不确定非仿射系统的引入动态逆的自抗扰控制器设计

针对一类不确定非仿射严反馈非线性系统, 提出一种引入动态逆的线性自抗扰控制器设计方法. 首先, 利 用微分同胚映射将严反馈非线性系统变换为积分串联型系统, 然后针对积分串联型系统设计线性自抗扰控制器. 提出的线性自抗扰控制器将闭环系统划分为3个时间尺度, 其中线性扩张状态观测器位于最快的时间尺度上, 用来 估计系统的状态和总和扰动, 动态逆位于次快的时间尺度上用以求解非仿射情况下的控制律, 系统动态位于最慢的 时间尺度上. 利用奇异摄动理论分析了闭环系统的稳定性和性能. 提出的自抗扰控制设计方法同样适用于控制增 益不确定的仿射非线性系统. 仿真和实验结果验证了提出的线性自抗扰控制器的可行性.

Active disturbance rejection controller for uncertain nonaffine systems by dynamic inversion

This paper presents a linear active disturbance rejection control (LADRC) for nonaffine nonlinear systems with strict-feedback form. Firstly, the strict-feedback nonlinear system is transformed into an integrator-cascaded system by the diffeomorphism, for which the proposed LADRC design method is proposed. The proposed LADRC results in a closed-loop system with a three-time-scale structure. A linear extended state observer (LESO) is designed to estimate unmeasured states and total disturbances in the fastest time scale and dynamic inversion is used to deal with nonaffine inputs in the intermediate time scale while the system dynamics evolves in the slowest time scale. The singular perturbation method is used to analyze the stability and performance of the system. The proposed LADRC can also be applied to affine nonlinear systems with uncertain control gain. Numerical simulations and experimental results are used to demonstrate the effectiveness of the proposed LADRC