A PID (proportional-integral-derivative) controller is a control loop mechanism that is widely used in industrial control systems and other applications requiring continuously modulated control. The basic idea behind a PID controller is to read a sensor, then compute the desired actuator output by calculating proportional, integral, and derivative responses and summing those three components. The three terms of the PID controller are:

• Proportional (P): This term produces an output that is proportional to the current error value, which is the difference between the desired setpoint and the measured process variable. The proportional term is responsible for reducing the steady-state error of the system.

• Integral (I): This term produces an output that is proportional to the accumulated error over time. The integral term is responsible for reducing the residual error of the system.

• Derivative (D): This term produces an output that is proportional to the rate of change of the error. The derivative term is responsible for reducing the overshoot and settling time of the system.

The PID controller continuously calculates an error value as the difference between a desired setpoint and a measured process variable and applies a correction based on proportional, integral, and derivative terms. The controllers PID algorithm restores the measured variable to the desired value with minimal delay and overshoot by increasing or decreasing the control output in a controlled manner. PID controllers are widely used in industry to regulate temperature, flow, pressure, speed, and other process variables. While simple in theory, design and implementation of PID controllers can be difficult and time-consuming in practice.