PID Tuning via Desired Step Response Curve Fitting
For control engineers, this provides a practical curve-fitting approach to PID tuning, but it is incremental as it applies existing optimization techniques to a known problem.
This paper proposes a PID tuning method that minimizes the root-mean-square error between desired and actual step responses using L2-norm optimization. The method matches closed-loop response to a desired step response and is shown to replace known analytical methods like Ziegler-Nichols and Lambda Tuning.
This paper presents a PID tuning method based on step response curve fitting (PID-SRCF) that utilizes L2-norm minimization for precise reference tracking and explicit transient response shaping. The algorithm optimizes controller parameters by minimizing the root-mean-square error between desired and actual step responses. The proposed approach determines optimal PID parameters by matching any closed-loop response to a desired system step response. Practically a first-order plus time delay model or a second-order system with defined settling time and overshoot requirements are preferred. The method has open-source implementation using constrained nonlinear optimization in MATLAB. Comparative evaluations demonstrate that PID-SRCF can replace known analytical methods like Ziegler Nichols, Lambda Tuning, Pole Placement, Dominant Pole and MATLAB proprietary PID tuning applications.