Robust Convergency Indicator using High-dimension PID Controller in the presence of disturbance

The PID controller currently occupies a prominent position as the most prevalent control architecture, which has achieved groundbreaking success across extensive implications. However, its parameters online regulation remains a formidable challenge. The majority of existing theories hinge on the linear constant system structure, contemplating only Single-Input, Single-Output (SISO) scenarios. Restricted research has been conducted on the intricate PID control problem within high-dimensional, Multi-Input, Multi-Output (MIMO) nonlinear systems that incorporate disturbances. This research, providing insights on the velocity form of nonlinear system, aims to bolster the controller's robustness. It establishes a quantitative metric to assess the robustness of high-dimensional PID controller, elucidates the pivotal theory regarding robustness's impact on error exponential convergence, and introduces a localized compensation strategy to optimize the robustness indicator. Guided by these theoretical insights, we exploit a robust high-dimensional PID (RH-PID) controller without the crutch of oversimplifying assumptions. Experimental results demonstrate the controller's commendable exponential stabilization efficacy and the controller exhibits exceptional robustness under the robust indicator's guidance. Notably, the robust convergence indicator can also effectively evaluate the comprehensive performance.