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2003 Course Advanced Control System (Elective I)

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Total No. of Questions : 6] P1484 [Total No. of Pages : 4 [3764] - 287 B.E. (Instrumentation & Control) ADVANCED CONTROL SYSTEM (Elective - I) (2003 Course) Time : 3 Hours] [Max. Marks :100 Instructions to the candidates: 1) Answer three questions from section I and three 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) b) Explain Jump resonance with suitable example. [6] Find the Describing Function for the Nonlinear system having characteristic as shown in figure 1. [12] OR P.T.O. a) What are different characteristics of Non-Linear system. [6] b) Find the Describing Function for the Nonlinearity as shown in Fig. Q.2. [12] Q2 ) Obtain the range of gain K for which given system shown in figure 3 is stable G ( s ) = 10 K . Investigate the stability of the system for K = 0.l. s ( s + 1) ( s + 2) [16] OR 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] [3764]-287 2 Q3) a) Explain MIT rule for continuous time Model Reference Adaptive Control scheme with reference to first order system. [8] b) Explain different elements of Model Reference Adaptive Control (MRAC) system with neat block diagram. [8] OR a) What are the limitations of describing function. Explain each in short. [8] b) Explain Model Reference Adaptive Control using Lyapunov approach for stability analysis of continuous time system. [8] SECTION - II Q4) a) In Self-Tuning Regulator (STR) following input output data has been obtained from real plant. [10] Time(t) Input data [u(t)] Output data [y(t)] 1 1.0 0.0 2 0.0 2.0 3 1.0 -1 4 1.0 2.5 5 0.0 0.750 Use any regression method to fit a model with the structure y(t) + a y(t -1) = bu(t -1)+ e(t) where e(t) is error signal b) Explain Self tuning regulator with reference to controller design and parameter estimation mechanism. [8] OR Consider the System G ( s ) = 1 s+a [18] where a is unknown parameter. Assume that the desired closed loop 2 . s 2 + 2 s + 2 Construct continuous time and discrete time indirect self tuning algorithm for the system. response of the system is Gm ( s ) = [3764]-287 3 Q5) a) b) Write a short note on: Linear Quadratic self tuning regulator. [8] Explain temperature control of a distillation column using adaptive control technique. [8] OR 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) Asea Brown Boveri (ABB) adaptive controller. Q6) Consider the system as shown in fig. 5 a) b) c) [16] Comment on stability of the closed loop system. Comment on controllability and observability of the system. Determine the optimal value of K such that J = e 2 dt is minimum. 0 OR Consider the plant [16] dx1 dt 1 0 x1 1 + u = dx2 1 2 x2 0 dt a) b) c) Is the system is unstable? Is the system is controllable? 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 J = ( xT Qx + uT Ru ) dt 20 Check that the resulting overall system is stable. TTT [3764]-287 4

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