分数阶系统模糊自适应分数阶PIλDμ控制器

摘要

针对分数阶被控对象,采用分数阶微积分的数值解法,提出了模糊自适应分数阶PIλDμ控制器的数值实现方法与步骤.由于分数阶闭环控制系统的模糊化难以实现,将分数阶PIλDμ控制器与分数阶被控对象构成闭环分数阶控制系统,求其闭环系统在时域内的表达式,再用分数阶微积分的数值解法并结合模糊推理规则,推导出了模糊分数阶PIλDμ控制器的实现步骤,并对其控制系统的单位阶跃响应性能进行了仿真分析.结果表明:所设计的模糊自适应分数阶PIλ Dμ控制器比分数阶PIλ Dμ及传统的整数阶PID控制器表现出较好的控制性能.%The numerical evaluation method of fuzzy self-adaptive fractional order PIλ Dμ controller for fractional order plant was presented by numerical solution of fractional order equation.It was difficult to realize the fuzzification of fractional order closed loop control systems.Therefore,the closed loop expression of fractional order control system was constructed by fractional order PIλ Dμ controller and fractional order plant in the time domain.Then,by the numerical solution of fractional order equation and fuzzy rules,the realized method of fuzzy self-adaptive fractional order PIλ Dμ controller was obtained.Lastly,the performance of control system was analyzed for the fractional order plant by fuzzy self-adaptive fractional order PIλDμ controller.Result shows that the fuzzy self-adaptive fractional order PIλDμ controller demonstrates the better performance compared with fractional order PIλDμ controller and classical PID controller.