Overview

The term PID controller is an acronym for a closed loop system with proportional, integral and derivative modes in its control algorithm. The fact that these three modes exist does not imply that all three modes are necessarily used for any given application.

The purpose of a closed loop control system is to reduce the error between the measurement and the setpoint. The ability of the system to reduce these errors depends on the different controller settings. There are three main modes that contribute to the final output as follows :

Control Modes

Proportional Mode - The proportional contribution to the output is equal to the error of the measurement from the setpoint multiplied by a gain value. Almost all feedback controllers use proportional mode.
Integral Mode - The integral contribution to the output is equal to the sum (integral) of the error multiplied by a gain value. As long as an error exists the integral action will continue to drive the output and work towards eliminating the error.
Derivative Mode - The derivative contribution to the output is equal to the rate of change (derivative) of the error with respect to time. It provides an anticipatory type of control that enables the use of higher gains, shortens oscillation, and reduces overshoot for a given setpoint change.
Final Output - The final output is the sum of these three mode as follows : Output = P + I + D

Tuning Methods

The quarter amplitude method as described here is one of many used for tuning closed loop control systems. It has proved to be effective in tuning many of the of the functions associated with engine control systems.

Turn the integral and derivative modes off and enable the closed loop control with proportional mode only.
Increment the proportional gain by a quarter of the previous value and monitor the output for oscillations.
Continue until the outputs successive peaks are about one quarter in ampitude of the previous peak.
Enable the integral mode and increment the gain in small steps to eliminate the output error.
Finally enable and add derivative control only if the control loop output needs better performance.

Notes

Special algorithms cannot do better than a well tuned PID controller for unmeasured load disturbances.
Integral mode eliminates offset but reduces stability and increases overshoot for setpoint changes.
Control loops with setpoint changes or excessive hysteresis need more derivative action and less integral.

Winning Edge Electronics