MU Control System Design - December 2015 Exam Question Paper

MU Instrumentation Engineering (Semester 5)
Control System Design
December 2015

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

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.
t_s≤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
K_v=12 /sec
ϕ_m=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 G_c(S).

10 M

More question papers from Control System Design

SPONSORED ADVERTISEMENTS