A Novel Approach to Model-Reference Adaptive PID Controllers

This study explores the adaptation of Proportional–integral–derivative (PID) controller coefficients using the model-reference method. Although this topic is classic and has been extensively explored in the literature, a definitive solution has yet to emerge. The paper introduces the general structure of adaptation laws for 2nd-order single-input, single-output systems via standard PID controllers by defining novel error dynamics. The stability of the adaptation laws is proven using the Lyapunov method, demonstrating that unlike conventional methods based on MIT rules, all necessary signals are computable. For the implementation of these laws, constant coefficients are needed, and systematic methods based on linear matrix inequality (LMI) conditions are introduced to calculate them. Furthermore, by applying the derived adaptation laws to the model of a DC-DC buck converter, it is illustrated that these adaptation laws can effectively estimate the ideal coefficients of the PID controller.