多电机驱动系统的保性能鲁棒Funnel控制

本文针对含参数不确定性的多电机驱动系统,提出一种基于最优保性能鲁棒的Funnel控制方法实现系统的规定跟踪性能.该控制方法通过构造Funnel函数对误差系统进行变换,并设计自适应反步控制器保证变换后系统的稳定性即可使跟踪误差的瞬态和稳态响应均被限制在给定的Funnel边界内.然而由于系统中存在的参数不确定性会影响系统的规定控制性能,本文在Funnel控制基础上又设计了最优保性能鲁棒控制器.它是通过将参数不确定性系统的保性能鲁棒控制问题转化为标称系统的最优控制问题,并求解新的黎卡提方程而得到的.因此所设计的控制器不但消除了参数不确定性对系统的影响并且能够使系统的性能指标达到一确定的上界.最后,对四电机驱动系统进行了仿真和实验验证,说明所提出控制方法的有效性.

Optimal robust guaranteed cost funnel control for multi-motor driving system

This paper proposes an optimal robust guaranteed cost funnel control scheme for the multi-motor driving system with parameter uncertainties to achieve the prescribed tracking performance. By constructing a funnel function to transform the tracking error system, an adaptive backstepping controller is designed to stabilize the transformed error system, which can guarantee the tracking error constrained within the funnel boundaries. However, since there are the parameter uncertainties existing in the system which may influence the prescribed tracking performance, an optimal robust guaranteed cost controller is constructed by transforming the robust guaranteed cost control problem of the uncertain system into the optimal control problem of the nominal system and then solving the new Riccati equation. Therefore, the proposed controller can not only deal with the influence of the parameter uncertainties on the system, but also make the cost function reach a certain upper bound. Finally, simulation and experimental results based on a four-motor driving system demonstrate the effectiveness of the proposed scheme.