Stability determination method of non-linear active-disturbance-rejection control system

Abstract

The invention discloses a stability determination method of a non-linear active -disturbance-rejection control system. The method comprises steps of non-linear auto-disturbance-rejection control system establishment, system conversion, and stability determination of an indirect lurie system based on a robustness Popov criterion. The method has the following beneficial effects: the non-linear auto-disturbance-rejection control system is converted into an indirect lurie system and the system stability can be determined by using the robustness Popov criterion, and thus stability of a nominal system as well as robustness stability of the parameter shooting system can be determined, so that the operation becomes convenient; and the original complex non-linear extended state observer is changed into a variable-gain linear extended state observer and then stability is determined based on a routh criterion, so that the operation becomes simple and convenient.

Description

technical field [0001] The invention belongs to the technical field of automation and relates to a method for judging the stability of a nonlinear active disturbance rejection control system. Background technique [0002] Active disturbance rejection control is a new practical control method proposed by researcher Han Jingqing of the Chinese Academy of Sciences. Its unique control concept has been recognized by people, and its excellent control performance has been confirmed by extensive theoretical analysis and practical applications. The nonlinear active disturbance rejection control proposed by Han Jingqing has certain advantages in terms of anti-disturbance ability and control accuracy because nonlinear functions are used in the design of the extended state observer and control law. However, the introduction of nonlinear functions makes the system motion more complex and the stability and performance analysis more difficult. The stability analysis of nonlinear extended s...

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Problems solved by technology

However, the introduction of nonlinear functions makes the system motion more complex, and the stability and performance analysis is more difficult. The stability analysis of nonlinear extended state observer and nonlinear active disturbance rejection control system has always been a difficult point.

[0003] Using the description function method to study the frequency domain stability of the active disturbance rejection control system with a single and two nonlinear links in the extended state observer, but due to the limited number of nonlinearities, the complexity of the graph transformation and the inherent limitations of the description function method , it is difficult to generalize to the general nonlinear active disturbance rejection system

Based on the Lyapunov stability theorem, the time-domain stability of single-input single-output and multi-input multi-output ADR control systems was studied, and some sufficient conditions for stability were proposed. However, due to too many restrictive conditions and a relatively complicated derivation process , it is difficult to deal with the general active disturbance rejection control system

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