执行器饱和和多速率采样的控制设计

Francesco Ferrante, R. Sanfelice, S. Tarbouriech
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引用次数: 1

摘要

研究了在存在饱和执行器和多速率(异步)非周期状态测量时的稳定反馈控制器设计问题。具体地说,我们考虑一个场景,在这个场景中,在控制器端以零星和异步的方式收集工厂状态的测量。采用混合控制器对不同时间采样的测量数据进行融合。在采样事件之间,控制器表现为对象的副本,并提供基于对象状态重建的反馈控制信号。在植物输入处饱和的存在将该信号的分量的值限制在一个有限的范围内。当新的测量值可用时,控制器状态经历瞬时跳转。最终的系统增加了一组计时器,触发新测量的到来,并在混合系统框架中进行分析。基于混合系统的Lyapunov工具和饱和条件下的控制设计技术,我们以矩阵不等式的形式提出了保证包含对象原点的闭集的区域指数稳定性的充分条件,即具有保证吸引区域的指数稳定性。具体地说,以椭球集的形式提供了吸引力盆地的显式估计。利用这些条件,提出了一种基于半确定规划的稳定控制器设计方法,以最大限度地提高流域吸引力。算例表明了所提方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Control Design under Actuator Saturation and Multi-Rate Sampling
The problem of designing a stabilizing feedback controller in the presence of saturating actuators and multi-rate (asynchronous) aperiodic state measurements is studied. Specifically, we consider a scenario in which measurements of the plant states are collected at the controller end in a sporadic and asynchronous fashion. A hybrid controller is used to perform a fusion of measurements sampled at different times. In between sampling events, the controller behaves as a copy of the plant and provides a feedback control signal based on the reconstruction of the plant state. The presence of saturation at the plant input limits the value of the components of this signal to a bounded range. When a new measurement is available, the controller state undergoes an instantaneous jump. The resulting system is augmented with a set of timers triggering the arrival of new measurements and analyzed in a hybrid systems framework. Relying on Lyapunov tools for hybrid systems and techniques for control design under saturation, we propose sufficient conditions in the form of matrix inequalities to ensure regional exponential stability of a closed-set containing the origin of the plant, i.e., exponential stability with a guaranteed region of attraction. Specifically, explicit estimates of the basin of attraction are provided in the form of ellipsoidal sets. Leveraging those conditions, a design procedure based on semidefinite programming is proposed to design a stabilizing controller with maximized size of the basin attraction. The effectiveness of the proposed methodology is shown in an example.
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