An optimal and adaptive design of the feedforward motion controller

The zero phase error tracking controller (ZPETC) in motion control, as proposed by Tomizuka (1987) , renders the desirable zero phase error, but with a limited gain response. Moreover, a ZPETC, which is basically in a feedforward control structure, is very sensitive to modeling error. To improve the tracking accuracy of the ZPETC, this paper presents an optimal ZPETC design with a concise polynomial digital prefilter (DPF). The parameters of this well-designed DPF are obtained through the derived L₂-norm optimization. By cascading the developed DPF to the ZPETC, the resultant optimal ZPETC greatly improves the bandwidth of the tracking control systems while maintaining the zero phase error. Compared with other optimal approaches, the present design leads to much simpler procedures and fewer computations. Furthermore, the proposed optimal ZPETC can be adequately implemented as an adaptive ZPETC by including real-time estimation technique to cope with the external load perturbation and parameter variation. Compared with the other adaptive approaches, the optimal concept is used in the present adaptive ZPETC, and it also renders more accurate results because of its improved magnitude response. Experimental results on a DC servo table with different controllers indicate that when there is no loading, the present optimal ZPETC achieves the best tracking performance. Moreover, the adaptive ZPETC achieves the most satisfactory results when an external load is applied