Among P, PD, PI, and PID controllers, which one typically exhibits the maximum stabilising (settling) time for a step change on a common process?

Introduction / Context:
Controller structure affects transient behaviour. Integral action removes steady-state offset but often slows the response, while derivative action anticipates changes and can speed up settling when tuned properly. This question asks which common structure tends to have the longest stabilising (settling) time under comparable tuning practices.

Given Data / Assumptions:

• Comparable loop configurations and reasonable tuning per standard methods.
• Stable, minimum-phase process.
• Focus on qualitative settling-time tendency, not one specific tuning rule.

Concept / Approach:
PI includes integral action but no derivative. The integral term eliminates offset by accumulating error, which also introduces an additional pole, typically making the transient slower and longer to settle compared with P or PD. PID can reduce settling time relative to PI by leveraging derivative action to counteract overshoot and sluggishness. Therefore, among the listed, PI commonly yields the largest settling time if tuned for comparable robustness.

Step-by-Step Solution:

Verification / Alternative check:
Textbook step-response comparisons under ZN or IMC-style tuning show PI loops typically settle more slowly than P or PD, and generally more slowly than well-tuned PID.

Why Other Options Are Wrong:

Common Pitfalls:
Equating zero steady-state error with superior speed; integral helps accuracy but may slow the loop if used alone.

Final Answer:
Proportional–Integral (PI)