Consider the following controllers for their system complexity and arrange them in increasing order of complexity. (A) Proportional controller Choose the most appropriate answer from the options given below :
(B) Proportional plus derivative controller
(C) Proportional plus integral plus derivative controller
(D) Proportional plus integral
(A), (B), (D), (C)
Complexity is measured by how many terms the controller has and how many parameters must be tuned, so the order runs P, PD, PI, PID — option 2.
| Controller | Transfer function | Parameters |
|---|---|---|
| (A) P | \(K_{p}\) | 1 |
| (B) PD | \(K_{p}+K_{d}s\) | 2 |
| (D) PI | \(K_{p}+\dfrac{K_{i}}{s}\) | 2 |
| (C) PID | \(K_{p}+\dfrac{K_{i}}{s}+K_{d}s\) | 3 |
The two ends are beyond dispute: P is the simplest with one gain, and PID the most complex with three. That alone eliminates options 3 and 4, which do not begin with P, and option 1, which places PID second. Only option 2 survives.
Why PD is ranked below PI, given that both have two terms. The integral term is the more demanding addition. It introduces a pole at the origin, which raises the system type and so eliminates steady-state error — but it also adds 90° of phase lag at every frequency, eating into the phase margin and pushing the system towards instability. It brings its own failure mode too: integral windup, where the accumulated error grows without limit while an actuator is saturated, so that the controller overshoots badly on recovery. Practical PI controllers need anti-windup logic, which PD controllers do not.
What each term contributes.
Proportional acts on the error now — raising \(K_{p}\) speeds the response and reduces but never removes the steady-state error.
Integral acts on the accumulated past — it drives the steady-state error to zero for a step input.
Derivative anticipates the future from the error's rate of change — it adds damping and reduces overshoot, at the cost of amplifying high-frequency noise, which is why the D term is nearly always filtered.
Complexity is a real cost, not merely a count: each extra parameter must be tuned, and the three PID gains interact, which is why systematic methods such as Ziegler-Nichols exist and why a plant that a P or PI controller can handle is rarely given a full PID.
Hence, the increasing order is (A), (B), (D), (C).
Similar Questions
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 :
Match List I with List II
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 Choose the correct 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:
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.
Important Questions from Controllers
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Which of the following is considered as a controller in an automatic toaster system ?
Slow response of an over-damped system can be made faster with the help of ______ controller.
In a feedback control system, the derivative (D) controller has an output proportional to:
