Sampled-data polydyne: Feedforward input for high-speed and high-precision positioning control system which does not excite specified mechanical resonant modes

Abstract

This paper proposed a sampled-data polydyne as feedforward input for a high-speed and high-precision positioning control system that does not excite specified mechanical resonant modes. The polydyne curve is an optimal cam profile that does not generate residual vibrations due to the follower's resonant mode. Research papers have reported applications of polydyne curve to feedforward control, and they have been formulated in continuous-time domain. However, when the frequency of vibration to be suppressed is high and the sampling frequency is relatively low, the reference trajectory for feedforward control should be generated in discrete-time domain. The author rederived the polydyne curve from the response of a 1-DOF vibration system driven by an input force defined as a continuous-time polynomial. After that, the sampled-data polydyne was derived in the same way and formulated in discrete-time domain. For suppressing one resonant mode, the order of polynomial must be seventh or higher, and eleventh or higher order is necessary for suppressing two modes. Simulations of seek control in a hard drive was performed to demonstrate the proposed feedforward input using sampled-data polydyne suppressed the residual vibration of control object. The simulation results were compared with the conventional method using sampled-data polynomial. Seventh- and eleventh-order polydynes were compared with the seventh-order sampled-data polynomial. In case of even-order polynomial, on the other hand, the eighth- and twelfth-order polydynes were compared with the sixth-order polynomial. In both cases, it is confirmed that the sampled-data polydyne suppressed the residual vibrations substantially and improved the tracking error after seek motion. Furthermore, it was confirmed that the apparent damping ratio of closed-loop system should be used in generating sampled-data polydyne instead of the mechanical one.

Keywords

• sampled-data system
• feed-forward control
• transient vibration
• residual vibration
• polydyne