Online Optimal Parameter Compensation method of High-dimensional PID Controller for Robust stability

Classical PID control is widely applied in an engineering system, with parameter regulation relying on a method like Trial - Error Tuning or the Ziegler - Nichols rule, mainly for a Single - Input Single - Output (SISO) system. However, the industrial nonlinear Multiple - Input Multiple - Output (MIMO) system demands a high - robustness PID controller due to strong state coupling, external disturbances, and faults. Existing research on PID parameter regulation for a nonlinear uncertain MIMO system has a significant drawback: it's limited to a specific system type, the control mechanism for a MIMO nonlinear system under disturbances is unclear, the MIMO PID controller over - relies on decoupled control, and lacks dynamic parameter compensation. This paper theoretically analyzes a high - dimensional PID controller for a disturbed nonlinear MIMO system, providing a condition for online dynamic parameter regulation to ensure robust stability. By transforming the parameter regulation into a two - stage minimum eigenvalue problem (EVP) solvable via the interior point method, it enables efficient online tuning. The experiment proves that the designed dynamic compensation algorithm can achieve online robust stability of system errors considering multi - channel input coupling, addressing the key limitation in the field.