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Active disturbance rejection control to stabilize one-dimensional wave equation with interior domain anti-damping and boundary disturbance. (Chinese. English summary) Zbl 1299.93247
Summary: The control objective is the asymptotic stabilization with disturbance rejection or the practical stabilization with disturbance attenuation. Back-stepping method and Active Disturbance Rejection Control (ADRC) approach are adopted in investigation. It is shown that the disturbance can be estimated in real time through an Extended State Observer (ESO) and be canceled in the feedback loop. Both constant gain and time-varying gain are used in ESO. To avoid the peaking value problem caused by the constant high gain in ESO, we use the saturated function method in feedback loop. The time-varying gain in ESO is first time used in an infinite-dimensional system to achieve complete disturbance rejection and peaking value reduction.

MSC:
93D20 Asymptotic stability in control theory
93C20 Control/observation systems governed by partial differential equations
93C73 Perturbations in control/observation systems
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