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(c)
For electrical system shown in Fig. Q1(C), obtain transfer function V

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_{2}(s)/V_{1}(s).:!mage

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(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(b)
An unity feedback system has \( G(s)=\dfrac{20(1+s)}{s^2(2+s)(4+s)},\) calculate its steady state error co-efficients when the applied input r(t) = 40 + 2t + 5t

^{2}.
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

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

4 M

4(b)
A unity feedback control system has \( G(s)=\dfrac{k(s+13)}{s(s+3)(s+7)}.\) 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(c)
Find the range of k for which the system, whose characteristic equation is given below is stable. F(s) = s

^{3}+ (k + 0.5) s^{2}+ 4ks + 50.
6 M

5(a)
Sketch the root locus for unity feedback having \( G(s)=\dfrac{k(s+1)}{s(s+2)(s^2+2s+2)}.\) 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

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

4 M

6(b)
A control system having \( G(s)=\dfrac{k(1+0.5s)}{s(1+2s)\left ( 1+\dfrac{s}{20} +\dfrac{s^2}{8}\right )}.\) 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(b)
Sketch the Nyquist plot of a unit feedback control system having the open loop transfer function \( G(s)=\dfrac{5}{s(1-s)}.\) 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 : \[x=\begin{bmatrix}
0 & 1\\
-2 & -3
\end{bmatrix}x+\begin{bmatrix}
1\\
0
\end{bmatrix}u\ \ y=[1\ \ 0]x.\]

8 M

8(b)
Obtain the state model for the electrical system given in Fig. Q8(b) choosing the state variables as i

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_{1}(t), i_{2}(t) and V_{C}(t).:!mage

12 M

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