MU Control System - 2 - December 2015 Exam Question Paper

MU Electrical Engineering (Semester 7)
Control System - 2
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

1 (a) Compare lag and lead compensator along with electrical equivalent circuit and pole-zero plot in s-plane.

5 M

1 (b) Explain in brief different forms of industrial PID controllers.

5 M

1 (c) Write a short note on modelling of the sampler in digital control system.

5 M

1 (d) Explain start/stop interlocking circuit in PLC programming with the help of suitable example.

5 M

1 (e) Explain the scan cycle of execution in PLC.

5 M

1 (f) Consider the system defined by

\dot{x} = A x + B u y = C x where A = [\begin{matrix} - 1 & 0 & 1 \\ 1 & - 2 & 0 \\ 0 & 0 & - 3 \end{matrix}] B = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] C = [\begin{matrix} 1 & 1 & 0 \end{matrix}]

$\dot{x}=Ax + Bu \ \ y=Cx \\ \text{where } A=\begin{bmatrix} -1 &0 & 1\\1 &-2 &0 \\0 &0 &-3 \end{bmatrix} \ \ B=\begin{bmatrix} 0\\0 \\1 \end{bmatrix} \ \ C=\begin{bmatrix} 1 &1 &0 \end{bmatrix}$ Transform the system equation into (i) controller canonical form and (ii) observer canonical form.

5 M

2 (a) Give a unit feedback system with

G (s) = \frac{1}{S (S + 1) (0.5 s + 1)}

$G(s)= \dfrac {1}{S(S+1)(0.5s+1)}$ Use frequency response method to design lead compensator to yield (i) Steady state error to a unit ramp input is less than 0.05 (ii) Phase margin more than 45 degree.

10 M

2 (b) Design a state variable feedback controller to yield a 20.8% overshoot and a settling time of 4 second for a plant.

\dot{x} = A x + B u y = C x + D u Where, A = [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ - 1 & - 5 & - 6 \end{matrix}] B = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] C = [\begin{matrix} 10 & 1 & 0 \end{matrix}] D = [0]

$\dot{x}=Ax + Bu \ \ y=Cx+Du \\ \text{Where, } A=\begin{bmatrix} 0 &1 &0 \\0 &0 &1 \\-1 &-5 &-6 \end{bmatrix} \ \ B=\begin{bmatrix} 0\\0 \\1\end{bmatrix} \ \ C=\begin{bmatrix} 10 &1 &0 \end{bmatrix} \ \ D=[0]$

10 M

3 (a) Write a short note on Proportional Band (PB) in case of PID controller.

5 M

3 (b) Explain the stability of Digital control system.

5 M

3 (c) Consider a linear system described by the differential equation

\ddot{y} + 2 \dot{y} + y = \dot{u} + u with x_{1} = y, x_{2} = \dot{y} - u

$\ddot{y}+2\dot{y}+y=\dot{u}+u \text{ with } \\ x_1 = y, \ x_2 = \dot{y}-u$
Determine whether this system is observable or not?

10 M

4 (a) Design a integral controller for the plant

\dot{x} = [\begin{matrix} 0 & 1 \\ - 7 & - 9 \end{matrix}] x + [\begin{matrix} 0 \\ 1 \end{matrix}] u y [4 1] x

$\dot{x}= \begin{bmatrix} 0 &1 \\-7 &-9 \end{bmatrix} x + \begin{bmatrix} 0\\1 \end{bmatrix}u \\ y[4 \ \ 1]x$ to yield a step response with 10% overshoot, a peak time of 2 seconds and zerd steady state error.

10 M

4 (b) Given a Z.O.H. in cascade with

G_{1} = (S) = \frac{s + 2}{s + 1}

$G_1 = (S) = \dfrac {s+2}{s+1}$ Find the sampled data transfer function, G(z) if a sampling time T is 0.5 second.

10 M

5 (a) Find T(z)=C(z)/R(z) for the given block diagram if T=0.3 sec.

10 M

5 (b) Draw and explain the PLC ladder diagram for manufacturing of 5 mH and 10mH inductor coils. When 5 mH inductor is produced, the machine makes 400 revolutions to wind the coil. If the inductor is produced 10 mH, the machine makes 800 revolutions before stopping.

10 M

6 (a) Explain relay logic instruction in PLC.

5 M

6 (b) Write a short note on PLC processor unit.

10 M

6 (c) Explain AC input module of PLC.

5 M

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