Research on Multirate Digital Control Systems

本文利用“扩展状态向量”导出了多采样率数字控制系统的状态方程。在此基础上，建立了Nyquist型稳定性条件和Gershgorin带理论。完成了稳定性分析的计算机程序和一个模拟器。同时，研究了多速率输入系统和多速率输出系统的极点配置问题。假设被控对象是完全可控和可观测的，证明了当多速率输入系统的输入重数大于或等于可控性指标时，当多速率输出系统的输出重数大于或等于可观性指标时，闭环系统的任意对称极点配置是可能的.此外，关于多速率输出的情况下，它表明，任意对称极点配置的控制器本身是可能的，如果输出的多重性设置大于或等于angmented系统（即系统添加了一个积分器在每个输出）的可观性指标。为了研究由上述极点配置方法得到的控制系统的性能，利用稳定性分析程序和仿真器研究了几个例子。

State equations are derived for the multirate digital control systems by using an "extended state vector." Based on this equation, a Nyquisttype stability condition and theory of Gershgorin bands are established. Computer programs for the stability analysis and a simulator are completed. At the same time, the pole assignment problem is studied both for multirate-input systems and multirate-output systems. Assuming that the controlled object is completely controllable and observable, it was proved that arbitrary symmetric pole assignment of the closed loop system is possible, if the input multiplicities are set larger than or equal to the controllability indices in the case of multirate-input systems, and if the output multiplicities are set larger than or equal to the observability indices in the case of multirate-output systems. In addition, concerning the multirate-output case, it was shown that arbitrary symmetric pole assignment of the controller itself is possible if the output multiplicities are set larger than or equal to the observability indices of the angmented system (i.e. the system added with an integrator at each output). To study the performance of the control systems obtained by the above mentioned pole-assignment method, several examples are studied by using the stability-analysis programs and the simulator.