Match List I with List II Choose the correct answer from the options given below:LIST I (Transfer function) LIST II (Controller) A. $\frac{K_{1}S + K_{2} + K_{3}S^{2}}{S}$ I. P-controller B. K1 II. PI-controller C. $\frac{K_1S + K_2}{S}$ III. PD-controller D. K1 + K2S IV. PID - controller
A-IV, B-I, C-II, D-III
The method. Expand each transfer function and look for the three characteristic terms: a constant (proportional), a 1/s term (integral) and an s term (derivative).
A → IV (PID).
\(\dfrac{K_1S+K_2+K_3S^{2}}{S}=K_1+\dfrac{K_2}{S}+K_3S\)
All three actions are present, so this is a PID controller. Note it contributes one pole at the origin and two zeros; the integral term kills the steady-state error while the derivative term restores speed and damping.
B → I (P). \(K_1\) is a pure gain — it scales the error and nothing more. Raising K1 reduces (but never eliminates) the steady-state offset and eventually degrades stability.
C → II (PI).
\(\dfrac{K_1S+K_2}{S}=K_1+\dfrac{K_2}{S}\)
Proportional plus integral: adds a pole at s = 0, raising the system type by one and driving the step error to zero, at the cost of a slower response.
D → III (PD). \(K_1+K_2S\) is proportional plus derivative: it adds a zero at \(s=-K_1/K_2\) and +90° of phase lead, which improves damping, reduces overshoot and speeds up the transient — but it does nothing for steady-state error and amplifies high-frequency noise.
Quick recognition rule. A pole at the origin (an s in the denominator) always signals integral action; an s in the numerator signals derivative action; a bare constant is proportional. Counting which of the three appear identifies the controller instantly.
Hence, the correct matching is A-IV, B-I, C-II, D-III.
Similar Questions
Consider the following controllers for their system complexity and arrange them in increasing order of complexity.
(A) Proportional controller
(B) Proportional plus derivative controller
(C) Proportional plus integral plus derivative controller
(D) Proportional plus integralChoose the most appropriate answer from the options given below :
Which of the following statement are correct for PI controller?
A. PI controller increases the system type by 1, therefore it improves the steady state error by one order.
B. PI controller reduce the rise time
C. PI controller increase the bandwidth.
D. PI controller is a high pass filter.
E. PI controller adds a pole at S=0 to the forward path transfer function, hence type of system increased by 1.
Choose the most appropriate answer from the options given below :
The value of Kp in Proportional, PI, PID, controllers are given
A. For proportional Kp = T/L
B. For PI, Kp = 0.9 T/L
C. For PI, Kp = 1.7 T/L
D. For PID, Kp = 1.2 T/L
E. For PID Kp = 0.9 T/L
Choose the correct answer from the options given below:
The pole-zero configuration of a PI controller is represented by
Read the following statements regarding PID controller :
(a) The system complexity of a PID controller is less than that of a PI controller.
(b) A PID controller produces no action for any constant error signal.
(c) A PID controller is used to increase the damping factor of the dominant poles of a PI controlled system.
(d) A PID controller is used to decrease the damping factor of the dominant poles of a PI controlled system.
Which of the above statements are correct ?
Assertion (A) : A PI controller introduces a pole in the system thereby increasing the order and type of system by one.
Reason (R) : The increase in the type of the system ensures a decrease in the steady state error of the system.
Select your answer using the codes given below.
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