On the conditions of exponential stability in active disturbance rejection control based on singular perturbation analysis. (English) Zbl 1380.93211
Summary: Stability of Active Disturbance Rejection Control (ADRC) is analyzed in the presence of unknown, nonlinear, and time-varying dynamics. In the framework of singular perturbations, the closed-loop error dynamics are semi-decoupled into a relatively slow subsystem (the feedback loop) and a relatively fast subsystem (the extended state observer), respectively. It is shown, analytically and geometrically, that there exists a unique exponential stable solution if the size of the initial observer error is sufficiently small, i.e. in the same order of the inverse of the observer bandwidth. The process of developing the uniformly asymptotic solution of the system reveals the condition on the stability of the ADRC and the relationship between the rate of change in the total disturbance and the size of the estimation error. The differentiability of the total disturbance is the only assumption made.
MSC:
| 93D20 | Asymptotic stability in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93B07 | Observability |
| 93C70 | Time-scale analysis and singular perturbations in control/observation systems |
Keywords:
active disturbance rejection control; extended state observer; singular perturbation theoryReferences:
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