P-type iterative learning control for systems that contain resonance.

*(English)*Zbl 1127.93365Summary: The effect of iterative learning control (ILC) on a plant containing resonance has been experimentally investigated using an industrial gantry robot. The plant is controlled by a PID controller and a P-type learning controller in a parallel configuration. It is demonstrated that the learning controller can cause the amplitude of resonant frequencies to grow at each trial, leading to instability. The reasons for this growth are analysed both theoretically and experimentally. In order to solve the problem with a resonance, a straightforward aliasing technique is developed which is experimentally shown to suppress the increase of resonant amplitudes. The novel aliasing technique is compared with three filtering methods, the aliasing technique giving the best experimental performance. Finally, it is found that additional velocity feedback combined with the aliasing technique can further help to limit the effect of residual resonance. Due to the straightforward implementation of these algorithms, they should be highly applicable to industrial systems.

##### MSC:

93E35 | Stochastic learning and adaptive control |

93E11 | Filtering in stochastic control theory |

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

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\textit{J. D. Ratcliffe} et al., Int. J. Adapt. Control Signal Process. 19, No. 10, 769--796 (2005; Zbl 1127.93365)

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