A model-free direct synthesis method for PI/PID controller design based on disturbance rejection

•Model-free direct synthesis design for PI/PID controllers based on disturbance rejection.•Controller tuning directly uses closed-loop data without resorting to process models.•Explicit controller tuning formulas are applicable to stable and integrating processes.•The proposed method is more effective than the model-based design methods.•The proposed method can be applied online to improve underperforming controllers.

This paper presents a novel model-free (data-based) design method for PI/PID controllers that is based on the direct synthesis approach and specification of the desired closed-loop transfer function for disturbances. The proposed design method directly exploits a set of closed-loop process data without requiring the use of a process model; therefore, it can be applied online to improve the performance of existing underperforming controllers. The tuning formulas for PI/PID controllers are analytically derived and are generally applicable to stable and integrating processes. Furthermore, the tuning formulas contain a single adjustable parameter that enables a designer to address the tradeoff between performance and robustness. Although the controllers are designed for disturbance rejection, the set-point response can be improved independently by using set-point weighting in the PID controllers. Simulation examples covering a wide variety of process dynamics showed that the proposed design method is superior to the model-based direct synthesis design and other existing tuning methods. Furthermore, the proposed method was applied to the nonlinear model equations of a CSTR to show its effectiveness in practical applications.