一阶滞后对象广义预测控制下的闭环稳定性分析

Closed-loop Stability Analysis of Time-delayed First-order Systems Under Generalized Predictive Control

利用参数模型和非参数模型相结合的方法,给出了一阶滞后对象在广义预测控制下闭环稳定的充要条件。发现:(1)对开环稳定的一阶滞后对象,总存在一组控制器参数,使得在该控制器控制下,无论对象的开环增益K与时间常数T如何变化,闭环系统都保持稳定;(2)对于开环不稳定的一阶滞后对象,无论控制器参数如何选取,当K和T的变化超出一定范围时,闭环系统就会失去稳定性。

The necessary and sufficient conditions are established for the closed loop stability of generalized predictive control （GPC） applied to first order systems with time-delay by combining parametric and non paramet tic models. It is shown that： （1） if the open-loop system is stable, then there must be a controller such that the closed-loop system will remain stable whatever the open-loop gain K and the time constant T change into; （2） while if the open loop system is unstable, then whatever the controller parameters are chosen as, the closed-loop stability will be lost when K and T go out of the stability region.