ProportioneelIntegraleDerivative

ProportioneelIntegraleDerivative, commonly known as a PID controller, is a widely used feedback control mechanism in industrial and scientific applications. It computes a corrective output by combining three terms that respond to the error between a target setpoint and the measured process variable: a proportional term, an integral term, and a derivative term. The goal is to achieve fast stabilization with minimal steady-state error while avoiding excessive overshoot or oscillations.

In continuous time, with e(t) as the error, the control action is u(t) = Kp e(t) + Ki ∫ e(τ) dτ + Kd de/dt, where Kp, Ki, and Kd are tuning gains. In discrete implementations, common forms are u[k] = Kp e[k] + Ki Ts Σ e[i] + Kd (e[k] − e[k−1])/Ts, with Ts the sampling period. Each term serves a purpose: the proportional term provides immediate correction, the integral term eliminates steady-state error, and the derivative term adds damping and speeds response but increases sensitivity to noise.

Practical use requires tuning the gains to balance responsiveness, stability, and robustness. Methods such as Ziegler–Nichols or Cohen–Coon offer starting points, followed by manual refinement. Common issues include integral windup, where the integral term accumulates excessively, and derivative kick or noise amplification. Anti-windup strategies (e.g., integrator clamping or back-calculation) and filtered derivatives are often employed.

Variants include PI and PD controllers, which omit one of the terms. PID remains versatile across domains such as temperature control, motor speed regulation, robotics, and process control, where reliable, adaptable performance is needed.