Code: A-11    Subject: CONTROL  ENGINEERING

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 11 Questions in all.

      Question 1 is compulsory and carries 16 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.

      Answer any THREE Questions each from Part I and Part II. Each of these questions carries 14 marks.

      Any required data not explicitly given, may be suitably assumed and stated.

Q.1       Choose the correct or best alternative in the following:                                           (2x8)

a.       Closed-loop transfer function of a unity-feedback system is given by . Steady-state error to unit-ramp input is

                                                                 (A)                                                 (B)  

                   (C)  1                                                  (D) 

b.      Effect of back emf in an armature-controlled dc servomotor is

                   (A)  to increase effective motor friction, thereby reducing motor time-constant.

                   (B)  to increase effective motor friction, thereby increasing motor time-constant.

(C)     to increase motor inertia, thereby increasing motor time-constant.

(D)    to increase motor inertia, thereby reducing motor time-constant.

c.       Feedback control systems are

(A)     Insensitive to both forward-and feedback-path parameter changes.

(B)     Less sensitive to feedback-path parameter changes than to forward-path parameter changes.

(C)     Less sensitive to forward-path parameter changes than to feedback-path parameter changes. 

(D)    Equally sensitive to forward-and feedback-path parameter changes.

     d.   The characteristic equation of a feedback control system is given by          

           .  The number of roots in the right-half of s-plane are      

                                                                       (A)  zero.         (B) 1.

(C)  2.                                                 (D) 3.

             e.   A unity feedback system has open-loop transfer function .  The peak overshoot in the step-input response of the system is approximately equal to

(A)   5%.                                              (B) 10%.

(C) 15%.                                             (D) 20%.

             f.    A unity feedback system with forward-path transfer function  is subjected to an input .  The steady-state error of the system is

                   (A)  infinity.                                         (B)  1.

                   (C)  zero.                                            (D) None of answers in (A), (B) & (C) is correct.

g.       A type-1 plant is changed to type-2 feedback system by the following cascade control action.

(A)     PD                                               (B)  PI      

(C)  Either PD or PI.                           (D)  Neither PD nor PI.

             h.  A unity feedback system has open-loop transfer function .  The gain margin of the feedback system is

                   (A) .                                                (B)  0.

                   (C) 1.                                                  (D) None of answers in (A), (B) & (C) is correct. 

PART I

Answer any THREE Questions. Each question carries 14 marks.

  Q.2     a.   The parameters of the mechanical system of Fig.1 are M = 1,000 Kg;          B = 10,000 N / (m / sec); K = 100,000 N / m .  A step force of 1000 Newton is applied to the mass at t=0.  The initial conditions are              y(0) =  (0) =0.  From the physical parameters of the system, obtain the following parameters: damping ratio, undamped natural frequency, and damped natural frequency which describe the dynamical behavior of the system.                                                                 (9)                                                                                                                            

b.      Obtain the step response of the system of Fig.1.                                                 (5)

  Q.3           Consider the system shown in Fig.2 with    ,  . 

                   Moment of inertia of load,

                   Moment of inertia of motor shaft,

                   Coefficient of viscous friction of load,

                   Coefficient of viscous friction of motor shaft,

                   (i)   Find the transfer function                                                         (9)

                   (ii)  A multi-loop (Consisting of speed-feedback loop, and a position feedback loop) feedback control system built around the system of Fig.2 with suitable additional hardware, drives the load to the commanded position inspite of load torque disturbances.  Make a sketch of the feedback control system showing how the hardware is to be connected.                                                           (5)                                                                        

  Q.4     a.   Show that a high loop gain in feedback systems results in

(i)                  good steady-state tracking accuracy;

(ii)                good disturbance signal rejection;

(iii)               low sensitivity to process parameter variations; and

(iv)              good relative stability, i.e., rate of decay of transients.                      (8)

             b.   What are the factors that limit the gain? (6)                                                                        

  Q.5     a.   Show that rise time, peak time, and settling time measures of performance of a standard second-order system are mutually dependent and therefore must be specified in a consistent manner.                                                         (5)

             b.   A unity feedback system has the plant  with a cascade controller .  Describe the effects of  and  on steady-state error, settling time and peak overshoot of system response.                  (9)

  Q.6     a.   Compare the power of Routh stability criterion with root locus analysis for investigation of closed-loop stability.                                                   (4)  

             b.   Find the range of gain K (K>0), for which the system shown in Fig.3 is stable.                                                                                                               (10)  

PART II

Answer any THREE Questions. Each question carries 14 marks.

  Q.7     a.   Consider a unity-feedback system with a forward path transfer function . Show that a part of the root locus is  a circle.                                                                                                (9)

             b.   Construct the root locus for the G (s) in part (a) and determine the damping ratio for maximum oscillatory response.  What is the value of K for this damping ratio?                                                                               (5)

  Q.8           a.                                                        Explain the terms gain margin and phase margin, with reference to Nyquist plots.                                                                                (4)

             b.   Using Bode plots, determine gain crossover frequency, phase crossover frequency, gain margin and phase margin of a feedback system with the open-loop transfer function .                                         (10)

  Q.9     a.   Define the terms resonance peak and bandwidth as applied to a closed-loop control system.                                                                                                             (4)

                b.   The experimental frequency response data of a system presented on Bode plot and asymptotically approximated is shown in Fig.4.  Find the transfer function of the system (the system is known to have minimum-phase characteristics).                                                                                                   (10)      

Q.10  The open-loop transfer function of a control system is 

(i)                  Determine approximate values of gain margin and phase margin.

(ii)                If a lag compensator with transfer function                                                  

 is inserted in the forward path, find the value of to keep the gain margin unchanged.                                                                 (6+8)

Q.11                                                                      Fig.5 shows a minor-loop feedback compensation scheme.  It is required to realize the control action by a digital controller with a uniform sampling interval of T sec. Give a digital control algorithm using the trapezoidal rule for integration.  Also give a block diagram of the digital control system.                   (14)