Sliding mode control of a discrete system.

*(English)*Zbl 0692.93043Summary: Conventional sliding mode control designed on the basis of a continuous system is known to be robust to the plant uncertainties. A realized digital system, however, not only yields chattering, but also may become unstable by a long sampling interval.

This paper presents a stable discrete sliding mode control insensitive to the choice of the sampling interval and not yielding chattering. The control system is designed on the basis of a discrete Lyapunov function and a sufficient condition of the control gain to make the system stable is given. Contrary to the continuous case, the derived switching plane of the control law is different from the sliding mode, and in its neighborhood, the control law is given by the linear state feedback. Simulations show the effectiveness of the proposed method.

This paper presents a stable discrete sliding mode control insensitive to the choice of the sampling interval and not yielding chattering. The control system is designed on the basis of a discrete Lyapunov function and a sufficient condition of the control gain to make the system stable is given. Contrary to the continuous case, the derived switching plane of the control law is different from the sliding mode, and in its neighborhood, the control law is given by the linear state feedback. Simulations show the effectiveness of the proposed method.

##### MSC:

93C10 | Nonlinear systems in control theory |

93C57 | Sampled-data control/observation systems |

93B35 | Sensitivity (robustness) |

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\textit{K. Furuta}, Syst. Control Lett. 14, No. 2, 145--152 (1990; Zbl 0692.93043)

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##### References:

[1] | Taran, V.A., Improving the dynamic properties of automatic control systems by means of nonlinear corrections and variable structure, Automat. remote control, 25, 140-149, (1964) |

[2] | Utkin, V.I., Variable structure systems with sliding mode, a survey, IEEE trans. automat. control, 22, 212-222, (1977) · Zbl 0382.93036 |

[3] | Utkin, V.I.; Yang, K.D., Methods for constructing discontinuity planes in multidimensional variable structure systems, Automat. remote control, 10, 72-77, (1978) · Zbl 0419.93045 |

[4] | Young, K.D.; Kokotovic, P.V.; Utkin, V.I., A singular perturbation analysis of high-gain feedback systems, IEEE trans. automat. control, 22, 931-938, (1977) · Zbl 0382.49029 |

[5] | Slotine, J.J., The robust control of robot manipulators, Internat. J. robotics res., 4, 49-64, (1985) |

[6] | Slotine, J.J.; Sastry, S.S., Tracking control of nonlinear systems using sliding surfaces, with application to robot manipulators, Internat. J. control, 38, 465-492, (1983) · Zbl 0519.93036 |

[7] | Harashima, F.; Maruyama, K.; Hashimoto, H., A microprocessor-based manipulator control with sliding mode, (), 9-14 |

[8] | Young, K.D.; Kwanty, H.G., Variable structure servomechanism design and applications to overspeed protection control, Automatica, 18, 385-400, (1982) · Zbl 0485.93047 |

[9] | Furuta, K.; Morisada, M., Implementation of sliding mode control by a digital computer, (), 453-458 |

[10] | Ddrakunow, S.V.; Utkin, V.I., On discrete-time sliding modes, (), to appear |

[11] | Furuta, K., VSS-type self-tuning control of direct-drive motor, (), 281-286 |

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