Attempt any Four questions

1(a)
Explain Adaptive control system.

5 M

1(b)
Explain lead and lag compensator

5 M

1(c)
Explain Controllability and Observability with its necessity for stability.

5 M

1(d)
Determine whether the following systems are stable, marginally stable, and unstable

(i) -2,0; (ii) -2+j, -2-j; (iii) -2+j4, -2-j4, -2; (iv) x(t) = cosωt; (v) x(t) = e

(i) -2,0; (ii) -2+j, -2-j; (iii) -2+j4, -2-j4, -2; (iv) x(t) = cosωt; (v) x(t) = e

^{-t}sin4t.
5 M

1(e)
Examine the stability of s

^{5}+2s^{4}+2s^{3}+4s^{2}+4s+8=0 using Routh's method.
5 M

2(a)
Obtain the overall transfer function from block diagram.

10 M

2(b)
Sketch the complete root locus for the system

G(s)H(s) = [K (s+1)(s+2)] / [(s+0.1)(s-1)], where K>0.

G(s)H(s) = [K (s+1)(s+2)] / [(s+0.1)(s-1)], where K>0.

10 M

3(a)
Obtain the state variable model of the parallel RLC network.

10 M

3(b)
Explain P, PI and PID controller.

10 M

4(a)
The state equation of a linear time-invariant system is given below: \[\begin{bmatrix}
\dot{x_1}\\
\dot{x_2}
\end{bmatrix}=\begin{bmatrix}
-2 & 0\\
1 & -1
\end{bmatrix}\begin{bmatrix}
x_1\\
x_2
\end{bmatrix}+\begin{bmatrix}
0\\
1
\end{bmatrix}u\]

Where u>0.

Determine the following:

(i) The state transition matrix.

(ii) Controllability of the system.

Where u>0.

Determine the following:

(i) The state transition matrix.

(ii) Controllability of the system.

10 M

4(b)
Sketch the bode plot for the open loop transfer function given by:

G(s) = [288(s+4)] / [s(s+1) (s

G(s) = [288(s+4)] / [s(s+1) (s

^{2}+4.8s+144)] and H(s) = 1.
10 M

5(a)
Derive the expression of Peak Overshoot when step input applied to the system.

5 M

5(b)
Sketch the polar plot of G(s) = 12 / [s(s+1)].

5 M

5(c)
For G(s)H(s) = 1+4s / [s

^{2}+(1+s)(1+2s)], draw the Nyquist plot examine the stability of the system.
10 M

Attempt any two

6(a)
Write a short note on Robust control system.

10 M

6(b)
Construct the signal flow graphs for the following set of equations:

Y

Y

Y

Where Y

Y

_{2}= G_{1}Y_{1}- G_{2}Y_{4}Y

_{3}= G_{3}Y_{2}+ G_{4}Y_{3}Y

_{4}= G_{5}Y_{1}+ G_{6}Y_{3}Where Y

_{4}is the output.
10 M

6(c)
Explain the Correlations between time and frequency domain specifications of the system.

10 M

More question papers from Principles of Control Systems