控制系统的脆弱性分析

Fragility analysis for control systems

脆弱性是指一闭环系统的稳定性对参数摄动极端敏感.这类系统的开环频率特性经过距临界点(1,j0)的近旁,这种与(1,j0)点之间脆弱的相对关系遇到任何可能的摄动就会遭到破坏.文中分析指出,控制系统的脆弱性可以用Bode积分来进行定量分析.对于一个非最小相位的不稳定对象的控制来说,控制器的不稳定极点与对象的不稳定极点加到一起会大大增加系统灵敏度函数的峰值.故这类系统的设计必然是脆弱的.对于不稳定的多变量对象的控制来说,如果其中一个等价的输出反馈回路中有一个较大的不稳定极点,那么其灵敏度函数也会出现大的峰值,会导致脆弱性,而利用Bode积分则可以避免设计的脆弱性.

Fragility means that the stability of a closed-loop system is extremely sensitive to parameter perturbations. For these systems, the open-loop frequency response is closely passing by the critical stability point （-1,j0）, and the fragile relationship with the point （-1, j0） can easily be violated by any possible perturbation. It is analyzed and pointed out that the fragility of a control system can be quantitatively analyzed by using the Bode integrals. For non-minimum- phase unstable plants, the unstable pole of the controller in addition with the unstable pole of the plant may greatly increase the peak of the sensitivity function. So the resulting design for such systems is unavoidably fragile. For multivariable unstable plants, there may be a rather large unstable pole in an equivalent output feedback loop, which can also cause a large peak of the sensitivity function and results in a fragile design. The Bode integral can also be used to avoid the fragility of the desien.