AUTOMATIC CONTROL SYSTEMS

AUTOMATIC CONTROL SYSTEMS
SEM-V, 2012-13
B.TECH EXAMINATION
UTTARAKHAND TECHNICAL UNIVERSITY
utu previous year question paper

Time : 3 Hours

Total Marks:100

Attempt any four parts of the following:

1. What is effect of adding pole to a system? Discuss.
2. What is feed forward compensation? Clearly show block diagram.
3. What is Mason's Gain formula?
4. For the above system find the integral square error given by
   
   and comment on the same. The input r(t) is unit-step input
   and u = unit step input, find x(t).
5. Find the damping factor ζ, natural frequency ω_n peak time T_p and percentage overshoot for the system
   .
   Draw its pole zero location.
6. Derive the close loop transfer C(S)/R(S) = M (S) for the system shown below and find its sensitivity with respect to G and H.
   

Attempt any four parts of the following:

1. Discuss the time response of first order system with unit step, unit impulse and unit ramp inputs.
2. What is steady state error? Discuss position and velocity error constants.
3. Define gain margin, phase margin, gain crossover frequency in a polar plot.
4. For a system with
    find the dynamic error coefficients.
5. Show that the polar of
    is a semicircle.
6. Discuss the general procedure of determination of transfer from Bode Plot.

Attempt any two parts of the following:

1. State the rules for construction of root loci of G(S)H(S). Find a breakaway points of
   
2. Sketch the Nyquist and discuss stability of a unity feedback system with
   
3. Sketch the Bode Plot for the transfer function.
   
   Determine:
   (i) Gain cross over frequency
   (ii) Phase cross over frequency
   (iii) G.M and P.M

Attempt any two parts of the following:

1. The loop transfer function
   
   Compensate the system such that, K_v = 5 sec^-1 and phase margin is at least 40^o and the margin is at least 10 db, with a lag compensator.
2. Discuss about lag-lead compensation with suitable diagram and also represent on S-plane clearly.
3. Explain about phase lag compensation by Root Locus method with proper expression and plot.

Attempt any two parts of the following:

1. Find e^-lt by Laplace transform method and Cayley Hamilton theorem for
   
2. Derive the phase Portraits. Explain the Stability from the Phase Plane.
3. What is Lyapunov Stability theorem? The system is given by
   x₁ = x₂
   x₂ = -x₁ – x₂³
   Investigate the system by Lyapunov's method using v = x₁² + x₂².

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