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**Robust control of discretized continuous systems using the theory of sliding modes.**
*(English)*
Zbl 0827.93014

Summary: The idea of sliding mode control (SMC) as a robust control technique is utilized to control systems where the dynamics can be described by \(\dot x(t)= (A+ \Delta A) x(t)+ (B+ \Delta B) u(t)+ d(t)\) where \(\Delta A\), \(\Delta B\) and \(d(t)\) characterize unknown plant parameters and unexpected disturbances, respectively. The analysis is described in the discrete form using the Euler operator. The proposed controller regards the influence of unknown disturbances and parameter uncertainties as an equivalent disturbance and generates a control function (estimate) to cancel their influence by the mechanism of time delay. The states of the uncertain plant are steered from an arbitrary initial state to a stable surface, \(s= 0\), and the plant output is subsequently regulated. One feature of the control is that the sliding conditions are satisfied without the discontinuous control action used in classical SMC. It therefore retains the positive features of SMC without the disadvantage of control chattering. The controller has been studied through simulations and experiment on an NSK direct drive robot arm driven by a DC motor. The results confirm that the control is robust to disturbances and parameter variations.

### MSC:

93B12 | Variable structure systems |

93C57 | Sampled-data control/observation systems |

34K35 | Control problems for functional-differential equations |

93B35 | Sensitivity (robustness) |

93C73 | Perturbations in control/observation systems |

### Keywords:

sliding mode control; robust; discrete; unknown disturbances; parameter uncertainties; time delay; chattering
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\textit{A. Tesfaye} and \textit{M. Tomizuka}, Int. J. Control 62, No. 1, 209--226 (1995; Zbl 0827.93014)

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### References:

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