Department of Automation Science and Engineering, South China University of Technology, Guangzhou, China.
ISA Trans. 2011 Jan;50(1):53-60. doi: 10.1016/j.isatra.2010.09.003. Epub 2010 Oct 25.
In a reference of the previous work, a new systematic design method for fractional order proportional and derivative (FOPD) controller is proposed for a class of typical second-order plants. Simulation and experimental results in the reference show that, the dynamic performance and robustness with the designed FOPD controller outperforms that with the optimized traditional integer order proportional integral (IOPI) controller at normal speed. Furthermore, it is found that, for the ultra low-speed position tracking with a significant friction effect, the tracking performance using the designed FOPD controller is much better than that using the optimized IOPI controller. However, the reason of this advantage is unclear. In this paper, using the describing function method and Bode plots analysis, the observed advantage of the designed FOPD controller over the optimized IOPI controller, for the nonlinear low-speed position tracking system with friction effect, is explained with the theoretical analysis. This explanation for the priority of the designed FOPD controller is consistently demonstrated by the extended experimental results in this paper.
在对以往工作的参考中，提出了一种针对典型二阶系统的分数阶比例导数（FOPD）控制器的新系统设计方法。参考文献中的仿真和实验结果表明，在正常速度下，设计的 FOPD 控制器的动态性能和鲁棒性优于优化的传统整数阶比例积分（IOPI）控制器。此外，研究发现，对于具有显著摩擦效应的超低速位置跟踪，使用设计的 FOPD 控制器的跟踪性能明显优于使用优化的 IOPI 控制器。然而，这种优势的原因尚不清楚。本文利用描述函数法和波特图分析，从理论上解释了设计的 FOPD 控制器相对于优化的 IOPI 控制器的优势，这种优势适用于具有摩擦效应的非线性低速位置跟踪系统。本文扩展的实验结果一致地证明了设计的 FOPD 控制器的优先级。
