P, PI, PD, PID Controllers and Lag, Lead, Lag-Lead Compensators - Topicwise Questions in Control Systems (1987 -2015)

2003
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

Answer: C

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

2005
1. Which one of the following polar diagrams corresponds to a lag network?

Answer: D

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

2006
1. The transfer function of a phase lead compensator is given by G_c(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

Answer: D

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

2007
1. A control system with a PD controller is shown in the figure.

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

Answer: B

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

2. 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

Answer: A

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


2008
1. 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 V_o/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

Answer: B

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

2009
1. 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

Answer: C

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

2. If the transfer function of the following circuit is V_o(s)/V_i(s) = 1/(2+sCR),_L is

then the value of the load resistor R
a) R/4
b) R/2
c) R
d) 2R

Answer: C

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

2010
1. A unity negative feedback closed loop system has a plant with the transfer function G(s) = 1/(s² + 2s + 2) and a controller G_c(s) in the feed forward path. For a unit step input, the tranfer function of the controller that gives minimum steady state error is

Answer: D

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


2012
Statement for Linked Answer Questions : 1 and 2
The transfer function of a compensator is given as G_c(s)= (s+a)/(s+b).
1. G_c(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

Answer: A

2. 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

Answer: A

Solution (1 & 2) : https://www.youtube.com/watch?v=CSWEFDPoSsA

2015
1. 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 ___________

Answer: 0.5

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

2. 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

Answer: A

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