State Compensation Linearization and Control

TL;DR

This paper introduces a novel state compensation linearization method for nonlinear systems, addressing limitations of existing linearization techniques and enabling the use of linear control methods.

Contribution

It proposes a new linearization approach called state compensation linearization and a control framework based on it, improving nonlinear system control.

Findings

The new method overcomes Jacobian linearization's local approximation issues.

It avoids feedback linearization's singularity and physical meaning loss.

Examples demonstrate the effectiveness of the proposed approach.

Abstract

The linearization method builds a bridge from mature methods for linear systems to nonlinear systems and has been widely used in various areas. There are currently two main linearization methods: Jacobian linearization and feedback linearization. However, the Jacobian linearization method has approximate and local properties, and the feedback linearization method has a singularity problem and loses the physical meaning of the obtained states. Thus, as a kind of complementation, a new linearization method named state compensation linearization is proposed in the paper. Their differences, advantages, and disadvantages are discussed in detail. Based on the state compensation linearization, a state-compensation-linearization-based control framework is proposed for a class of nonlinear systems. Under the new framework, the original problem can be simplified. The framework also allows different control methods, especially those only applicable to linear systems, to be incorporated. Three illustrative examples are also given to show the process and effectiveness of the proposed linearization method and control framework.