### 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

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

2006
1. 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

2007
1. 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

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

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 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

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?
b) Lag compensator
c) PID compensator

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

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 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

2012

The transfer function of a compensator is given as Gc(s)= (s+a)/(s+b).
1. 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

2. The phase of the above lead compensator is maximum at
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 ___________

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