基于等价输入干扰滑模观测器的磁悬浮球系统模型预测控制

本文针对系统不确定性和外部干扰引起的磁悬浮球系统控制性能下降的问题,提出了一种基于等价输入干扰滑模观测器的模型预测控制(MPC+EIDSMO)方法.首先将原系统转化为EID系统,采用等价输入干扰滑模观测器对EID系统状态变量及等价输入干扰进行估计;然后基于状态估计值设计模型预测控制器,并将等价输入干扰估计值以前馈的方式补偿后得到最终的复合控制律,实现对参考位置跟踪的快速性,准确性以及对总扰动的鲁棒性.值得注意的是,与传统EID结构中的龙伯格观测器相比,等价输入干扰滑模观测器中增加的非线性观测误差反馈项有助于提高状态估计的快速性和精确性.从理论上证明了该系统是全局一致毕竟有界的.仿真和实验结果表明,相较于基于EID观测器的模型预测控制方法和基于龙伯格观测器的积分模型预测控制方法,所提方法提高了磁悬浮球系统的跟踪性能,并且有效的抑制了系统不确定性和外部干扰.

Model predictive control for magnetic levitation ball system based on equivalent input disturbance sliding mode observer

To deal with the problem of degradation in control performance of the magnetic levitation ball system caused by uncertainties and external disturbances, this paper presents an equivalent-input-disturbance-sliding-mode-observer based model predictive control (MPC+EIDSMO) scheme. First, an original system is transformed into an EID system, and an equivalent-input-disturbance-sliding-mode-observer is then used to estimate not only the system states but also the equivalent input disturbance. Then, a model predictive controller is designed based on the state estimations, by compensating the estimation of equivalent input disturbance in a feedforward manner, a composite control law is obtained to achieve the rapid and accurate tracking of the reference positions, as well as the robustness against lumped disturbances. It is worth noticing that compared with the conventional EID with a Luenberger observer, an extra nonlinear observation error feedback term from the equivalent-input-disturbance-sliding-mode-observer helps to improve the rapidity and accuracy of the state estimation. This system is proven theoretically to be globally uniformly ultimately bounded. Simulations and experimental results show that compared with the EID observer based model predictive control and Luenberger observer based integral model predictive control, the proposed method improves the tracking performance and suppresses both the uncertainties and the external disturbances effectively for the magnetic levitation ball system