P, PD and PID controllers & Lead and Lag Compensators - Topic wise Questions in Control Systems ( from 1987)

1. A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has
a) a higher type number
b) reduced damping
c) higher noise amplification
d) larger transient overshoot

Solution : https://www.youtube.com/watch?v=flVQh4IItX4

2. Which one of the following polar diagrams corresponds to a lag network?

Solution : https://www.youtube.com/watch?v=essJrzYsfPg

3. The transfer function of a phase lead compensator is given by Gc(s) = (1 + 3Ts)/(1 + Ts) where T ≥ 0. The maximum phase shift provided by such a compensator is
a) π/2
b) π/3
c) π/4
d) π/6

Solution : https://www.youtube.com/watch?v=B6_LDoAZ3-I

4. A control system with a PD controller is shown in the figure.

If the velocity error constant Kv = 1000 and the damping ratio ξ = 0.5, then the values of Kp and KD are
a) Kp = 100, KD = 0.09
b) Kp = 100, KD = 0.9
c) Kp = 10, KD = 0.09
d) Kp = 10, KD = 0.9

Solution : https://www.youtube.com/watch?v=vxHx4zTs5vg

5. The open loop transfer function of a plant is given as G(s) = 1/(s2 – 1). If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

Solution : https://www.youtube.com/watch?v=HJ09FtxcO-I

6. Group – I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition R2C2>R1C1. The transfer function Vo/V1 represents a kind of controller. Match the impedance's in Group – I with the types of controllers in Group – II.
a) Q – 1, R – 2
b) Q – 1, R – 3
c) Q – 2, R – 3
d) Q – 3, R – 2

Solution : https://www.youtube.com/watch?v=Q3O1G2CU5Xw

7. The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. Which of the following compensator has such a magnitude plot?
a) Lead compensator
b) Lag compensator
c) PID compensator
d) Lead – Lag compensator

Solution : https://www.youtube.com/watch?v=JVBUSrYEb7Q

8. If the transfer function of the following circuit is Vo(s)/Vi(s) = 1/(2+sCR), then the value of the load resistor RL is
a) R/4
b) R/2
c) R
d) 2R

Solution : https://www.youtube.com/watch?v=0bJX_BCy6bc

9. A unity negative feedback closed loop system has a plant with the transfer function G(s) = 1/(s2 + 2s + 2) and a controller Gc(s) in the feed forward path. For a unit step input, the tranfer function of the controller that gives minimum steady state error is

Solution : https://www.youtube.com/watch?v=zdwjtNkiBxg

Statement for Linked Answer Questions : 10 and 11
The transfer function of a compensator is given as Gc(s)= (s+a)/(s+b).
10. Gc(s) is a lead compensator if
a) a = 1, b =2
b) a = 3, b =2
c) a = –3, b = –1
d) a = 3, b =1

11. The phase of the above lead compensator is maximum at
a) √2 rad/sec
b) √3 rad/sec
c) √6 rad/sec
d) 1/√3 rad/sec

Solution (6 & 7) : https://www.youtube.com/watch?v=CSWEFDPoSsA

12. A lead compensator network includes a parallel combination fo R and C in the feed-forward path. If the transfer function of the compensator is GC(s) = (s+2)/(s+4) , the value of RC is ___________

Solution : https://www.youtube.com/watch?v=DeKH-DPUdMo

13. The transfer function of a first order controller is given as Gc(s) = K(s+a) / (s+b), where K, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is
a) a < b
b) a > b
c) K < ab
d) K > ab

Solution : https://www.youtube.com/watch?v=uKr3VkkMkow

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