PID Control Design for Uncertain Planar Nonlinear Systems via Feedback Domination Technique

This work investigates the issue of designing a proportional–integral–derivative (PID) controller for the regulation problem of uncertain planar nonlinear systems suffering from parameter uncertainties and external constant disturbances. The underlying philosophy lies in skillfully leveraging the idea of the feedback domination technique that induces a mechanism equipped with a domination gain in support of offering a constructive methodology (intuitive guideline) of specifying PID control gains leading to an effective PID controller which not only cleverly conquers system nonlinearities, parameter uncertainties, and external constant disturbances but also productively ensures the successful achievement of the regulation task with guaranteeing the boundedness of the overall system states. Building on the developed method, both the proportional–derivative (PD) and proportional–integral (PI) controllers with valid gains are also delicately explored and constructed to effectively address the regulation problem in specific/various scenarios of uncertain nonlinear systems. The primary novelty of this work involves dealing with the issue/challenge of synthesizing a competent PID/PD/PI controller for uncertain nonlinear systems undergoing parameter uncertainties and external constant disturbances, as well as providing a systematic framework for selecting applicable PID/PD/PI control gains in consideration of the regulation problem. Finally, two numerical simulations are presented to illustrate the feasibility and effectiveness of the proposed approach.