针对复杂高阶被控对象控制器设计及参数整定困难问题, 提出了一种基于模型降阶的分数阶鲁棒控制器设计方法。首先将复杂高阶模型近似为含时滞环节的降阶分数阶模型, 根据原模型的奈奎斯特曲线特征, 结合序列二次规划法, 得到降阶近似模型的参数值。在此基础上完成分数阶控制器的结构设计, 通过公式推导, 给出了最大灵敏度鲁棒性指标与控制器整定参数的新的计算方法, 最后结合复合时域性能指标整定控制器参数。仿真结果表明, 所设计模型降阶参数求解无需全局寻优, 收敛速度快, 且降阶模型很好地逼近原系统, 设计的鲁棒控制器使原系统具有良好的控制品质。

In order to overcome the difficulty of controller design and parameter tuning for complex high-order controlled object, a design method for fractional-order robust controller based on model order reduction is proposed. Firstly, the complex high-order model is approximated to a reduced-order fractional-order model with time-delay links. According to the Nyquist curve characteristics of the original model and by using the sequential quadratic programming method, the parameters of the reduced-order approximated model are obtained. Based on this, the structure of a fractional-order controller is designed, and the new numerical calculation methods of the robust index of maximum sensitivity and the controller parameters to be tuned are deduced. Finally, the controller parameters are tuned based on the performance index in composite time domain. Simulation results show that the proposed parameter solving method for model order reduction does not need global optimization, has a fast convergence speed, and the reduced-order model approximates the original system very well. The designed robust controller enables the original system to have a good control quality.