Fractional order ultra low-speed position servo: improved performance via describing function analysis

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.