PIDRegler

PIDRegler, or PID controller, is a feedback control element used to drive a process variable toward a desired setpoint by adjusting a manipulated variable. It combines proportional, integral and derivative actions to respond to current error, accumulated past error, and predicted future error. The result is improved response speed, reduced steady-state error and enhanced stability in many systems.

In continuous time, the controller output u(t) is given by u(t) = Kp e(t) + Ki ∫ e(τ) dτ + Kd de/dt, where e(t) = setpoint − y(t). In discrete form, commonly used in digital controllers, u[k] = Kp e[k] + Ki Ts Σ_{i=0}^{k} e[i] + Kd (e[k] − e[k−1])/Ts, with Ts the sampling period. Derivative action is often filtered to reduce sensitivity to noise, and some implementations use a rolling or incremental form.

Tuning selects the gains Kp, Ki, Kd to meet performance goals such as rise time, overshoot and settling time. Common methods include Ziegler–Nichols, Cohen–Coon, and model-based approaches like IMC. Practical issues include integral windup when the actuator saturates, necessitating anti-windup strategies (back-calculation, conditional integration, or saturation handling). Noise sensitivity is particularly relevant to the derivative term, often mitigated by filtering.

Applications span process control, robotics, motor speed and position control, and HVAC systems. While highly versatile, PIDRegler assumes a relatively linear, measurable process and may require adaptation or alternatives for highly nonlinear or time-varying plants.