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The multi-period repetitive control system is a type of servomechanism for a periodic reference input. Even if a plant does not include time-delays, using multi-period repetitive controllers, the transfer function from the periodic reference input to the output and that from the disturbance to the output of the multi-period repetitive control system generally have infinite numbers of poles. To specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada and Takenaga proposed the concept of simple multi-period repetitive control systems, such that the controller works as a stabilizing multi-period repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles.
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