Editing Proportional–integral–derivative controller (section)

{{Short description|Control loop feedback mechanism}}
{{Use American English|date=June 2019}}

A '''proportional–integral–derivative controller''' ('''PID controller''' or '''three-term controller''') is a [[feedback]]-based [[control loop]] mechanism commonly used to manage machines and processes that require continuous control and automatic adjustment. It is typically used in [[industrial control systems]] and various other applications where constant control through [[modulation]] is necessary without  human intervention. The PID controller automatically compares the desired target value ([[Setpoint (control system)|setpoint]] or SP) with the actual value of the system ([[process variable]] or PV). The difference between these two values is called the ''error value'', denoted as <math>e(t)</math>.

It then applies corrective actions automatically to bring the PV to the same value as the SP using three methods: The proportional ({{Var|P}}) component responds to the current error value by producing an [[Output (computing)|output]] that is directly proportional to the magnitude of the error. This provides immediate correction based on how far the system is from the desired setpoint. The integral ({{Var|I}}) component, in turn, considers the cumulative sum of past errors to address any [[Errors and residuals|residual]] [[steady-state]] errors that persist over time, eliminating lingering discrepancies. Lastly, the derivative ({{Var|D}}) component predicts future error by assessing the rate of change of the error, which helps to mitigate [[Overshoot (signal)|overshoot]] and enhance system stability, particularly when the system undergoes rapid changes. The PID output signal can directly control actuators through voltage, current, or other modulation methods, depending on the application. The PID controller reduces the likelihood of [[human error]] and improves [[automation]].

A common example is a vehicle’s [[Cruise control|cruise control system]]. For instance, when a vehicle encounters a hill, its speed will decrease if the engine power output is kept constant. The PID controller adjusts the engine's power output to restore the vehicle to its desired speed, doing so efficiently with minimal delay and overshoot.

The theoretical foundation of PID controllers dates back to the early 1920s with the development of automatic steering systems for ships. This concept was later adopted for automatic process control in manufacturing, first appearing in [[pneumatic actuator]]s and evolving into electronic controllers. PID controllers are widely used in numerous applications requiring accurate, stable, and optimized [[automatic control]], such as [[temperature regulation]], motor speed control, and industrial process management.