基于鲁棒稳定性的多速率采样控制系统设计

Optimal Design of a Multirate Sampled-Data Control System Based on Robust Stability

提出了基于鲁棒稳定性的多速率采样控制系统设计方法.对于具有给定补偿F的系统,首先拓展Lyapunov上限法得出鲁棒稳定性判定新条件.当系统具有边界不定的不确定性时,定义最大可承受边界为鲁棒稳定半径(Robust Stability Radius,RSR).通过对鲁棒稳定判定条件的分析,可将求解RSR的问题归结为求解一个复杂非线性方程,并利用数值计算方法求解该方程得到解析解.作为F的函数,通过一般优化方法即可实现F优化设计,使得系统RSR最大,而且在保证鲁棒稳定的同时可以承受不确定参数的变化范围最大.最后给出实例,说明了所提方法的可行性和有效性.

This paper concerne bust stability. For a system with a given F＇, a new condition for robust stability test of uncertain system was developed by extending Lyapunov upper bound method. For a system with an unknown uncertainty bound, the robust stability radius （RSR） was defined. The RSR calculation problem could be converted to a mathematical process of solving an equation by analyzing the robust stability test condition proposed. The equation was solved using numerical mathematical methods to get the analytical sol function of F＇, the F＇ optimization design could be achieved by a general optimization me gest RSR. With this F, the system could remain stable with the uncertain parameters v largest. Finally, a simple example was provided to test the feasibility of the proposed.