STUPIDSID
Attempt the following:
1 (a)
State the advantages of modern control theory over conventional theory.
5 M
1 (b)
Obtain the transfer function of the system. \[ i) \ \dot{x_1}= -2x_1-x_2+u \ ii) \ \dot{x}_2 = -3x_1 - x_2+ u \ \ y=x_1 \]
5 M
1 (c)
Compare lead / lag / lag-lead compensator. Also draw poles & zeros plot of all.
5 M
1 (d)
What is caley Hamilton theorem? Explain the steps to solve for STM using the Caley Hamilton theorem.
5 M
2 (a)
Derive the transfer function of lag-lead compensator.
10 M
2 (b)
Obtain diagonalized matrix (M) for seven system matrix: \[ A = \begin{bmatrix}
0 &1 &0 \0
&0 &1 \\-1
&-3 &-3
\end{bmatrix} \]
10 M
3 (a)
For the unity feedback control system with PID controller is used to control the system. The plant transfer function is \[ G(s) = \dfrac {K}{s(s+1) (s+5)} \] Determine PID controller.
10 M
3 (b)
An open loop control system with: \[ G(s) = \dfrac {K}{s^2} \] The system is compensated to meet the following specifications using lag compensator. Kv=5/sec.
10 M
4 (a)
Determine the state transition matrix for the system: \( A= \begin{bmatrix}
-2 &1 \\-2
&-3
\end{bmatrix} \) also find the response if the initial condition is \[ x(0) = \begin{bmatrix}
1\2 \end{bmatrix} \]
10 M
4 (b)
Explain the design steps of lag compensator using Bode plot.
10 M
5 (a)
Design an observer for the plan \[ G(s) = \dfrac {10 (s+2)}{s(s+4)} \] Desired observer poles are at -5, 5.
10 M
5 (b)
Check the following systems are completely controllable & observable: \[ i) \ \dot{x} = \begin{bmatrix}
0 &1 \\-2 &-3 \end{bmatrix}x + \begin{bmatrix}
0\1\end{bmatrix}u \ y=\begin{bmatrix}
1 &0\end{bmatrix}x \ ii) \ \dot{x}= \begin{bmatrix}
-2 &1 \1
&-2
\end{bmatrix}x + \begin{bmatrix}
1 \ 2
\end{bmatrix} u \ y= \begin{bmatrix}
1 & -1
\end{bmatrix}x \]
10 M
6 (a)
Consider a plant transfer function \[ G(s) = \dfrac {10}{(s+1)(s+5)} \] Design state feedback gain matrix to meet the following specifications:
ξ=0.5
Wn= 5 rad/sec.
ξ=0.5
Wn= 5 rad/sec.
10 M
6 (b)
For a unity feedback system \[ G(s) = \dfrac {K}{s(s+1)} \] Design a suitable compensator with the following specifications:-
Kv=12/sec
Phage margin = 40°.
Kv=12/sec
Phage margin = 40°.
10 M
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