.0 3 2.0 2.0 4 1.5 4.0 5 b) Input data [u(t)] 1.0 2.0 Use any regression method to fit a model with the structure y(t) + ay(t 1) = b u(t 1) + e(t) where e(t) is error signal. Write short note on Indirect Self Tuning Regulator. [3864]-287 3 [4] OR Q8) a) Write short note on : [12] i) ii) b) Continuous time self tuners. Linear quadratic Self Tuning Regulator. With the help of neat diagram explain different element of Self Tuning Regulator. [4] Q9) Explain following industrial adaptive controllers with reference to parameter estimation, control design, prior information & industrial experiences.[18] a) EXACT : The Foxboro adaptive controller. b) Asea Brown Boveri (ABB) adaptive controller. OR Q10)a) b) Q11)a) Explain temperature control of a distillation column using adaptive control technique. [10] Enlist the considerations in design of Robust Control System. [8] Obtain the control law that minimizes the performance index [8] J= ( x1 + u 2 2 )dt for the system. 0 x1 0 1 X1 0 x = 0 0 X + 1 u 2 2 using reduced matrix Riccati eqn b) State eqns are [8] x1 2 4 x1 0 x = 1 4 x + 2 [ u] 2 2 x y = [ 0] 1 1 x2 determined feedback gain matrix for a system & desired pole locations at 50, 50. [3864]-287 4 OR Q12)Consider the plant [16] dx1 dt 1 0 x1 1 dx = 1 2 x + 0 u 2 2 dt a) b) c) Prove that the system is unstable. Prove that the system is controllable Select the values of matrices Q and R with the constraint that they are positive definite and design a controller for the plant so as to minimize. J= 1 2 (x Qx + u T T ) Ru dt 0 check that the resulting overall system is stable. vvvv [3864]-287 5

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