同步多速率系统H_∞控制的J-无损失共轭化设计

J-lossless conjugated design for synchronous multirate sampled-data system H-infinity control

针对提升后同步多速率控制器存在的因果约束问题,利用J-无损失共轭因子同H∞控制相关的性质,提出了同步多速率系统H∞控制的J-无损失共轭化设计.这一方法将提升后同步多速率系统的H∞控制问题转化成求解共轭因子的问题,即只需求解相关特征值和Lyapunov方程,就可得到满足因果约束条件的控制器和相应闭环系统的参数化形式,同时对提升控制器的因果约束转化为范数有界真有理稳定传递函数矩阵空间BH∞中任意参数的因果约束,同常规的逼近理论相比具有设计过程简单、计算量小等特点.

<Abstrcat> In the illumination of the causal constraint problem for lifted synchronous multirate controller,this article proposes a (J-lossless) conjugator design approach by making use of the properties of the J-lossless conjugator.First,lift the Synchronous multirate sampled-data system (SMRSDS) and deal with it by equivalent discretization.Now the H-infinity control of SMRSDS is equivalent to that of the system with a causal constraint lifted controller.Second,the H-infinity control of discrete system is transformed to the solution of a conjugator which only needs to solve the eigenvalue problem and a Lyapunov equation.At the same time,the causal constraint of the lifted controller is changed to the causal constraint of a random element in BH-infinity.Finally the parameterized forms of the controller are obtained,which satisfy the causal constraint and the corresponding closed-loop system.It has the characteristics of simple design procedure and less computation quantity in comparion with the routine theories.