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Author: search.filters.author.Prasitmeeboon, PitchaSubject: search.filters.subject.Repetitive control

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    Repetitive Control Compensator Design for Frequency Response near Singularities
    (2021-12-01)
    Prasitmeeboon, Pitcha
    ;
    Longman, Richard W.
    Repetitive control (RC) aims to achieve zero error from a feedback control system that is subject to a periodic disturbance of known period, or that is executing a periodic command. It can be used in spacecraft for jitter mitigation, for creating active vibration isolation mounts that theoretically can produce complete cancellation of periodic jitter. RC is a feedback loop around an existing feedback control system that adjusts the control system’s command aiming for that command that produces zero error. The design requires creating a compensator that cancels the phase lag through the feedback controller within a tolerance of less that ±90 degrees. The phase behavior of digital systems is presented in detail, exhibiting the possibility of step discontinuities in phase that approach ± 90 degrees. The issue of whether stable RC systems can be designed for sample rates near such discontinuities is addressed. It is shown in numerical studies that compensators that use as few as 2 or 4 gains times previously recorded errors can be sufficient for not only stability, but can give rather fast convergence to zero error for nearly all frequencies except approaching Nyquist frequency. For systems with even pole excess, there can be a different kind of phase singularity that occurs as the sample rate tends to infinity. When designing for fast sample rate it is best to use a larger set of gains to obtain good convergence rate for all frequencies except approaching Nyquist. It was expected that these discontinuities might make it hard to design the RC compensators, but the results indicate that the singularities do not cause serious difficulty in RC design.
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    Min-max merged with quadratic cost for repetitive control of minimum phase systems
    (2018-06-08)
    Prasitmeeboon, Pitcha
    Repetitive control (RC) is an effective method to eliminate the effects of a periodic disturbance to a feedback control system. Applications of RC include an active vibration isolation mount in spacecraft, servomechanisms, and robotic manipulators. Previous work develops a repetitive controller design for non-minimum phase systems using optimization in frequency domain. The objective of the design is to minimize the maximum error merged with quadratic cost, formulated as quadratically constrained linear programming. This work studies how to make use of the Min-Max merged with quadratic cost design for minimum phase systems. An understanding of how to make design choices for the interchange between Min-Max and quadratic cost for each frequency range is developed. The performance of the proposed design choice evaluated by using a simulation of a commercial robot link shows that the design can produce an effective compensator design for minimum phase systems.