广义离散时间系统的P-D反馈控制器设计

The design of P-D feedback controller for descriptor discrete time systems

针对广义离散时间系统的比例–微分(P-D)反馈控制器的设计问题,本文提出了一种更为简单的方法,使得广义闭环系统正则化,更具因果性、稳定性和容许性。通过线性变换将原系统转化成为正常系统,采用控制理论和变量替换法将双线性不等式转化为严格的线性矩阵不等式(LMI)。基于这种方法,得到广义闭环系统容许性的LMI条件和P-D反馈控制器,最后通过仿真说明该方法的正确性和有效性。

In this paper,the design of the proportional and derivative(P-D)feedback controller for descriptor discrete time systems is studied.A simpler method is proposed to regularize the generalized closed-loop system,which is more causal,stable and admissible.The original system is transformed into a normal system by using the linear transformation,and the bilinear inequality is transformed into a strict linear matrix inequality(LMI)by the control theory and variable substitution method.Based on this method,the LMI conditions and P-D feedback controller of the descriptor closed-loop system admissibility are obtained.The simulation experiment shows that the method is correct and effective.