PIDregulatoren

PIDregulatoren, often called a PID controller, is a feedback control mechanism used to regulate process variables in industrial systems. It computes a control signal from the error between a desired setpoint and the measured process variable by combining proportional, integral, and derivative actions.

Mathematical form: Let e(t) = SP - PV. The control output u(t) is u(t) = Kp e(t) + Ki ∫ e(τ) dτ + Kd de/dt. In discrete time with sampling period T: u[k] = Kp e[k] + Ki T e[k] + Kd (e[k] - e[k-1]) / T.

Tuning and behavior: The coefficients Kp, Ki, Kd determine present, past, and anticipated error. Tuning aims to achieve adequate responsiveness without excessive overshoot. Common methods include Ziegler-Nichols, Cohen-Coon, and manual tuning; modern approaches include model-based or auto-tuning. Anti-windup strategies and derivative filtering are often used to improve performance and prevent instability due to actuator limits or noisy measurements.

Implementation and variants: PID regulators can be implemented as analog circuits or digitally in microcontrollers and PLCs. In digital implementations, integral and derivative actions are computed from sampled data, and anti-windup and low-pass filtering are common. They are used in temperature control, level control, position and speed control, and many other processes.

Limitations and considerations: PID control performs best on linear, relatively slow processes with moderate noise; highly nonlinear or time-delayed systems may require gain scheduling, feed-forward, or alternative controllers. Proper tuning remains essential for stability and performance.