University of Mumbai 2008-5th Sem B.E Electrical and Electronics Engineering Control System-I - Question Paper

T'- CetejLtJ apno'31 (pcu/). Jlilog¹ Coa/ro) Susiem-X

(REVISED COURSE)

CD-5982

(3 Hours)

N.B.(1)    Question No. 1 is pompulsory.

(2)    Attempt total five questions.

(3)    Figures to the right indicate marks.

(4)    Make suitable assumptions w]

^/T*

1. (a) A system is governed by the differential equation    20

deiaa ,,0,(0. sum

Where y(t) is the output and u(t) is the input of the system; obtain state space representation of the system.

(b) Find the transfer function for the system represented by flow graph.

(c) Obtain the transfer function from the log-magnltude plot shown below

(d) Applying Routh's criterion, find range of K for stability of a system, whose characteristic equation is given by

s³ + 3K s^a + (K + 2) s 4- 4 = 0.

2. (a) Determine C/R for the following block diagram.

10

VJ . 4k<U4V    *'

2 mli jo

3. (a) The system shown below uses a rate feed back controller. Determine the tachometer constant 10 K_t, so as to obtain the damping ratio of 0-5, calculate corresponding T_pp M_p, W_d and T_#.

CcO

(b) A certain feed back control system is described by the transfer function 10

G{s)*-a--- and H(s) 1, Determine steady state error coefficients and

s² (s + 20)(s + 30) ^w    *

also determine the value of K to limit steady state error to 10 units, due to input r(t) = 1 + 10 t + 20 t².

K

4.    (a) For the unity feed back system with G (s) =

(s + 1)^d (s + 4)

(i)    Find the range of K for stability

(ii)    Find the frequency of oscillations when the system is Marginally stable.

(b) Show the pole zero location and unit step response for the following second order systems : 10

(i)    Under damped

(ii)    Over damped (ill) Critically damped

(iv) Undamped.

5.    (a) Draw the complete root locus for the system represented by open loop transfer function, 10

G(s)H(s) = r-(s + 2)

(b) Draw the complete Nyquist plot for the system whose open loop transfer function is 10

G (s) H (s) =* _s(g ₊ g) (s + 10) ctetei'mine the range of K for which close loop system is stable.

6.    (a) Explain how the system 'type' can be determined from the logrmagnitude curve, hence explain 10

how K_p, K_v and K_# can be determined.

K

r

(b) Determine the value of K for a unity feed back control system having G (s) =

s(s + 2)(s + 10)

such that

(i)    Gain margin 10 db

(ii)    Phase margin = 50

(iii)    System is marginally stable.

7. (a) Sketch approximate nature of polar plot for the system having transfer function 20

K

s²(1 + sT₁) *

(b)    Discuss in detail any one type of damping for a Second Order System.

(c)    Derive expression for peak time-up.

(d)    Explain the co-relation between time and frequency domain specifications.

Attachment: university-of-mumbai-2008-b-e-electrical-and-electronics-engineering-51238-1.pdf

Earning:   Approval pending.