---
title: "Control evaluation steps; PD and PI design"
subject: "Embedded System"
chapter: 7
key: "semester_6/embedded_system:control-evaluation-steps-pd-pi"
source: https://www.bctengineer.com/q/semester_6/embedded_system/control-evaluation-steps-pd-pi
site: BCT Engineering
---

# Control evaluation steps; PD and PI design

Embedded System · Chapter 7: Control System

- Asked in: 2071 Bhadra, 3+5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/embedded_system/control-evaluation-steps-pd-pi
- Whole chapter: https://www.bctengineer.com/md/semester_6/embedded_system/chapter-7

## Question

What are the evaluation steps used in general control systems input? Explain controller design using PD and PI controller.

## Short answer

Apply step input, record output, compute rise time, overshoot, settling time, steady-state error; check disturbance and stability. PD: u=Kp·e+Kd·de/dt; Kp sets speed, Kd adds damping, reduces overshoot, amplifies noise. PI: u=Kp·e+Ki·∫e dt; Kp for response, Ki eliminates steady-state error, too large Ki causes oscillation; use anti-windup.

## Answer

#### Evaluation steps

To evaluate a control system, the response to a standard input (usually a step) is examined:

1. Apply the reference (step) input and record the output over time.
2. Compute the metrics: rise time, overshoot, settling time and steady-state error.
3. Apply a disturbance and check the disturbance rejection.
4. Check stability (no unbounded output, damping) and robustness to parameter change.
5. Compare with the specifications and re-tune the controller if not met.

#### PD controller design

Control law: u = Kp·e + Kd·de/dt.

- Kp sets the speed of response; Kd adds damping from the error's rate of change, reducing overshoot and improving stability.
- Procedure: choose Kp for the required rise time, then increase Kd until the overshoot is acceptable.
- Result: faster and well damped, but the steady-state offset of the plant remains, and noise is amplified.

#### PI controller design

Control law: u = Kp·e + Ki·∫e dt.

- Kp gives the main response; the integral accumulates the error and drives the steady-state error to zero.
- Procedure: choose Kp first, then increase Ki gradually; too large a Ki gives overshoot and oscillation.
- Result: zero steady-state error (a constant disturbance is rejected), at the cost of slower response; limit the integral for anti-wind-up.

```text
 PD:  e --> [Kp + Kd s] --> u
 PI:  e --> [Kp + Ki/s] --> u
```

## Check yourself

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

1. What input is usually used to evaluate?
   A. Step input
   B. Random noise
   C. Zero
   D. Sine only
   Answer: A. Step response gives metrics. (Key point: Standard input)

2. Role of Kd in PD design?
   A. Removes offset
   B. Speeds up integral
   C. Nothing
   D. Adds damping, reducing overshoot
   Answer: D. Increase Kd until overshoot acceptable. (Key point: PD)

3. Result of PI?
   A. Offset remains
   B. Noise amplified
   C. Zero steady-state error at cost of slower response
   D. No gains
   Answer: C. Integral removes error. (Key point: PI)

4. Large Ki gives?
   A. Faster zero
   B. Overshoot and oscillation
   C. Less overshoot
   D. Stable always
   Answer: B. Increase gradually. (Key point: PI tuning)

## Related in Embedded System

- [Closed loop diagram; P, PI, PD, PID](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aclosed-loop-block-diagram-pid-types) — Embedded System, chapter 7
- [Steps to design closed loop control system](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aclosed-loop-design-steps) — Embedded System, chapter 7
- [Open-loop automobile cruise controller design](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aopen-loop-cruise-controller) — Embedded System, chapter 7, asked 3×
- [Full-custom, semi-custom and PLD design steps](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Afull-semi-custom-pld-steps) — Embedded System, chapter 8, asked 2×
- [Closed loop speed control design conditions](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aclosed-loop-speed-control-conditions) — Embedded System, chapter 7
- [Define controller, plant, actuator](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Adefine-controller-plant-actuator) — Embedded System, chapter 7

## Related in other subjects

- [Short note: PD and PI controller](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Ashort-pd-pi) — Control Systems, chapter 7
- [Short note: Characteristics of PI and PD control](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Ashort-pi-pd-characteristics) — Control Systems, chapter 7
- [Digital PD controller design for plant 1/s²](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Apd-design-double-integrator) — Digital Control System, chapter 4, asked 2×
- [P, I, D controllers and role of PI, PD](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Apid-pi-pd-role) — Control Systems, chapter 7