一种非最小相位系统的非线性控制器设计方法

为解决非线性系统状态反馈线性化过程中出现的非最小相位问题，设计了一种非线性控制器实现对非最小相位环节的有效控制；通过微分同胚映射将原非线性系统变换为线性化标准型形式，此标准型由线性子系统描述的外部动态和由非线性子系统描述的内部动态(即零动态)构成；基于极点配置和李雅普诺夫稳定性理论，给出了一种零动态不稳定系统(即非最小相位系统)非线性控制器设计方法。数值算例仿真结果表明，该方法所设计的控制器既能确保外部动态满足性能要求同时也能保证零动态稳定。

A nonlinear controller design method for non-minimum phase systems

In order to solve the non-minimum phase problem that arises from the nonlinear control method of state-feedback linearization, a nonlinear controller was designed to control the non-minimum phase effectively. First, through a differential homeomorphism transformation, the original nonlinear systems were transformed into a linearization canonical form, which was composed of the external dynamics described by a linear sub-system and the internal dynamics(namely zero dynamics)described by a nonlinear sub-system. Then, a nonlinear controller design method was developed for the non-minimum phase system, in which zero dynamics were unstable, based on pole assignment and Lyapunov stability theory. Numerical simulations show that, not only can the controller designed by the developed method meet the performance requirements of external dynamics, it can also guarantee the stability of zero dynamics.