基于降阶Koopman模型与改进等效输入扰动估计器的非线性系统控制

The Koopman operator enables the representation of nonlinear systems through global linear models. However, such models have high dimensionality and suffer from modeling errors. To address these challenges, the balanced truncation method is first employed to obtain a reduced-order Koopman model that preserves dominant dynamics while mitigating dimensionality. An improved equivalent-input-disturbance (IEID) estimator is then designed based on the reduced-order model to reject the modeling errors and external disturbances. The IEID estimator introduces an additional compensation channel with an adjustable gain to the conventional EID estimator, thus enhancing design flexibility and disturbance-rejection performance. Furthermore, a matrix decomposition technique is employed to decouple the system stability conditions, allowing for the independent design of the controller and the IEID estimator. Simulation results demonstrate that the proposed method achieves superior performance compared to the PI and EID methods in the presence of disturbances and modeling errors.