<p>Suspension control is the core technology for ensuring the operational safety of medium–low-speed maglev trains. To address control performance degradation caused by unknown disturbances and measurement noise, this paper proposes an Adaptive Virtual Extended State Observer-based backstepping control (AVESO-B-S) method. The core innovation lies in expanding the integral of noise-containing measurement output into a new virtual state variable, which effectively decouples the observer gain from noise amplification through an integral filtering mechanism. Furthermore, a gradient-based adaptive law is designed to dynamically optimize the observer bandwidth. This enables the system to autonomously restore stability by driving the bandwidth back into the stable domain, even when initial parameters are suboptimal. Lyapunov analysis establishes asymptotic stability for the nominal error dynamics under the ideal estimation condition, and uniform ultimate boundedness of the actual closed-loop system in the presence of bounded observer error and disturbances. Simulations on the original nonlinear plant model are provided to verify the effectiveness and robustness of the proposed method. Simulation results demonstrate significant performance enhancements across multiple dimensions: (1) in fluctuation response tests, AVESO-B-S achieves a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$61.71\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>61.71</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> reduction in settling time (0.047 s) and a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$56.93\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>56.93</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> decrease in steady-state error (0.263 mm) compared to traditional backstepping. (2) Under external interference, the recovery time is shortened by <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$68.57\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>68.57</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, maintaining a steady-state error of only 0.038 mm. (3) Tracking performance experiments reveals an overshoot-free characteristic, with a response speed <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$50\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>50</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> faster than the ESO-B-S method. (4) Robustness tests show that maximum amplitude fluctuations are suppressed by <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$76.25\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>76.25</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> under magnetic field interference. These results demonstrate that AVESO-B-S can provide improved dynamic adaptability and noise suppression, indicating its potential for practical maglev suspension applications.</p>

Research on Backstepping Control of Maglev System Based on Adaptive Virtual Extended State Observer

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发表日期：

2026年5月7日

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Hongtao Wu,
Jie Yang,
Hailin Hu

摘要

Suspension control is the core technology for ensuring the operational safety of medium–low-speed maglev trains. To address control performance degradation caused by unknown disturbances and measurement noise, this paper proposes an Adaptive Virtual Extended State Observer-based backstepping control (AVESO-B-S) method. The core innovation lies in expanding the integral of noise-containing measurement output into a new virtual state variable, which effectively decouples the observer gain from noise amplification through an integral filtering mechanism. Furthermore, a gradient-based adaptive law is designed to dynamically optimize the observer bandwidth. This enables the system to autonomously restore stability by driving the bandwidth back into the stable domain, even when initial parameters are suboptimal. Lyapunov analysis establishes asymptotic stability for the nominal error dynamics under the ideal estimation condition, and uniform ultimate boundedness of the actual closed-loop system in the presence of bounded observer error and disturbances. Simulations on the original nonlinear plant model are provided to verify the effectiveness and robustness of the proposed method. Simulation results demonstrate significant performance enhancements across multiple dimensions: (1) in fluctuation response tests, AVESO-B-S achieves a $61.71\%$ $61.71 %$ reduction in settling time (0.047 s) and a $56.93\%$ $56.93 %$ decrease in steady-state error (0.263 mm) compared to traditional backstepping. (2) Under external interference, the recovery time is shortened by $68.57\%$ $68.57 %$ , maintaining a steady-state error of only 0.038 mm. (3) Tracking performance experiments reveals an overshoot-free characteristic, with a response speed $50\%$ $50 %$ faster than the ESO-B-S method. (4) Robustness tests show that maximum amplitude fluctuations are suppressed by $76.25\%$ $76.25 %$ under magnetic field interference. These results demonstrate that AVESO-B-S can provide improved dynamic adaptability and noise suppression, indicating its potential for practical maglev suspension applications.