What is a PID controller and what do P, I, and D stand for?

PID controller is the most common feedback control algorithm combining three modes: Proportional (P) produces output proportional to current error, Integral (I) accumulates past errors to eliminate steady-state offset, and Derivative (D) predicts future error based on rate of change. Together, these provide responsive, accurate control. The controller output is: Output = Kp*e + Ki*integral(e) + Kd*de/dt, where e is the error between setpoint and process variable.