---
title: "True/false: derivative controllers always used with others"
subject: "Control Systems"
chapter: 7
key: "semester_3/control_systems:derivative-always-with-others"
source: https://www.bctengineer.com/q/semester_3/control_systems/derivative-always-with-others
site: BCT Engineering
---

# True/false: derivative controllers always used with others

Control Systems · Chapter 7: Performance Specifications and Compensation Design

- Asked in: 2081 Bhadra, 4 marks; 2074 Asoj, 1+3 marks; 2068 Baisakh (old course), 1+3 marks (asked 3 times)
- Video: [#182 P, PI, PD, PID controllers || EC Academy](https://www.youtube.com/watch?v=F1ciGVHhL4A) — EC Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/control_systems/derivative-always-with-others
- Whole chapter: https://www.bctengineer.com/md/semester_3/control_systems/chapter-7

## Question

State whether the statement "Derivative controllers are always used with other controllers" is true or false and justify your answer.

## Short answer

True. A pure derivative controller produces zero output for constant error, cannot eliminate steady-state error, and amplifies high-frequency noise. It is always combined with proportional and/or integral control (PD/PID) to provide corrective action and damping.

## Answer

**True.** A derivative (D) controller is never used alone; it is always combined with a proportional and/or integral controller, as PD or PID.

#### Justification

A derivative controller gives an output proportional to the **rate of change** of the error:

$$
u(t)=K_d\frac{de(t)}{dt},\qquad G_c(s)=K_ds
$$

1. **No action on constant error:** if the error is constant (even large), $de/dt=0$, so the controller output is zero. A steady error is never corrected, so D alone cannot hold the output at the set point.
2. **Blocks DC signals:** $G_c(0)=0$. In the loop it acts like a zero at the origin, which can cancel the plant's integrator and reduce the system type, so the steady-state error grows.
3. **Noise amplification:** $|G_c(j\omega)|=K_d\omega$ rises with frequency, so high-frequency noise is amplified strongly. With a P term the useful low-frequency action dominates.
4. **Anticipatory, not corrective:** D action predicts the error trend and adds damping; it only improves the transient part of the response.

#### How it is used

With proportional action (PD):

$$
G_c(s)=K_p+K_ds=K_p(1+T_ds)
$$

- The P part removes and holds the error.
- The D part adds a zero, increases damping, reduces overshoot and settling time, and improves stability.

| Controller | Steady error correction | Damping / overshoot |
|---|---|---|
| D alone | none | improves |
| PD | yes (P) | improves |
| PID | eliminated (I) | improves |

**Example:** in a position servo, a PD controller lets the motor slow down as it nears the target (D) while still pushing it there (P). A pure D controller would stop acting once the motor is at rest away from the target.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Is the statement 'Derivative controllers are always used with other controllers' true or false?
   A. False, D alone is best for steady-state accuracy
   B. False, D alone is used for noise removal
   C. True, D is combined with P and/or I as PD or PID
   D. True, but only with integral control
   Answer: C. A D controller is never used alone; it is combined as PD or PID. (Key point: Verdict)

2. Why can a derivative controller alone not correct a constant steady error?
   A. Its output is Kd times de/dt, which is zero when the error is constant
   B. It has a pole at the origin that saturates
   C. It amplifies the error too much
   D. It adds a lag that slows the response
   Answer: A. For constant error de/dt = 0, so controller output is zero and nothing corrects the offset. (Key point: No action on constant error)

3. In a PD controller, what does the D part contribute?
   A. Removes steady-state error
   B. Adds a zero, increasing damping and reducing overshoot
   C. Increases system type by one
   D. Attenuates high-frequency noise
   Answer: B. D adds a zero (phase lead), increasing damping and reducing overshoot and settling time, while P removes and holds the error. (Key point: Role of D with P)

## Related in Control Systems

- [True/false: air conditioner is closed loop](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-air-conditioning-closed) — Control Systems, chapter 1
- [True/false: feedback makes response faster](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-feedback-faster) — Control Systems, chapter 1
- [True/false: higher forward gain reduces disturbance](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-disturbance-forward-gain) — Control Systems, chapter 1
- [True/false: proportional controller makes error zero](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-proportional-sse-zero) — Control Systems, chapter 7

## Related in other subjects

- [True/false: series motor started at no load](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atf-dc-series-motor-start-noload) — Electrical Machine, chapter 4
- [DC series motor started at no load: true/false](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Adc-series-no-load-true-false) — Electrical Machines, chapter 4
- [True/false: CT secondary kept open](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atf-false-ct-secondary-open) — Electrical Machine, chapter 2
- [True/false: rotor core loss neglected](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atf-rotor-core-loss-neglected) — Electrical Machine, chapter 5