Sampled‐Data PID Control Design for a Class of Uncertain Planar Nonlinear Systems

This work addresses the synthesis of a sampled‐data proportional—integral—derivative (PID) controller for the regulation problem of a class of uncertain planar nonlinear systems in the presence of parametric uncertainties and unknown exogenous constant disturbances. The foundational and underlying philosophy behind the proposed methodology is primarily grounded in an ingenious and judicious leveraging of the feedback domination principle, which elegantly establishes a subtle framework endowed with a tunable domination gain and thereby technically constitutes a transparent and intuitive approach for specifying the control gains and quantifying the maximum allowable sampling period , leading to the construction of a valid sampled‐data PID controller that productively compensates for uncertain nonlinearities, parametric uncertainties, and unknown exogenous constant disturbances while competently and rigorously guaranteeing the attainment of the regulation objective. The notable novelty of this work mainly owes to an explicit design strategy addressing the challenging issue of constructing a viable sampled‐data PID controller for uncertain planar nonlinear systems, together with a concrete guideline directing the systematic joint selection of validated sampled‐data PID control gains and an admissible sampling period toward the regulation purpose. An illustrative numerical example is provided to demonstrate the applicability and efficacy of the presented scheme.