PIregler

PIRegler, or proportional-integral regulator, is a feedback controller used to regulate a process variable by combining proportional and integral actions. It aims to eliminate steady-state error that a proportional-only controller cannot remove for many processes. In continuous time, the control signal u(t) is given by u(t) = Kp e(t) + Ki ∫0^t e(τ) dτ, where e(t) is the difference between the reference setpoint and the process variable. The proportional term reacts to the current error, while the integral term accumulates past errors to cancel residual offset. The transfer function in the Laplace domain is C(s) = Kp + Ki/s.

In discrete-time implementations, a common form is u[k] = Kp e[k] + Ki ∑ e[i] from i = 0 to k, with Ki scaled by the sampling period. Anti-windup measures are frequently included to prevent integrator buildup when the actuator saturates.

Tuning of a PIRegler can follow empirical rules such as Ziegler-Nichols or Cohen-Coon, or be based on model-based or autotuning methods. The goal is to achieve a balance between fast response, minimal overshoot, and robust stability. Practical considerations include sensitivity to measurement noise, particularly in the integral term, and the need for anti-windup to avoid degraded performance during actuator saturation.

Common applications include temperature control, level and flow regulation, chemical process control, HVAC, and robotics. The PIRegler is a foundational element in control systems, offering a simpler alternative to full PID controllers when derivative action is undesirable or unnecessary.