基于模糊奇异摄动模型的直接型自适应控制器的设计

Design of a Direct Adaptive Controller Based on Singularly Perturbed Model

一大类非线性奇异摄动系统可以由模糊奇异摄动模型进行近似逼近,由于柔性模态的影响,对该类系统的控制比较困难。特别在被控对象数学模型未知时,很难获得模糊奇异摄动模型的规则后件参数。为解决此种情况下的模型跟踪控制问题,提出一种新型的基于模糊奇异摄动模型的直接型自适应控制器,该控制器的状态反馈增益能够在线自适应调整,不需要已知被控对象的数学模型,就能使得闭环系统的状态跟踪参考模型状态。闭环系统的稳态及动态性能可以通过选择稳定参考模型的参数矩阵和参考输入向量进行设计。应用李亚普诺夫合成方法证明闭环系统稳定性。最后,仿真结果验证了该方法的有效性。

A class of nonlinear singularly perturbed systems can be approximated by the Fuzzy Singularly Perturbed Model（FSPM）.It is not easy to design a controller for them.The consequence parameters of the FSPM can be hardly attained when the mathmatic model of the plant is unknown.In this paper,we proposed a new direct adaptive controller on the basis of the FSPM to solve the above-mentioned problem.The gains of the states feedback controller could be adjusted online to make the states of the closed-loop system follow those of the reference model,even with model unknown in prior.The stable and the dynamic performances of the whole closed-loop system could be designed by choosing the appropriate parameter matrix and input of the stable reference models.Lyapunov constitute techniques were used to prove the stability of the closed loop systems.Finally the simulations illustrate the effectiveness of this approach.