STUPIDSID
Answer the following:
1 (a)
Explain the need of compensator.
5 M
1 (b)
State advantages of modern control over traditional control system.
5 M
1 (c)
Obtain transfer function using state model. \[ \dot{x} = \begin{bmatrix}
0 &1 \\-2
&-3
\end{bmatrix} x + \begin{bmatrix}
0\1
\end{bmatrix} u, \ \ Y=\begin{bmatrix}
1 &0
\end{bmatrix}x. \]
5 M
1 (d)
Derive the transfer function of lead compensator.
5 M
2 (a)
Construct state models of the following: \[ i) \ T(S) = \dfrac {S+2}{S^3 + 5S^2 + 6S+7} \ ii) \ \dfrac {d^3 y}{dt^3} + 5 \dfrac {d^2 y}{dt^2} + 7 \dfrac {dy}{dt}+ 4y = 3 \dfrac {du}{dt} + 4u \]
10 M
2 (b)
Explain design steps of lag compensator using root locus.
10 M
3 (a)
A unity feedback type 2 system with \( G(S) = \dfrac {K} {S^2} .\) It is desired to Compensate the system so as to meet the following transient specifications.
ts≤4 sec
%Mp ≤ 20 %.
ts≤4 sec
%Mp ≤ 20 %.
10 M
3 (b)
State controllability and observability. Check following system is controllable or observable? \[ \dot{x} = \begin{bmatrix}
0 &1 &0 \0
&0 &1 \0
&-2 &-3
\end{bmatrix} \begin{bmatrix}
x_1\x_2
\x_3
\end{bmatrix} + \begin{bmatrix}
0\0
\0\end{bmatrix} u \ y \begin{bmatrix}
3 &4 &1\end{bmatrix} \begin{bmatrix}
x_1\x_2
\x_3\end{bmatrix} \]
10 M
4 (a)
Design state observer for the system which is given as: \[ \dot{x} = \begin{bmatrix}
1 &2 &0 \3
&-1 &1 \0
&2 &0
\end{bmatrix} \begin{bmatrix}
x_1\x_2
\x_3 \end{bmatrix} + \begin{bmatrix}
2\1
\1\end{bmatrix} u \ y=\begin{bmatrix}
0 &0 &1
\end{bmatrix} \begin{bmatrix}
x_1\x_2
\x_3\end{bmatrix} \] The desired poles are -4, -3±j \]
10 M
4 (b)
Find STM where, \(A= \begin{bmatrix}
0 &1 \\-2
&-3
\end{bmatrix} \) and obtain homogeneous response when initial conditions \( x_0 = \begin{bmatrix}1\0 \end{bmatrix} \)
10 M
5 (a)
For the plant \( G(S) = \dfrac {10(S+10)}{S(S+3)(S+12)}\) Give steps to be used to design the phase variable feedback gain to yield 5% over shoot and peak time 0.3 sec. Find the state feedback gain vector.
10 M
5 (b)
A unity feedback system with an open loop T.F. \( G(s) = \dfrac {k}{S(S+1)} \) where
Kv=12 /sec
ϕm=40°.
Design suitable compensator.
Kv=12 /sec
ϕm=40°.
Design suitable compensator.
10 M
6 (a)
Explain design steps for lead compensator using bode plot.
10 M
6 (b)
Design PID controller for the system \[ G(S) = \dfrac {K}{S(S+1) (s+2)} \] Determine compensated block Gc(S).
10 M
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