高频增益符号未知时的变结构模型参考自适应控制:任意相对阶的控制律设计

讨论被控对象相对阶大于1且高频增益符号未知时的变结构模型参考自适应控制问题,从而将相对阶为1时的结果推广到任意相对阶.首先对关键信号构造监控函数,并在此基础上提出了一种控制信号切换律.进而证明,当被控对象相对阶大于1、高频增益符号未知时,在监控函数的监测下,相关控制信号经至多有限次切换后将停止切换,跟踪误差将收敛到一个残集内,且该残集可通过减小某些设计参数而变得任意小.特别,本文证明,与相对阶为1时相同,当对象相对阶大于1时,若系统的某些初始条件为零,则至多只需要一次切换.

Variable structure model reference adaptive control with unknown high frequency gain sign:general case

A switching method is presented for the design of a variable structure model reference adaptive control for plants with relative degree greater than one without the knowledge of the sign of the plant high frequency gain.The design is based on some properly chosen monitoring functions.It is shown that under the supervision of the monitoring functions,the switching of control signal will stop after a finite number of switching and the tracking error will converge to a residual set that can be made arbitrarily small by choosing some design parameters sufficiently small.In particular,the same as the earlier work for plants with relative degree one,if some initial states of the system are zero,it is shown that at most one switching is needed.