Nonlinear Robust Control Laws Synthesis for a Magnetic Levitation System: Methods Comparison

The article presents an extended comparative analysis of four modern methods of nonlinear robust control for a magnetic levitation system: adaptive backstepping, the integral adaptation method of synergetic control theory, the synthesis of sliding mode control based on a sequential set of invariant manifolds within synergetic control theory, and classical sliding mode control. For each method, the procedure for synthesizing the control law is described in detail, considering parametric disturbances caused by changes in the active resistance of the electromagnet, which is a typical problem in real systems. А detailed analysis of the closed-loop system stability is performed, and the dynamics are simulated under parametric disturbance. The simulation and comparison results show that methods based on synergetic control theory provide a simpler and more transparent stability analysis, as well as increased robustness to changes in system parameters. In particular, these methods allow avoiding the effect of high-frequency switching in control signals (chattering), typical for classical sliding mode control, which is a significant advantage for practical implementation in industrial and scientific applications. The adaptive backstepping method with dynamic disturbance parameter estimation demonstrated some sensitivity to parametric changes, requiring additional tuning for optimal operation. The obtained results highlight the practical applicability and effectiveness of synergetic control theory methods over classical approaches, opening new prospects for the development of reliable, stable, and precise control systems in high-tech areas, including transportation magnetic levitation technologies, nanopositioning systems, and vibration isolation. This work contributes to expanding the methodological toolkit in the field of adaptive and robust control of nonlinear electromechanical systems, focusing on improving positioning accuracy while maintaining control quality and system stability under internal disturbances.

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