概率方法在鲁棒性裕度分析中的应用

将概率思想和方法引入到系统鲁棒性裕度分析中,研究被控对象不确定参数的摄动范围、被控对象的范数摄动范围与概率风险之间的关系,并对传统意义下的鲁棒性裕度和概率意义下的鲁棒性裕度进行了比较和分析.研究结果和计算实例表明,如果允许系统以非常小的概率不稳定,往往可以得到比传统结果显著增大的摄动范围,即在概率意义下提高了系统的鲁棒性裕度,从而在一定程度上克服了传统结果所带来的保守性.这一研究结果具有重要理论意义和工程应用参考价值.

A Probabilistic Approach to the Margin Analysis of Robustness

Probability ideas and approaches are applied to the margin analysis of the robustness of control systems. The relationship between the perturbation range of the controlled plant and probability risk are studied. Comparison between the robustness margin in traditional sense and that in probabilistic sense is made in detail. Research results and examples have shown that on allowing the stability demands to be unfulfilled with a very meager probability, the robustness margin can often be magnified dramatically in the probabilistic sense. These results have important theoretical sense and reference value in the engineering practice.