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- Advanced Control Systems - ACS
- 2017
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Electronics and Instrumentation Engineering
- B.Tech
**9961 Views**- 224 Offline Downloads
- Uploaded 1 year ago

Registration no: Total Number of Pages: 02 B.Tech PEEC5414 7th Semester Regular / Back Examination 2017-18 Advanced Control Systems BRANCH : AEIE, ECE, EIE, ETC, IEE Time: 3 Hours Max Marks: 70 Q.CODE: B368 Answer Question No.1 which is compulsory and any five from the rest. The figures in the right hand margin indicate marks. Q1 a) b) c) d) e) f) g) h) i) j) Q2 Q3 Answer the following questions: Define convolution theorem of Z-transform. Find the Z-transform of f(t)=t2 Find the resolution and dynamic range of a 12-bit D/A converter. (2 x 10) Write down the relation between continuous and discrete state equation. Write down the properties of STM. If a 3rd order system matrix A is in companion form & its eigen values are , , , then write down the modified Vander monde matrix for A. If the transfer function of a nth order single-input-single-output linear time invariant system is given by ( ) = ( ) + +⋯+ + then, write the system matrix A in Bush & normal form. Define an autonomous system. Give a mathematical expression. What are the phenomena exhibited by a non-linear system that are not found in a linear system? Distinguish between incidental and intentional nonlinearity. Give one example of each. a) Write the state variable formulation of the network shown in Fig.1, where all component values are of unity magnitude. Find the eigen values of the system. (5) b) Design a full order state observer with desired eigen values of the observer matrix are = −10 , = −10 .The state model is given by: ̇ 0 1 0 = + , = [ 2 0] ̇ −2 −3 1 (5) a) Diagonalize the system matrix A using modal matrix . 0 1 0 Where, A= 0 0 1 −2 −5 −4 (5)

Q4 b) Obtain the time response of the following system 1 0 ̇ = 0 + , = [ 1 0] −6 −5 1 Where, u(t) is a unit step input & initial conditions are (0) = 0 & (0) = 0 (5) a) Obtain the continuous time state-space representation of the system described by the transfer function ( ) = ( ) + Discretize the system & obtain the discrete-time state-pace representation. Obtain the inverse Z.T of 3 +4 +1 ( )= +3 +1 (5) Solve the following difference equation by the use of Z-Transform method ( + 2) + 3 ( + 1) + 2 ( ) = 0 , (0) = 0, (1) = 1 Find out and compare the stability of the system shown in Fig.2, with & without a sample-and-hold on the error signal.Sampling time T=0.4 sec . (5) b) Q5 a) b) Q6 a) b) Q7 a) ∗ E(s) R(s) + - (s) ZOH Q8 a) b) c) d) (5) (5) (6) For the non-linear system shown in Fig.3, determine the amplitude and frequency of limit cycle . 1 + - 0.1 ( )= (5) C(s) Fig.2 State Liapunov’s theorem for asymptotic stability of the system ̇ =A x Hence show the following linear autonomous model 0 1 ̇= x − − Is asymptotically stable if a>0,k>0. In the following quadratic form negative definite? Q=- -3 -11 +2 -4 -2 R(s) b) 1 +1 (5) 10 (0.4 + 1)(2 + 1) C(s) Fig.3 Distinguish between the concepts of stability, asymptotic stability & global stability. Write short answer on any TWO : Derive the describing function of the ideal on off relay type non linearity. Pole placement by state feedback. Stability analysis of sampled data control system Phase plane portrait (4) (5 x 2)

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