Active disturbance rejection in affine nonlinear systems based on equivalent-input-disturbance approach.

*(English)*Zbl 1386.93085Summary: This paper presents a disturbance rejection method for an affine nonlinear system. The control system is constructed based on the equivalent-input-disturbance (EID) approach. An affine nonlinear state observer is used to reconstruct the state of the affine nonlinear system and to estimate an EID. The well-known differential mean value theorem enables us to describe the closed-loop system in the state space as a linear-parameter-varying system. This makes it easy to derive sufficient conditions of global uniform ultimate boundedness in term of linear matrix inequalities (LMIs) by using a Lyapunov function and convexity theory. Controllers are designed based on the LMIs. A numerical example is used to illustrate the design of the control system. And a comparison between the EID-based control and the sliding-mode control demonstrates the effectiveness and advantages of the EID-based control method.

##### MSC:

93B35 | Sensitivity (robustness) |

93C10 | Nonlinear systems in control theory |

93C73 | Perturbations in control/observation systems |

93D30 | Lyapunov and storage functions |

93C15 | Control/observation systems governed by ordinary differential equations |