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<p>Modern active suspensions require controllers that can suppress vibration, satisfy hard physical constraints, and remain robust under nonlinear dynamics, road disturbances, and parameter uncertainties. Robust sliding mode control (SMC) is well suited to this task, but its performance strongly depends on the sliding-surface and switching parameters, whose tuning involves a conflicting trade-off between ride comfort and energy consumption. Although multi-objective particle swarm optimization (MOPSO) is a natural solver for this problem, standard variants often suffer from premature convergence because their search parameters are scheduled in an open-loop manner and cannot react to the real-time diversity state of the swarm. To address this tuning bottleneck, this paper proposes an entropy-driven adaptive MOPSO (EAMOPSO) for robust SMC co-design. The proposed method introduces a normalized disorder coefficient derived from Shannon entropy to quantify the swarm’s exploration-exploitation state and adaptively regulate the velocity-update parameters and Gaussian mutation process. A Lyapunov analysis proves the stability of the robust SMC under bounded uncertainties, and the computational complexity of EAMOPSO is analyzed. The proposed framework is validated on a nonlinear quarter-car active suspension model under slope-step, impulsive bump, non-stationary random, and parameter-uncertainty scenarios. Compared with non-optimized SMC, EAMOPSO-SMC reduces the vehicle body acceleration index by 47.26% and 30.07% under bump and random excitations, respectively. Under bump excitation, it also reduces the ride-comfort index by 96.0% relative to a conventional PID controller. Additional case studies further show that the proposed method consistently outperforms representative baseline controllers and preserves feasible constraint satisfaction under parameter uncertainties. These results demonstrate that the proposed entropy-driven mechanism improves Pareto-front quality and provides a robust, energy-aware controller design for nonlinear active suspensions.</p>

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Entropy-driven adaptive MOPSO for enhancing robust sliding mode control of nonlinear active suspensions under diverse road excitations

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Benzhe Zhao,
  • Ying Xin,
  • Zhichang Qin

摘要

Modern active suspensions require controllers that can suppress vibration, satisfy hard physical constraints, and remain robust under nonlinear dynamics, road disturbances, and parameter uncertainties. Robust sliding mode control (SMC) is well suited to this task, but its performance strongly depends on the sliding-surface and switching parameters, whose tuning involves a conflicting trade-off between ride comfort and energy consumption. Although multi-objective particle swarm optimization (MOPSO) is a natural solver for this problem, standard variants often suffer from premature convergence because their search parameters are scheduled in an open-loop manner and cannot react to the real-time diversity state of the swarm. To address this tuning bottleneck, this paper proposes an entropy-driven adaptive MOPSO (EAMOPSO) for robust SMC co-design. The proposed method introduces a normalized disorder coefficient derived from Shannon entropy to quantify the swarm’s exploration-exploitation state and adaptively regulate the velocity-update parameters and Gaussian mutation process. A Lyapunov analysis proves the stability of the robust SMC under bounded uncertainties, and the computational complexity of EAMOPSO is analyzed. The proposed framework is validated on a nonlinear quarter-car active suspension model under slope-step, impulsive bump, non-stationary random, and parameter-uncertainty scenarios. Compared with non-optimized SMC, EAMOPSO-SMC reduces the vehicle body acceleration index by 47.26% and 30.07% under bump and random excitations, respectively. Under bump excitation, it also reduces the ride-comfort index by 96.0% relative to a conventional PID controller. Additional case studies further show that the proposed method consistently outperforms representative baseline controllers and preserves feasible constraint satisfaction under parameter uncertainties. These results demonstrate that the proposed entropy-driven mechanism improves Pareto-front quality and provides a robust, energy-aware controller design for nonlinear active suspensions.