Download GTU BE/B.Tech 2019 Summer 6th Sem New 2161707 Control System Design Question Paper

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Subject Code: 2161707

GUJARAT TECHNOLOGICAL UNIVERSITY

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SEMESTER-VI(NEW) — EXAMINATION — SUMMER 2019

Subject Name: Control System Design

Date: 10/05/2019

Time: 10:30 AM TO 01:00 PM

Total Marks: 70

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Instructions:

1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1

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1. (a) Derive state space model of series RLC circuit. [03]
2. (b) Check for observability of a system having following coefficient matrices using Kalmann’s test. [04]
   A = $$\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1& 0\\ -24& -26& -9& 1\end{array}\right]$$ and C = [2 1 0]
3. (c) Perform diagonalization of a given matrix A [07]
   A= $$\left[\begin{array}{ccc}0& 1& 0\\ 3& 0& 2\\ -12& -7& -6\end{array}\right]$$ , B= $$\left[\begin{array}{c}0\end{array}\right]$$

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OR

Q.1

1. (a) Discuss about the advantages of state space method over conventional method. [04]
2. (b) Give the design steps of lag compensator in frequency domain. [07]
3. (c) Obtain the time response of the following system [07]
   

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   [x'] = [G+1] where u(t) is a unit step occurring at t =0, and x^T(0) =[1 0].

Q.2

1. (a) State and derive Ackermann’s formula for determination of the state feedback gain matrix K. [03]
2. (b) What is state transition matrix? Give its properties. [04]
3. (c) Obtain the transfer function for the control system having state space model as [07]
   

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   $$\left[\begin{array}{cc}X1\text{'}& X2\text{'}\end{array}\right]$$ = $$\left[\begin{array}{cc}-4& 1\\ 2& -1\end{array}\right]$$ $$\left[\begin{array}{cc}X1& X2\end{array}\right]$$ + $$\left[\begin{array}{c}3\\ 2\end{array}\right]$$ u
   y= [2 3] $$\left[\begin{array}{cc}X1& X2\end{array}\right]$$

OR

Q.2

1. (a) Describe the parameters that are used to analyze the robustness of control systems. [03]

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2. (b) Discuss the various Uncertainties in Parameter variation for robust control system design. [04]
3. (c) Write steps to design a lead-lag compensator for a given system in frequency domain. [07]

Q.3

1. (a) The open-loop transfer function of a unity feedback control system is given by [03]
   G(s) = 6 / s(1+0.2s)
   

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   Design a suitable compensator in frequency domain for Kv = 10 and PM =50°.

Q.4

1. (a) Find F(A) = e^At for given matrix A using Cayley-Hamilton technique. [03]
   A = $$\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]$$
2. (b) Derive the transfer function of lead compensator using electrical network. [04]

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3. (c) Write a short note on the design of robust PID controlled system. [07]

OR

Q.4

1. (a) Write a short note on Internal Model design. [03]
2. (b) Discuss about systems with prefilter. [04]

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3. (c) The open loop transfer function of a unity feedback system is [07]
   G(s)H(s) = 1 / s(s+4)(s+5)
   Design a suitable lag compensator using root locus technique for velocity constant > 5 and damping ratio = 0.707.

Q.5

1. (a) Explain positive definite and negative semi definite function. [03]

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2. (b) Discuss about Lyapunov’s stability criteria. [04]
3. (c) Explain LQR and Riccatti equation. [07]

OR

Q.5

1. (a) Describe the design of dead beat response with example. [03]

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2. (b) Discuss about the considerations to be kept in mind while designing the robust control system [04]
3. (c) Explain Optimal Control Design. [07]

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