State Compensation Linearization and Control

TL;DR

This work introduces state compensation linearization (SCLC), a novel linearization method built on additive state decomposition that complements Jacobian and feedback linearization. By decomposing a nonlinear system into a linear primary plant and a nonlinear secondary system, SCLC enables a two-controller framework: stabilize the nonlinear secondary while regulating the linear primary, with an observer estimating both subsystems. The approach preserves physical state interpretation, avoids local limitations and singularities, and enables the use of classical linear control techniques within the primary system. Through three simulation examples, SCLC shows enhanced robustness, better tracking, and superior handling of disturbances, saturations, and delays compared to traditional linearization methods. The framework offers a practical pathway to leverage mature linear control tools for a broad class of nonlinear systems, with future work in stability margins and broader applicability.

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.

Figures (6)

• Figure 1: The construction diagram of the linear primary system from the input $\mathbf{u}_{\text{p}}$ to the state $\mathbf{x}_{\text{p}}$. The primary system can be obtained by subtracting the complementary secondary system from the real system.
• Figure 2: The closed-loop control diagram based on the state-compensation-linearization-based stabilizing control for a class of nonlinear systems
• Figure 3: The state compensation linearization structure. The primary system (\ref{['PSys1']}) from the input $u_{\text{p}}$ to the state $x_{\text{p }}$ is linear, which can be obtained by subtracting the complementary secondary system (\ref{['SSys1']}) from the original system (\ref{['Ex1']}).
• Figure 4: Output response of system (\ref{['Ex1']}) based on the state compensation linearization method (Example 1)
• Figure 5: Output response (Example 2): (a) Compensation linearization method; (b) Jacobian linearization method.