Advance the stability of the vehicle by using the pneumatic suspension system integrated with the hydraulic actuator

Nguyen, Tuan Anh

doi:10.1590/1679-78256621

Abstract 抽象的

The stability and comfort of vehicles depend on the operation of the suspension system. To increase the smoothness and comfort for passengers in the vehicle, the stiffness of the suspension system needs to be changed flexibly. The conventional pneumatic suspension system can partially meet these requirements. However, the change is not much. This paper introduces a model of the pneumatic suspension system integrated with a hydraulic actuator. This is a completely novel and unique method. In the case that the excitation is random, average values of displacement and acceleration of the sprung mass are only 12.56 (mm) and 3.78 (m/s²) if the vehicle uses the integrated pneumatic suspension system. In contrast, this value is very large, up to 30.70 (mm) and 6.53 (m/s²) if the passive suspension system is used. Similarly, this change is also very large in the remaining survey situations. Overall, the values of acceleration and displacement of the sprung mass are significantly reduced when the vehicle is equipped with an integrated pneumatic suspension system. The results of the research showed the advantages of this method compared to other methods.
车辆的稳定性和舒适性取决于悬架系统的运行。为了增加车内乘客的平顺性和舒适性，需要灵活改变悬架系统的刚度。传统的气动悬挂系统可以部分满足这些要求。不过，变化并不大。本文介绍了一种集成液压执行器的气动悬架系统模型。这是一种完全新颖且独特的方法。在随机激励的情况下，如果车辆采用集成式气动悬架系统，簧上质量的位移和加速度平均值仅为12.56（mm）和3.78（m/s ² ）。相比之下，如果采用被动悬架系统，这个值就非常大了，可达30.70（mm）和6.53（m/s ² ）。同样，这个变化在剩下的调查情况中也非常大。总体而言，当车辆配备集成气动悬架系统时，簧载质量的加速度和位移值显着降低。研究结果显示了该方法相对于其他方法的优势。

Keywords: 关键词：
Pneumatic suspension system; hydraulic actuator; integrated suspension; comfort; stability
气压悬挂系统；液压执行器；集成悬架；舒适;稳定

Graphical Abstract 图形概要

1 INTRODUCTION 1 简介

The vibration of the vehicle when moving on the road is one of the extremely important issues. Oscillation usually occurs when there is an external stimulus. To quell these oscillations, the suspension system is fitted on all models today. The syspension system separates the vehicle into two completely separate parts, including the sprung mass and the unsprung mass. All the components above the suspension system (passengers, cargoes, etc.) are called the sprung mass. It takes up most of the vehicle's total mass. In contrast, the components below the suspension system (wheels, axles, brakes, etc.) are assumed to be unsprung mass [¹[1] Yin, J., Chen, X., Li, J., and Wu, L. (2015). Investigation of Equivalent Unsprung Mass and Nonlinear Features of Electromagnetic Actuated Active Suspension, Shock and Vibration.]. The optimal division of these two values is extremely important, it helps to control the oscillations properly.
车辆在道路上行驶时的振动是极其重要的问题之一。当有外部刺激时，通常会发生振荡。为了平息这些振荡，当今所有车型都安装了悬架系统。系统悬架系统将车辆分成两个完全独立的部分，包括簧载质量和簧下质量。悬挂系统上方的所有部件（乘客、货物等）称为簧载质量。它占据了车辆总质量的大部分。相反，悬架系统下方的部件（车轮、车轴、制动器等）被假定为非簧载质量 [ ¹ ]。这两个值的最佳划分极其重要，它有助于正确控制振荡。

