Data-driven generalized minimum variance regulatory control for model-free PID gain tuning

The data-driven generalized minimum variance (GMV) regulatory control derives the control parameters, which minimize the variance of the generalized output, from plant operating data without the plant model. The approach realizes model-free control parameter tuning, but it cannot be applied to the closed-loop system where a PID controller has already been implemented because of mismatch of controller structure between GMV control and PID control. The present work, therefore, modifies the data-driven GMV regulatory control so that it can be applied to model-free PID gain tuning. A modified data-driven cost function is introduced, and an analytical result on the relation between the data-driven cost function and the model-based cost function is presented. The results show that the proposed data-driven cost function is a good approximation of the model-based one. The approach contributes toward saving the effort of tuning PID gains. Finally, a numerical example is shown to demonstrate the effectiveness of the proposed model-free PID gain tuning method.