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- Control System Engineering-II - CS-2
- 2018
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Electrical Engineering
- B.Tech
**7086 Views**- 96 Offline Downloads
- Uploaded 1 year ago

d) e) f) g) h) i) j) Q3 Q4 Q5 Q6 State the Initial value theorem in the time domain of a function F(z) defined in z-domain. Derive the expression for the Z-transform of unit ramp signal. What do you understand by limit cycle? What do you mean by output controllability and how is it different from state controllability? What do you understand by Jump resonance? Is the assessment of stability by direct method of Lyapunov’s for linear systems conservative? Justify your answer. What do you mean by phase plane and phase trajectory? a) Part – B (Answer any four questions) Solve the following difference equation by use of the z transform method: ( + 2) + 5 ( + 1) + 6 ( ) = 0, (0) = 0, (1) = 1 (10) b) Find the Z- transform of ( ) = (5) a) Consider the following characteristic equation: + 2.1 + 1.44 + 0.32 = 0 Determine whether any of the roots of the characteristic equation lie outside the unit circle centered at the origin of the plane. Also, comment upon its stability. (10) b) Find the inverse z transform of the function by long division 2 +4 ( )= ( − 1)( − 0.3) (5) a) Consider a control system with state model (0) ̇ 0 2 0 [ ]; 0 = + = , u = unit step ̇ (0) −3 −5 1 1 Compute the state transition matrix and therefrom find the state response, i.e., ( ) for t>0. (10) b) A discrete-time system has state equation given by 0 2 ( + )= ( ) −6 −7 Use Cayley-Hamilton approach to find out its state transition matrix. (5) a) A regulator system has the plant described by ̇ 0 1 0 0 ̇ = 0 + 0 [ ] 0 1 ̇ 1 −1 −5 −6 Design a state variable feedback controller which will place the closed loop poles at − 2 ± 5and−6. (10) b) Check the observability of the following system ̇ 0 1 0 0 ̇ = 0 + 0 [ ] 0 1 ̇ 1 −6 −11 −6 (5) = [4 5 1]

Q7 a) (10) Consider a matrix A given below 0 = 3 −12 i) Find out the eigen values ii) Find out the eigen vectors iii) Find out the modal matrix iv) Find out the diagonalizedmatix Q8 b) Derive the state space equation from the transfer function 10( − 1) ( + 4)( + 1) (5) a) What are singular points in a phase plane? Explain the following types of singularity with sketches - Stable node, unstable node, saddle point, stable focus, unstable focus, vortex (10) b) Draw the phase plane trajectory for a nonlinear system is described by (5) + When the initial conditions are (0) = Q9 1 0 0 2 −9 −6 = 0.7 /3 , ̇ (0) = 0. Use −method. a) i) Define a) Stable system, b) Asymptotically stable system, andc) Globally asymptotically stable system ii) State and explain the Lyapunov’s Theorem (direct method) for stability analysis. (10) b) Check the stability of the system described by ̇ = ̇ = − − (5)

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