LINEAR CONTROL SYSTEMS PAPER 1

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LINEAR CONTROL SYSTEM (New) IC 204 4th Sem May 2k5

Max marks 60

Note: Section A is compulsory. Attempt any Four questions from section B and two from Section C.

Section A Marks 2 each

1.
(a) Consider the mechanical system shown in the figure given below. If the system is set into motion by unit impulse force, fine out the equation of oscillation.

(b) Calculate the sensitivity SGM of the system having the transfer function
M = G/(1+GH)
(c) Find out the C(s)/R(s) for the system shown in the fig 2

(d) Calculate the value of k for which the unity feedback system
G(s) =k/[s(s+2)(s+4)]
crosses the imaginary axis.

(e) Consider the system having transfer function
C(s)/H(s) = 4/(s2+1.6s+4)
Calculate the settling time for 2% tolerance band, for the unit step response

(f) A closed loop system is shown in the figure 3. Find out the largest possible value of b for which this system would be stable.

(g) Calculate the natural frequency of a second order system described by the differential equation. (please see the attachment)

(h) Find out the phase angle for a transfer function
G(a) = 1/{1+sT)3
at corner frequency.

(i) The loop transfer function of a feedback control system is given by
G(s)H(s) = k/[s(s+2)(s2 + 2s + 2)]
Calculate the number of asymptotes of its root loci.

(j) In a two-phase a.c. servomotor, the rotor has a resistance R and a reactance X. Give the condition for which torque-speed characteristic of the servomotor will be linear.

Section B Marks 5 each

2. Discuss in brief three different canonical state model to study the controllability and observability properties of a system.

3. List the advantages and disadvantages of hydraulic controllers.

4. Sketch the desirable range of the location of the poles of the transfer function of a system if the system’s damping ratio is to lie between 0.3 and 0.7 and its natural frequency is to lie between 2 and 4 rad/s

5. Consider the closed loop feedback system shown in figure 4 . Determine the range of K for which the system is stable.

6. Explain the construction and working principle of Synchro error detector.

Section C Marks 10 each

7.Show that the lead network and lag network inserted in cascade in an open loop acts as proportional plus derivative control (in the region of small w) and proportional plus integral control (in the region of large w), respectively.

8 (a) Obtain the transfer function C(s) / R(s) for the multi-loop control system shown. (please see the attachment)

(b) Explain what is meant by the relative stability of a system. How do we specify relative stability in terms of:
(i) closed-loop pole locations
(ii) gain margin and phase margin?

9. (a) Draw the root locus diagram for the following control system (plese see the attachment) and calculate the breakin and breakaway points.

(b) Discuss the various salient features of Root Locus Plot