一类具有量化误差的多步长非线性采样系统的镇定

Stabilization of multirate nonlinear sampled-data systems with quantization

中文关键词  非线性  多步长采样  量化误差  实用稳定  欧拉近似  一致最终有界

英文关键词  nonlinearity  multirate sampling  quantization error  practical stability  Euler approximation  uniformly ultimately bounded

中文摘要

      基于连续时间系统模型进行控制器设计, 离散化后执行采样控制的方法, 研究一类具有量化误差的多步长非线性采样系统的镇定问题. 由于非线性因素而无法使用提升技术以及系统状态仅在采样时刻可检测的事实, 控制器中不可检测的系统状态被以采样时刻的状态为初始状态的欧拉叠代近似所获得的近似状态所替换. 在采样系统的保持周期可调节的情况下, 运用此修正控制器来镇定整个多步长非线性采样系统, 可得系统近似误差和采样量化误差可分离的结果; 同时利用李雅普诺夫函数方法, 克服近似误差和量化误差的双重影响, 得到系统实用镇定的结果. 最后, 仿真例子验证了本文的结果有效.

英文摘要

      The stabilization of multirate nonlinear sampled-data systems with quantization is studied in this paper for designing a controller based on the continuous-time plant model and discret sampled-data implementation. Since the lifting technique is not applicable for the case of nonlinearity and the plant states are measured only at sampling times, the controller’s state is replaced by the approximate state obtained by taking the sampling state as the initial state for the process of Euler iterative approximation. When this modified controller is applied to stabilize a closed-loop sampled-data control system with adjustable holder period, the approximate error and sampling quantization error can be separated. Moreover, the system is practical stabilizable by using the Laypunov function method to deal with the double affects of approximate error and sampling quantization error. Finally, the simulation example shows the desired result.