H_∞鲁棒控制中的加权阵选择

Weighting function matrix selection in H ∞ robust control

研究了线性时不变系统Ｈ∞鲁棒控制中的加权阵选择问题，探讨了在一般的跟踪控制问题的Ｈ∞设计中如何选择三个合适的加权阵，确定广义受控对象，使设计满足多目标的要求等问题。提出了在频率域中选择加权阵，再转化到状态空间进行优化设计。考虑一大类存在低频参数摄动和高频未建模动态的情况，给出了鲁棒控制兼顾闭环动态特性和干扰抑制时的加权阵选择方法与具体步骤。并就一具体例子进行了仿真，结果表明将控制量的加权阵作为调整参数进行设计对提高闭环系统的鲁棒性是有益的。这里加权阵的选择方法，既适用ＳＩＳＯ系统，也适用ＭＩＭＯ系统。

To discuss the selection of weighting function matrixes in H ∞ robust control system design for linear time invariant systems shows rules for selecting three weighting function matrixes to satisfy multiple H ∞ design targets for general tracking control problems. Weighting function matrixes are selected in the frequency domain with feedback tracking properties and output disturbance rejection considered. Optimization is made in the state space. Existing low frequency parametric perturbations and high frequency unmodelled dynamics are considered. Steps of weighting function matrix selection are given. Simulation is performed for an actual plant model. The result shows that it is useful for the good closed loop system robust performance to adjust weighting function of control output in H ∞ design. This method can be applied to both SISO and MIMO systems.