Self-adaptive control method for fractional order system influenced by saturated nonlinear input

Abstract

The invention discloses an adaptive control method for a fractional order system influenced by saturated nonlinear input, and the method specifically comprises the following steps: building a fractional order system mathematic model for describing a class of physical objects or processes, and carrying out the designing of a fractional order sliding mode surface according to a fractional order calculus theory; determining an adaptive updating law of unknown parameters in the fractional order mathematical model; designing a self-adaptive controller of the controlled system according to a fractional order stability theory and a saturated nonlinear input characteristic; and searching an appropriate Lyapunov function to verify the finite time accessibility of a sliding mode approaching stage. According to the invention, the adaptive control of the fractional order system under the influence of input nonlinearity can be realized; when unmodeled dynamics with unknown upper bound and external interference occur in the system, it can be guaranteed that a state trajectory reaches a sliding mode surface within limited time under the action of a designed controller; through the sliding mode action, the purpose that the state trajectory of the controlled system converges to zero is achieved, the self-adaptive identification of unknown parameters is achieved, and the control purpose is achieved.

Description

technical field [0001] The invention belongs to the technical field of stabilizing control of fractional-order systems, and in particular relates to a fractional-order system self-adaptive control method with a special structure affected by saturated nonlinear input. Background technique [0002] Due to the uniqueness of fractional calculus operators, fractional-order systems are particularly suitable for describing physical transformation processes that are time-dependent, have memory properties, and are related to history, such as the memory properties of viscoelastic materials and the viscous properties of rheological mechanics , the spacecraft is subjected to dynamic and static loads, etc., and objects with such properties or dynamic characteristics can be seen everywhere in the actual system. Gyroscopes are widely used in spacecraft and other mechanical equipment. The accuracy of mathematical modeling of gyroscopes directly affects the control performance of the designe...

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Problems solved by technology

In the production and control of complex industrial systems, the input is often affected by nonlinearity. Saturation nonlinearity is one of the common ones. The input nonlinearity will seriously affect the system performance and even destroy the system stability.

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