一种高阶系统的分数阶IMC-ID^μ控制器设计

Design of a fractional order IMC-IDμcontroller for high order systems

针对高阶系统提出了一种模型降阶以及分数阶内模IDμ控制器设计方法。首先基于积分平方误差(ISE)性能指标,利用微粒群优化(Particle Swarm Optimization,PSO)算法将高阶系统模型降阶为含有时滞环节的分数阶模型;然后根据内模控制(Internal Model Control,IMC)原理,并用一阶泰勒表达式逼近模型中的时滞环节,推导出了分数阶IMC-IDμ控制器,该控制器仅包含一个可调参数;最后根据系统的最大灵敏度指标,实现了控制器参数的鲁棒整定。仿真结果表明,本文方法可使系统同时具有较好的动态响应、干扰抑制性能以及克服参数摄动的鲁棒性。

A method of model reduction and fractional order internal model IDμcontroller design was presented for higher order systems.At first,based on the performance index of integral square error （ISE）,particle swarm optimiza-tion （PSO）was used to reduce the higher order system model and a fractional order model with time-delay was ob-tained.Then,according to the principle of internal model control （IMC）,a fractional order IMC-IDμcontroller was derived by approximating the time-delay term of the model with the first-order Taylor series.The controller contained only one adjustable parameter.Finally,the robust tuning of the controller parameter was realized using the maximum sensitivity index of the system.The simulation results showed that the proposed method could make the system having a better dynamic response characteristic,disturbance suppression performance and robustness against the parameters per-turbation of the system.