Control Systems

Comparison of Proportional Integral Derivative Controllers (PID)

The components of a PID controller – Proportional (P), Integral (I), and Derivative (D) each have distinct characteristics and applications. These controllers can also be used independently or in combinations like PI, PD, etc.

Comparison of Proportional Integral Derivative Controllers

The following table shows the differences between the P, I, and D controller functions.

Parameter	P Controller	I Controller	D Controller
Principle of Operation	Proportional to error	Integral of error	Derivative of error
Error Elimination	Steady-state error	Eliminates steady-state error	Does not eliminate any error
Stability	Moderate	May reduce stability	Increases stability
Overshoot	Moderate	High	Low
Response Time	Fast	Slow	Fast
System Type Suitability	First order systems	Systems with steady-state errors	Systems requiring damping
Implementation Complexity	Low	Moderate	Moderate
Cost	Low	Moderate	Moderate
Application Examples	Level control, temperature control	Cruise control, HVAC	Damping control, robotics
Tuning Complexity	Low	Moderate	Moderate
Control Action	Proportional to present error	Based on accumulated past errors	Predictive, based on rate of error change

Explanation of the terms:

Principle of Operation: The mathematical relationship that dictates how each controller type reacts to the error signal.
Error Elimination: How effective the controller is at eliminating system error.
Stability: How the controller affects the system’s stability.
Overshoot: The extent to which the system exceeds its setpoint.
Response Time: How quickly the controller reacts to an error.
System Type Suitability: Types of systems where each controller is most effective.
Implementation Complexity: The complexity involved in implementing each type of control.
Cost: The relative cost of implementing each control type.
Application Examples: Common applications where each type of control is often used.
Tuning Complexity: How difficult it is to tune the parameters for optimal performance.
Control Action: Describes what aspect of the error signal the controller acts upon.