Key Takeaways & Executive Findings
- •• Proposes a novel linear motor active suspension integrated with quasi-zero stiffness air spring to enhance ride comfort and stability for commercial vehicles. • Utilizes polynomial chaos expansion to model and handle random parameter uncertainties in the linear motor, improving control robustness. • Develops a PCE-H2 robust controller with Kalman filter, demonstrating superior ride comfort and stability compared to conventional H2 control. • Validates the proposed approach through both simulation and hardware-in-the-loop experiments, confirming practical applicability.
Abstract
As a crucial component of intelligent chassis systems, air suspension significantly enhances driver comfort and vehicle stability. To further improve the adaptability of commercial vehicles to complex and variable road conditions, this paper proposes a linear motor active suspension with quasi-zero stiffness (QZS) air spring system. Firstly, a dynamic model of the linear motor active suspension with QZS air spring system is established. Secondly, considering the random uncertainties in the linear motor parameters due to manufacturing and environmental factors, a dynamic model and state equations incorporating these uncertainties are constructed using the polynomial chaos expansion (PCE) method. Then, based on H2 robust control theory and the Kalman filter, a state feedback control law is derived, accounting for the random parameter uncertainties. Finally, simulation and hardware-in-the-loop (HIL) experimental results demonstrate that the PCE-H2 robust controller not only provides better performance in terms of vehicle ride comfort compared to general H2 robust controller but also exhibits higher robustness to the effects of random uncertain parameters, resulting in more stable control performance.
1. Introduction
As a core and critical technology of new energy vehicles, the intelligent electronically controlled chassis not only boasts high degrees of freedom and compact structure but also offers significant advantages in improving the natural environment and the utilization of new energy sources [1–5]. Among these technologies, electronically controlled suspension has garnered widespread attention for its role in enhancing ride comfort and driving stability [6, 7]. Air suspension, characterized by its strong load-bearing capacity and low natural frequency, is widely applied in intelligent chassis technology [8–10]. However, with increasingly complex driving environments, a single air suspension system can no longer meet the demands of vehicle operation.
Quasi-zero stiffness (QZS) structures, known for their high static stiffness and low dynamic stiffness, have attracted significant research interest. Chen et al. designed a novel QZS isolator using a pair of torsion springs, inclined rods, and linear bearings to form the positive stiffness part, and connected inclined rods with linear springs perpendicular to the motion direction to provide negative stiffness. This isolator significantly reduces peak vibration amplitude and broadens the isolation frequency range [11]. Yuan et al. proposed a new QZS isolator by arranging three annular coils coaxially with annular magnets to form a linear electromagnetic spring, which is connected in parallel with a traditional linear isolation system. This structure exhibits excellent vibration isolation performance under large excitation conditions [12]. In summary, QZS structures have shown outstanding effects in isolator design, making the design of an air suspension with QZS characteristics crucial for improving the comfort and stability of commercial vehicles on rough roads.
However, our previous research found that while QZS air suspension systems significantly improve ride comfort, the use of magnetorheological dampers and other semi-active suspension actuators is limited by their control output, failing to meet real-time requirements [13–16]. Active suspension systems, compared to semi-active suspension systems, can achieve more precise control to adapt to various driving conditions [17–19]. Linear motors, with their fast response and good controllability, have become a research hotspot in active suspension. Wu et al. designed an active suspension with delay control using linear motors as actuators to improve ride comfort and suspension control efficiency. Simulations and experiments demonstrated significant improvements in vehicle performance [20]. Deng et al. designed an active suspension with energy recovery capabilities using a linear motor and hydraulic hybrid actuator. Simulations and experiments showed stable improvement.
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Pai Li, Xing Xu, Cong Liang, Te Chen, Jiachen Jiang, Vincent Akolbire Atindana (2025). Modeling and Control of the Linear Motor Active Suspension with Quasi-zero Stiffness Air Spring System Using Polynomial Chaos Expansion. Chinese Journal of Mechanical Engineering. https://doi.org/10.1186/s10033-025-01273-z
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Frequently Asked Questions
What is the main contribution of this paper?
The paper proposes a linear motor active suspension with quasi-zero stiffness air spring and develops a robust controller using polynomial chaos expansion to handle parameter uncertainties, improving ride comfort and stability.
How does the polynomial chaos expansion method help in this study?
PCE is used to model random parameter uncertainties in the linear motor, allowing the design of a robust H2 controller that accounts for these uncertainties, leading to more stable control performance.
What are the key findings from the simulation and HIL experiments?
The PCE-H2 robust controller outperforms a general H2 controller in ride comfort and exhibits higher robustness to random parameter variations, as validated by simulation and hardware-in-the-loop tests.
Why is quasi-zero stiffness important for air suspension?
QZS structures provide high static stiffness and low dynamic stiffness, which can significantly reduce vibration transmission and improve isolation performance, making them ideal for enhancing suspension comfort.
What are the practical applications of this research?
The proposed active suspension system can be applied in commercial vehicles to improve ride comfort and stability under complex road conditions, contributing to the development of intelligent chassis systems.
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