Normally, the suspension system consists of three parts: spring, damper, and lever arm. For the conventional passive suspension system, the stiffness of the spring and damper is constant. As a result, the stability and comfort of the vehicle can be greatly affected. In order to improve this problem, it is necessary to change the characteristics of the spring and damper, or both. The method of using the semi-active suspension system (changing the damping stiffness) has been introduced and equipped on some models [²[2] Basargan, H., Mihaly, A., Gaspar, P., and Sename, O. (2021). Adaptive Semi-Active Suspension and Cruise Control through LPV Technique, Applied Sciences 11(1)., ³[3] Pang, H., Fu, W., and Liu, K. (2015). Stability Analysis and Fuzzy Smith Compensation Control for Semi-active Suspension Systems with Time Delay, Journal of Intelligent & Fuzzy Systems 29(6): 2513-25.]. However, this method can only help the vehicle to partially extinguish the vertical vibration. It is not able to guarantee stability in other cases. The improvement of the suspension system's smoothness through changing the stiffness of the spring is appreciated. The conventional metal spring will be replaced by the pneumatic spring, which can control stiffness through internal pneumatic pressure [⁴[4] Melo, F. J. M. Q., Pereira, A. B., and Morais, A. B. (2018). The Simulation of an Automotive Air Spring Suspension Using a Pseudo-dynamic Procedure, Applied Sciences 8(7).]. The pneumatic suspension system is often equipped on high-end vehicles or large passenger vehicles, its price is very expensive.
通常，悬架系统由三部分组成：弹簧、阻尼器和杠杆臂。对于传统的被动悬架系统，弹簧和阻尼器的刚度是恒定的。结果，车辆的稳定性和舒适性会受到很大影响。为了改善这个问题，需要改变弹簧和阻尼器，或者两者的特性。采用半主动悬架系统（改变阻尼刚度）的方法已被引进并装备在部分车型上[ ² 、 ³ ]。但这种方法只能帮助车辆部分消除垂直振动。其他情况下无法保证稳定性。通过改变弹簧的刚度来提高悬架系统的平滑度受到赞赏。传统的金属弹簧将被气动弹簧取代，气动弹簧可以通过内部气压控制刚度[ ⁴ ]。气动悬架系统常配备在高端车辆或大型客车上，其价格非常昂贵。

The pneumatic suspension system model has been studied in recent years. Characteristics of the pneumatic suspension system were introduced and analyzed in [⁵[5] Alonso, A., Gimenez, J. G., Nieto, J., and Vinolas, J. (2010). Air Suspension Characterisation and Effectiveness of a Variable Area Orifice, Vehicle System Dynamics 48: 271-86.]. According to Yin et al., the pneumatic suspension system has a direct effect on the stiffness and height of the vehicle [⁶[6] Yin, Z., Khajepour, A., Cao, D., Ebrahimi, B., and Guo, K. (2012). A New Pneumatic Suspension System with Independent Stiffness and Ride Height Tuning Capabilities, Vehicle System Dynamic 50(12): 1735-46.]. These problems are again exemplified by Eskandary et al. based on their paper [⁷[7] Eskandary, P. K., Khajepour, A., Wong, A., and Ansari, M. (2016). Analysis and Optimization of Air Suspension System with Independent Height and Stiffness Tuning, International Journal of Automotive Technology 17(5): 807-16.]. Various models of the pneumatic suspension system have been used such as the Nishimura model, the VAMPIRE model, the SIMPAC model, and the GENSYS model. In which, GENSYS model is the novel model and it is appreciated [⁸[8] Abid H. J., Chen J., and Nassar, A. A. (2015). Equivalent Air Spring Suspension Model for Quarter Passive Model of Passenger Vehicles, International Scholarly Research Notices.]. In [⁹[9] Gavriloski, V., Jovanova, J., Tasevski, G., and Djidrov, M. (2014). Development of a New Air Spring Dynamic Model, FME Transactions 42(4): 305-10.], Gavriloski et al. used this model for their paper. Besides, Moheyeldein et al. also evaluated the effectiveness of the GENSYS model in their research [¹⁰[10] Moheyeldein, M. M., Tawwab, A. M. A. E., Elgwwad, K. A. A., and Salem, M. M. M. (2018). An Analytical Study of the Performance Indices of Air Spring Suspension Over the Passive Suspension, Beni-Suef University Journal of Basic and Applied Sciences 7: 525-34.]. In addition, a nonlinear dynamic model of pneumatic spring with damper has also been introduced by Zhu et al. [¹¹[11] Zhu, H., Yang, J., Zhang, Y., Feng, X., and Ma, Z. (2017). Nonlinear Dynamic Model of Air Spring with a Damper for Vehicle Ride Comfort, Nonlinear Dynamics 89: 1545-68.]. Similarly, the pneumatic suspension model used novel damper has also been proposed by Xiao et al. They have come up with an optimal control algorithm PID for the system [¹²[12] Xiao, P., Gao, H., Shi, P., and Niu, L. (2018). Research on Air Suspension with Novel Dampers Based on Glowworm Swarm Optimization Proportional Integral Derivative Algorithm, Advances in Mechanical Engineering 10(8).].
近年来对气动悬架系统模型进行了研究。 [ ⁵ ]中介绍并分析了气动悬架系统的特点。 Yin等人认为，气动悬架系统对车辆的刚度和高度有直接影响[ ⁶ ]。 Eskandary 等人再次举例说明了这些问题。基于他们的论文 [ ⁷ ]。已经使用了各种模型的气动悬架系统，例如Nishimura模型、VAMPIRE模型、SIMPAC模型和GENSYS模型。其中，GENSYS模型是一种新颖的模型，受到赞赏[ ⁸ ]。在[ ⁹ ]中，Gavriloski 等人。在他们的论文中使用了这个模型。此外，Moheyeldein 等人。还在他们的研究中评估了 GENSYS 模型的有效性[ ¹⁰ ]。此外，Zhu等人还介绍了带有阻尼器的气动弹簧的非线性动力学模型。 [ ¹¹ ]。同样，Xiao等人也提出了使用新型阻尼器的气动悬架模型。他们提出了系统的最优控制算法PID[ ¹² ]。

