Vector motion processing using spectral windows

Rapid stepping between constant-velocity segments (vectors) is a common task in industrial motion control. This article describes a procedure for creating smooth and efficient transition motion between arbitrary vectors. Simple linear manipulations permit the functions known as spectral windows to be applied to this problem. Spectral windows are a highly developed technique from digital signal processing and provide a rich source of potentially useful waveforms. The wide range of the windows available in the literature permits us to tailor transitions for a particular system. The ultimate goal is to create a motion preprocessor for industrial systems that improves performance by structuring transition paths to better match the system limitations. In many industry applications, the time spent moving between constant-velocity segments is overhead during which no useful work is performed. Consequently, minimizing the transition period is a desirable goal. By simply inserting an abrupt transition in the commanded position, the resulting motion is determined by the system’s closed-loop response. Practical limitations in the control system response can produce extended settling periods. For example, excessive acceleration can saturate motor current capabilities. Instead of relying on the control system to define the path between vectors, the commanded position can be shaped to produce smooth vector transitions. Depending on the system implementation, settling time can be reduced by preprocessing the raw vectors to explicitly define a vector transition [1]. The preprocessor can dynamically control peak motor current and spectral characteristics. Invariably, the selection of a motion profile involves a tradeoff between conflicting parameters. With respect to spectral characteristics, the selection of an ideal motion profile is analogous to the selection of a spectral windowing function. Windowing functions were created for signal processing applications to tailor the spectral characteristics of a limited-duration waveform. This article describes the application of spectral windows to the generalized problem of vector motion preprocessing. The goal is to control the characteristics of the transition between vectors using the established techniques of spectral windows. A selective group of potentially useful spectral windows is examined, with particular attention to their characteristics for motion control. Finally, to demonstrate the advantage of spectral windows, a specific case involving rapid stepping of a laser beam is investigated.