多变量系统l^1最优反馈控制器的解耦设计方法

Design of l^1 Optimal Feedback Controller for MIMO Systems with Decoupling

本文提出了一种多变量系统l^1最优反馈控制器设计方法。通过解耦灵敏度函数,使多变量系统的设计问题转化为若干个单变量系统设计问题。分别求解后,求出l^1优化控制器。文中还进一步讨论了在z平面单位圆内有重零、极点的单变量系统l^1优化控制器的求解问题,给出了这种情况下最优灵敏度函数次数的上界。

A new design method for an l1 optimal controller for MIMO systems is presented. By decoupling the sensitivity function, a multivariable system design problem can be transformed into one with several SISO problems. After solving these SISO system problems, the l1 optimal controller for a MIMO system can be obtained from the decoupled optimal sensitivity function. This design method simplifies the computation and eliminates the interaction of disturbance signals to the system outputs. The design problem of optimal controller for SISO system with repeated zeros and poles in unit disk is also discussed with the upper bound of the degree of the optimal sensitivity function given.