The pneumatic suspension system is not only used in passenger vehicles, but it is also widely used on special vehicles. According to [¹³[13] Li, Z., Song, X., Chen, X., and Xue, H. (2021). Dynamic Characteristics Analysis of the Hub Direct Drive Air Suspension System from Vertical and Longitudinal Directions, Shock and Vibration.], the pneumatic suspension system has been mounted in the hub of the electric vehicle, which uses the motor in-wheel. Therefore, the structure of the vehicle is very compact. However, it still meets the requirements of the vehicle’s stability and safety. On agricultural vehicles, the pneumatic suspension system has also been equipped, which achieves very high performance [¹⁴[14] Ikrama, K., et al. (2020). Development of Active Air Suspension System for Small Agricultural Vehicles, Big Data in Agriculture 2(2): 23-28.]. In addition, the pneumatic suspension system can be integrated with the energy harvesting system that is found on some special models. It can provide optimum efficiency in terms of energy when the vehicle oscillates [¹⁵[15] Genovese, A., Strano, S., and Terzo, M. (2020). Design and Multi-physics Optimization of an Energy Harvesting System Integrated in a Pneumatic Suspension, Mechatronics 69.]. Further, the hydropneumatic suspension system has been equipped on many specialized vehicles such as trains, tanks, soil compactor, etc. to improve the vibration efficiency of the vehicle [¹⁶[16] Kwon, K., Seo, M., Kim, H., Lee, T., Lee, J., and Min, S. (2020). Multi-objective Optimisation of Hydro-pneumatic Suspension with Gas-online Emulsion for Heavy-duty Vehicles, Vehicle System Dynamics 58(7): 1146-65.

[17] Jiao, R., Nguyen, V., and Le, V. (2020). Ride Comfort Performance of Hydro Pneumatic Isolation for Soil Compactors Cab in Low Frequency Region, Journal of Vibroengineering 22(5): 1174-86.

[18] Qin, B., Zeng, R., Li, X., and Yang, J. (2021). Design and Performance Analysis of the Hydropneumatic Suspension System for a Novel Road-rail Vehicle, Applied Sciences 11(5).-¹⁹[19] Garcia, I. M., Laborda, N. G., Mallabiabarrena, A. P., and Berg, M. (2020). A Survey on the Modelling of Air Spring - Secondary Suspension in Railway Vehicles, Vehicle System Dynamics.]. Overall, this system can meet the vehicle's stability requirements well.
气动悬架系统不仅应用于乘用车，在特种车辆上也广泛应用。据[ ¹³ ]报道，气动悬架系统已安装在电动汽车的轮毂中，该电动汽车采用轮内电机。因此，整车的结构非常紧凑。但仍然满足车辆稳定性和安全性的要求。在农用车上，也配备了气动悬架系统，实现了非常高的性能[ ¹⁴ ]。此外，气动悬架系统可以与某些特殊车型上的能量收集系统集成。当车辆振荡时，它可以提供最佳的能量效率[ ¹⁵ ]。此外，油气悬挂系统已装备在许多专用车辆上，如火车、坦克、土壤压实机等，以提高车辆的振动效率[ ¹⁶ - ¹⁹ ]。总体而言，该系统能够很好地满足车辆的稳定性要求。

