Linear Motor Waveform Ramping for Smooth Startup and Stop

The patent applies preliminary action by pre-processing the steady-state waveform to add smooth transition segments at the beginning and end. Before the motor starts, the waveform gradually increases from zero amplitude to the target amplitude over the startup time period. Before the motor stops, the waveform gradually decreases from the target amplitude to zero over the stop time period. This preliminary shaping of the waveform prevents sudden amplitude changes that cause overdrive, while maintaining the ability to operate at non-resonant frequencies.

The patent segments the waveform into distinct phases: a startup phase where amplitude smoothly transitions from zero to the target level, a steady-state phase where the motor operates at the desired frequency, and a stop phase where amplitude smoothly transitions back to zero. By dividing the waveform into these segments with different characteristics, the patent eliminates abrupt amplitude changes that cause overdrive and noise, while keeping each segment relatively simple in structure.