不确定机械系统的二阶逼近模糊滑模控制
Fuzzy Sliding Mode Control of Uncertainty Mechanical System with Second Order Approximation Accuracy

针对不确定机械系统，利用模糊逻辑系统的万能逼近特性对未知非线性函数建模，以便设计控制方法。基于一阶逼近精度的模糊逻辑系统需要足够多的模糊规则才能保证一定的逼近精度，然而规则数的增多必然导致计算量的增大，不利于实时控制。本文中设计了具有二阶逼近精度的模糊逻辑系统对机械系统中的非线性未知部分进行实时逼近，并结合鲁棒性能好的滑模控制对不确定机械系统进行轨迹跟踪控制。从仿真实验证明，具有二阶逼近精度的模糊系统可以以很少的规则高精度的逼近任意非线性函数，并以此为基础构成的模糊滑模控制器不仅可以达到所希望的控制精度，比起规则数量多得多的模糊滑模控制，甚至位置误差和速度误差更小，跟踪速度更快。故采用特殊隶属函数所设计的自适应模糊逻辑系统，解决了逼近精度和模糊规则数量之间的矛盾，为机械系统的高精度的实时控制提供了保证。
The universal approximation of a fuzzy logic system is used to establish the unknown nonlinear function model of an uncertainty mechanical system. The fuzzy logic system based on the first-order approximation accuracy needs many fuzzy rules to ensure the certain approximation accuracy. However, the increase of the number of rules will inevitably lead to the increase of computational complexity. In this paper, a fuzzy logic system with second-order approximation accuracy is designed to approximate the unknown nonlinear part of the uncertainty mechanical system, whose trajectory tracking control is carried out with the sliding mode control. Simulation results prove that the fuzzy logic system with second-order approximation accuracy can greatly reduce the number of fuzzy rules and can approximate any nonlinear functions with high precision. Therefore, the adaptive fuzzy logic system designed with the special membership function solves the contradiction between approximation accuracy and number of fuzzy rules and provides guarantees for the high-accuracy and real-time control of the uncertainty mechanical system