VTU Control Systems - June 2012 Exam Question Paper

VTU Electronics and Communication Engineering (Semester 4)
Control Systems
June 2012

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) Distinguish between open loop and closed loop system with examples.

6 M

1 (b) Write the differential equations of performance for the mechanical system shown in Fig. Q1 (b). Draw its F-V analogous circuit.

6 M

1 (c) Obtain the transfer function of an armature controlled DC servomotor.

6 M

2 (a) Obtain the transfer function of the block diagram shown below, using block diagram reduction technique.

10 M

2 (b) Obtain the closed loop transfer function C(s)/R(s) for the signal flow graph of a system shown in Fig. Q2(b) by use of Mason's gain formula.

10 M

3 (a) Derive expression for peak response time t_p and maximum overshoot M_p of an under damped second order control system subjected to step input.

6 M

3 (b) A second order control system is represented by a transfer function given below:

\frac{0_{0} (s)}{T (s)} = \frac{1}{J s^{2} + F s + K}

$\dfrac {0_0(s)}{T(s)}= \dfrac {1}{Js^2+Fs+K}$ where ?₀ is the proportional output and T is the input torque. A step unit of 10 N-m is applied to the system and test results are given below:
i) Maximum overshoot is 6%
ii) Peak time is 1 sec
iii) The steady state value of the output is 0.5 radian.
Determine the values of J, F and K.

8 M

3 (c) For a unity feedback control system with

G (s) = \frac{10 (s + 2)}{s^{2} (s + 1)}

$G(s)= \dfrac {10(s+2)}{s^2 (s+1)}$ find:
i) The static error coefficients
ii) Steady state error when the input transform is

R (s) = \frac{3}{s} - \frac{2}{s^{2}} - \frac{1}{3 s^{2}}

$R(s)= \dfrac {3}{s}- \dfrac {2}{s^2}- \dfrac {1}{3s^2}$

6 M

4 (a) Explain Routh-Hurwitz's criterion for determining the stability of a system and mention any three limitations of R-H criterion.

10 M

4 (b) A unity feedback control system is characterized by the open loop transfer function:

G (s) = \frac{K (s + 13)}{s (s + 3) (s + 7)}

$G(s) = \dfrac {K(s+13)} {s(s+3)(s+7)}$ i) Using the Routh's criterion, calculate the range of values of K for the system to be stable.
ii) Check if for K=1, all the roots of the characteristic equation of the above system are more negative than -0.5.

10 M

5 (a) Sketch the root locus for a unity feedback control system with open loop transfer function:

G (s) = \frac{K (s + 2) (s + 3)}{s (s + 1)}

$G(s)= \dfrac {K(s+2)(s+3)}{s(s+1)}$

12 M

5 (b) Show that the root Loci for unity feedback control system with

G (s) = \frac{K (s^{2} + 6 s + 10)}{(s^{2} + 2 s + 10)}

$G(s)=\dfrac {K(s^2 +6s +10)}{(s^2+2s+10)}$ are the areas of circle of radius √10 and centred at the origin.

8 M

6 (a) Sketch the Bode plot of a unity feedback system whose open loop transfer function is given by

G (s) = \frac{K}{s (1 + 0.1 s) (s + 0.05 s)}

$G(s)= \dfrac {K}{s(1+0.1s)(s+0.05s)}$ i) Find the value of K for a gain margin of 10dB.
ii) Find the value of K for a phase margin of 30°.

14 M

6 (b) Determine the open loop transfer function of a system whose approximate plot is shown below.

6 M

7 (a) State and explain Nyquist stability criterion.

6 M

7 (b) Sketch the Nyquist plot for a system whose open loop transfer function is

G (s) H (s) = \frac{K (4 s + 1)}{s (2 s - 1)}

$G(s)H(s)= \dfrac {K(4s+1)}{s(2s-1)}$ Determine the range of K for which the system is stable.

14 M

8 (a) Define state variable and state transition matrix. List the properties of the state transition matrix.

8 M

8 (b) Obtain the state model of the electrical network shown in below, by choosing V₁(t) and V₂(t) as state variables.

12 M

More question papers from Control Systems

SPONSORED ADVERTISEMENTS