🎛️ PID Controller

A PID controller is a feedback control algorithm that computes a correction signal from three terms: proportional (reacts to the current error), integral (accumulates past error to eliminate steady-state offset) and derivative (reacts to the rate of change of error to damp overshoot). Formalized for industrial process control in the early 20th century, PID remains the most widely deployed controller in engineering — driving everything from thermostats and cruise control to drone stabilization and robotic arms — because tuning its three gains (Kp, Ki, Kd) lets a single simple equation balance responsiveness against stability across an enormous range of physical systems. The proportional term alone would leave a permanent offset between the setpoint and the actual output under constant load, so the integral term slowly drives that offset to zero by summing error over time; push it too hard, though, and the system can overshoot or oscillate, which is exactly what the derivative term counteracts by anticipating where the error is heading. Because no single set of gains is optimal for every plant, engineers tune PID loops experimentally or with methods like Ziegler-Nichols, trading off rise time, overshoot and settling time for the specific system being controlled.