一类线性不确定系统控制器设计的参数空间方法

On Parameter Space Approach to Design of Linear System with Uncertain Parameters

讨论了线性不确定系统控制器的设计问题.首先将不确定系统表述成多模形式,然后用参数空间方法解决了多模系统控制器的设计问题.提出了一种新的方法——网格法,它较 Ackermann 等人提出的方法更加简单,可方便地求出三阶和三阶以上系统满足—稳定性的参数空间.最后将此方法成功地用于设计实例中.

In 1980,Ackermann proposed a method for computing parameter space of linear system withuncertain parameters;it is still widely used in the case of one pole assignment region.In the case of manypole assignment regions,Ackermann's method becomes too complicated.In this paper,a new method——Net Method——is presented that is quite convenient to use regardless of the number of pole assignmentregions.First,the pole assignment regions are divided into nets.The net points in pole assignment regions aremade up of a set of points.Then the set of points is mapped into parameter space of the system using poleassignment theory.The map in parameter space represents the set of points of parameter space.Anyparameter vector in it can place closed-loop poles of system within preseribed regions.Finally,continulityof parameter space is utilized to obtain the boundary of the set of points.Such a boundary is the requiredsolution.Two design examples are given.They indicate that the Net Method is successful.