# Control Systems July 2007

Note : Answer any FIVE full questions.

1 a. Define a control system. Explain the difference between open loop and closed loop control systems with one example for each.

b. Far the mechanical system shown in fig.l (b), i) Draw the mechanical network

ii) Write the differential equation of the system.

2 a. Obtain of the system shown in fig.2(a) by using block diagram reduction method:

b.   Draw the signal flow graph for the system of equation given below and obtain the using MGF

 X over all transfer  function —— X, x2 = GtX, -h,x2– -h2x3 x3 = GiXj +g2x2 -H3X3 x4 = G2X2 +G3X3 -H4X5 X5 =g«x4 -H5X6 X6 = GsX5

3  a. For a spring mass damper system shown in fig.3(a), an experiment was conducted by applying a force of 2 Newtons to the mass. The response x(t) was recorded using an xy plotter and the experimental result is as shown in fig.3(a) below. Find the values

b.  Consider unity FBCS, whose OLTF is given by G(s) = —~~S . Obtain the s(s + 0.6)

response to step input. For the same, calculate rise time, maximum peak overshoot, peak time and settling time.

c. A unity FB system has G(s) =1-1 s(s + 2)(s + 2s + 5^

i) For a unit ramp input, it is desired ess < 0.2, find K t2

ii) Determine ess if input r(t) = 2 + 4t + — .

4 a.  Derive the condition on the impulse response so that the system is bounded input bound output (BIBO) stable.

b.  A unity FB system has G(s) = —- v v———- r using RH criteria; find the range s(s + 2)(s + 4)(s + 6) of K for stability. Also find Kmax and Wmax.-

c.   Determine the range of value of K (K>0) such that the characteristic equation is: s3+3(K + l)s2 +(7K + 5)s + (4K + 7) = 0 has roots more negative than S = – L           (07 Marks)

5  a.   State the different rules for the construction of root locus.

b.Sketch the root locus diagram of a control system having,

K(s + l) G(s) = -71s(s~l)(s +4s + 16j

6 a.  State and explain Nyquist stability criterion.

b.  Sketch the Nyquist plot of a unity feedback control system having the open loop transfer function G(s) = —{        r. Determine the stability of the system using Nyquist s(l-s) stability criterion.

7 a.The open loop transfer function of a unity FBCS is given by, “ s(l + 0.001sXl + 0.25sXl + 0.1s) Determine the value of K so that the system will have a phase margin of 40°. What will be the gain margin then? Use Bode plot.

b.  With figure define the frequency domain specifications.

8  a.  Given G(s)H(s) = ^^. Draw the polar plot and hence determine if system

s(s + l)(s + 2) is stable and its gain margin and phase margin.

b.  The OLTF of an unity FBCS is, G(s) = . s(s + a)

i)    Find the values of K and a so that mr – resonant peak = 1.04 and wr = resonant frequency = 11.55 rad/sec.                                                         ii)   For the values of K and a found in part (i), calculate the settling time and bandwidth of the system.