VTU Control Systems - May 2016 Exam Question Paper

VTU Electronics and Communication Engineering (Semester 4)
Control Systems
May 2016

Total marks: --
Total time: --

INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1(a) What are the properties of good control system?

4 M

1(a) What are the properties of good control system?

4 M

1(b) Construct mathematical model for the mechanical system shown in Fig. Q1(b). Then draw electrical equivalent circuit based on F-V analogy.
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8 M

1(b) Construct mathematical model for the meachanical system shown in Fig. Q1(b). Then draw electrical equivalent circuit based on F-V analogy.
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8 M

1(c) For electrical system shown in Fig. Q1(C), obtain transfer function V₂(s)/V₁(s).
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8 M

1(c) For electrical system shown in Fig. Q1(C), obtain transfer function V₂(s)/V₁(s).
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8 M

2(a) List the features function for the block diagram shown in Fig. Q2(b), using block diagram reduction method.
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8 M

2(a) List the features of transfer function.

4 M

2(b) Obtain the transfer function for the block diagram shown in Fig. Q2(b), using block diagram reduction method.
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8 M

2(c) For the electrical circuit shown in Fig. Q2(c), obtain over all transfer function using Mason's gain formula.
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8 M

2(c) For the electrical circuit shown in Fig. Q2(c), obtain over all transfer function using Mason's gain formula.
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8 M

3(a) What are static error coefficients? Derive expression for the same.

6 M

3(a) What are static error coefficients? Derive expression for the same.

6 M

3(b) An unity feedback system has

G (s) = \frac{20 (1 + s)}{s^{2} (2 + s) (4 + s)},

$G(s)=\dfrac{20(1+s)}{s^2(2+s)(4+s)},$ calculate its steady state error co-efficients when the applied input r(t) = 40 + 2t + 5t².

6 M

3(b) An unity feedback system has

G (s) = \frac{20 (1 + s)}{s^{2} (s + 2) (4 + s)},

$G(s)=\frac{20(1+s)}{s^2(s+2)(4+s)},$ calculate its steady state error coefficients when the applied input r(t) = 40 + 2t + 5t².

6 M

3(c) A R-L-C series circuit is an example of second order function. If R = 1 Ω, α = 1H and C = 1F, find response for a step voltage of 10 V connected as input and output across R.

8 M

3(c) A R-L-C series circuit is an example of second order function. If R = 1Ω, α = 1H and C = 1F, find response for a step voltage of 10V connected as input and output across R.

8 M

4(a) List the advantages and disadvantages of Routh's criterion (R-H-criterion).

4 M

4(a) List the advantages and disadvantages of Routh's criterion (R-H-criterion).

4 M

4(b) A unity feedback control system has

G (s) = \frac{k (s + 13)}{s (s + 3) (s + 7)} .

$G(s)=\dfrac{k(s+13)}{s(s+3)(s+7)}.$ Using Routh's criterion calculates the range of k for which the system is i) stable ii) has closed loop poles more negative than -1.

10 M

4(b) A unity feedback control system has

G (s) = \frac{k (s + 13)}{s (s + 3) (s + 7)} .

$G(s)=\frac{k(s+13)}{s(s+3)(s+7)}.$ Using Routh's criterion calculated the range of k for which the system is i) stable ii) has closed loop poles more negative than-1.

10 M

4(c) Find the range of k for which the system, whose characteristic equation is given below is stable. F(s) = s³ + (k + 0.5) s² + 4ks + 50.

6 M

4(c) Find the range of k for which the system, whose characteristic equation is given below is stable. F(s) = s³ + (k+0.5)s² + 4ks + 50.

6 M

5(a) Sketch the root locus for unity feedback having

G (s) = \frac{k (s + 1)}{s (s + 2) (s^{2} + 2 s + 2)} .

$G(s)=\dfrac{k(s+1)}{s(s+2)(s^2+2s+2)}.$ Determine the range of k for the system stability.

16 M

5(a) Sketch the root locus for unity feedback having

G (s) = \frac{k (s + 1)}{s (s + 2) (s^{2} + 2 s + 2)} .

$G(s)=\dfrac{k(s+1)}{s(s+2)(s^2+2s+2)}.$ Determine the range of k for the system stability.

16 M

5(b) Explain how to determine angle of arrival from poles and zeros to complex zeros.

4 M

5(b) Explain how to determine angle of arrival form poles and zeros to complex zeros.

4 M

6(a) What are the limitations of frequency response methods?

4 M

6(a) What are the limitations of frequency response methods?

4 M

6(b) A control system having

G (s) = \frac{k (1 + 0.5 s)}{s (1 + 2 s) (1 + \frac{s}{20} + \frac{s^{2}}{8})} .

$G(s)=\dfrac{k(1+0.5s)}{s(1+2s)\left ( 1+\dfrac{s}{20} +\dfrac{s^2}{8}\right )}.$ draw bode plot, with k = 4 and find gain margin and phase margin.

16 M

6(b) A control system having

G (s) = \frac{k (1 + 0.5 s)}{s (1 + 2 s) (1 + \frac{s}{20} + \frac{s^{2}}{8})}

$G(s)=\dfrac{k(1+0.5s)}{s(1+2s)\left ( 1+\dfrac{s}{20}+\dfrac{s^2}{8} \right )}$ draw bode plot, with k = 4 and find gain margin and phase margin.

16 M

7(a) What is polar plot? Explain procedure to sketch polar plot for type 0 and type 1 systems.

8 M

7(a) What is polar plot? Explain procedure to sketch polar for type 0 and type 1 systems.

8 M

7(b) Sketch the Nyquist plot of a unit feedback control system having the open loop transfer function

G (s) = \frac{5}{s (1 - s)} .

$G(s)=\dfrac{5}{s(1-s)}.$ Determine the stability of the system using Nyquist stability criterion.

12 M

7(b) Sketch the Nyquist plot of a unit feedback control system having the open loop transfer function

G (s) = \frac{5}{s (1 - s)} .

$G(s)=\dfrac{5}{s(1-s)}.$ Determine the stability of the system using Nyquist stability criterion.

12 M

8(a) Find the transfer function for a system having state model as given below :

x = [\begin{matrix} 0 & 1 \\ - 2 & - 3 \end{matrix}] x + [\begin{matrix} 1 \\ 0 \end{matrix}] u y = [1 0] x .

$x=\begin{bmatrix} 0 & 1\\ -2 & -3 \end{bmatrix}x+\begin{bmatrix} 1\\ 0 \end{bmatrix}u\ \ y=[1\ \ 0]x.$

8 M

8(a) Find the transfer function for a system having state model as given below :

x = [\begin{matrix} 0 & 1 \\ - 2 & - 3 \end{matrix}] x + [\begin{matrix} 1 \\ 0 \end{matrix}] u y = [1 0] x .

$x=\begin{bmatrix} 0 & 1\\ -2 & -3 \end{bmatrix}x+\begin{bmatrix} 1\\ 0 \end{bmatrix}u\ \ \ y=[1\ \ 0]x.$

8 M

8(b) Obtain the state model for the electrical system given in Fig. Q8(b) choosing the state variables as i₁(t), i₂(t) and V_C(t).
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12 M

8(b) Obtain the state model for the electrical system given Fig. Q8(b) choosing the state variables as i₁(t), i₂(t) and V_c(t).
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12 M

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