When the vehicle is equipped with a pneumatic suspension system, the vehicle's vibrations are better controlled than with a conventional passive suspension system [²⁰[20] Le, V. Q. (2017). Comparing the Performance of Suspension System of Semi-trailer Truck with Two Air Suspension Systems, Journal of Vibroengineering 14: 220-26.]. This has also been demonstrated experimentally by Kumbhar et al. [²¹[21] Kumbhar, M. B., Salunkhe, V. G., Borgaonkar, A. V., and Jagadeesha, T. (2020). Mathematical Modeling and Experimental Evaluation of an Air Spring-Air Damper Dynamic Vibration Absorber, Journal of Vibration Engineering & Technologies.]. The pneumatic suspension system can also be supposed as a form of the active suspension system. Therefore, control methods for the active suspension system are proposed to be used for the pneumatic suspension system. If the system is considered to be linear, PID and LQR control methods can be applied. In [²²[22] Anh, N. T. (2020). Control an Active Suspension System by Using PID and LQR Controller, International Journal of Mechanical and Production Engineering Research and Development 10(3): 7003-12.], Anh compared the effectiveness of these two methods. When the LQR controller is combined with the Gaussian filter, it becomes the LQG controller [²³[23] Pang, H., Chen, Y., Chen, J., and Liu, X. (2017). Design of LQG Controller for Active Suspension without Considering Road Input Signals, Shock and Vibration.]. Besides, many nonlinear and intelligent control methods for the suspension system have also been proposed. In [²⁴[24] Zhao, R., Xie, W., Wong, P. K., Cabecinhas, D., and Silvestre, C. (2019). Robust Ride Height Control for Active Air Suspension Systems with Multiple Unmodeled Dynamics and Parametric Uncertainties, IEEE Access, 7: 59185-199.], Zhao et al. introduced a robust control method for the pneumatic suspension system. This method helps the height of the vehicle body to be controlled stably, the input parameters can be changed continuously. Compared with conventional linear control methods, this method helps the vehicle oscillation approach the desired threshold. In addition, robust control methods for the active suspension system can also be applied to pneumatic suspension systems [²⁵[25] Kaleemullah, M., Faris, W. F., and Ghazaly, N. M. (2019). Analysis of Active Suspension Control Policies for Vehicle Using Robust Controllers, International Journal of Advances Science and Technology 28(16): 836-855., ²⁶[26] Rizvi, S. M. H., Abid, M., Khan, A. Q., Satti, S. G., and Latif, J. (2018). H∝ Control of 8 Degrees of Freedom Vehicle Active Suspension System, Journal of King Saud University - Engineering Sciences 30(2) 161-69.]. In [²⁷[27] Nieto, A. J., Morales, A. L., Chicharro, J. M., and Pintado, P. (2016). An Adaptive Pneumatic Suspension System for Improving Ride Comfort and Handling, Journal of Vibration and Control 22(6): 1492-503.], Nieto et al. controlled the active suspension system by the adaptive control method. This method was again used in the study of Fu et al. According to [²⁸[28] Fu, Z. J., Li, B., Ning, X. B., and Xie, W. D. (2017). Online Adaptive Optimal Control of Vehicle Active Suspension System Using Signal-network Approximate Dynamic Programming, Mathematical Problems in Engineering.], the displacement and the acceleration of the sprung mass are almost unchanged even though the sprung mass changes continuously. Besides, intelligent and integrated control methods have also been proposed. In [²⁹[29] Rui, B. (2019). Nonlinear Adaptive Sliding Mode Control of the Electronically Controlled Air Suspension System, International Journal of Advanced Robotic Systems.], Rui introduced a nonlinear adaptive sliding mode controller for a pneumatic suspension system. This is a combination of two nonlinear control methods. The tracking nonlinear controller was also used in the paper of Zhao et al. [³⁰[30] Zhao, R., Xie, W., Zhao, J., Wong, P. K., and Silvestre, C. (2021). Nonlinear Ride Height Control of Active Air Suspension System with Output Constraints and Time-varying Disturbances, Sensors 21(4).]. The predictive control model for the pneumatic suspension system has also been used, the effect of which is extremely positive [³¹[31] Sun, X., Yuan, C., Cai, Y., Wang, S., and Chen, L. (2017). Model Predictive Control of an Air Suspension System with Damping Multimode Switching Damper Based on Hybrid Model, Mechanical Systems and Signal Processing 94: 94-110.]. The sliding mode control method has also been shown in the studies of Chen et al. and Zhou et al. [³²[32] Chen, Y., Zhang, S., Mao, E., Du, Y., Chen, J., and Yang, S. (2020). Height Stability Control of a Large Sprayer Body Based on Air Suspension Using the Sliding Mode Approach, Information Processing in Agriculture 7(1): 20-9., ³³[33] Zhou, C., Liu, X., Xu, F., and Chen, W. (2020). Sliding Mode Switch Control of Adjustable Hydro-pneumatic Suspension Based on Parallel Adaptive Clonal Selection Algorithm, Applied Sciences 10(5).]. Besides, other control methods for the active suspension system that have been highly effective can also be applied to the pneumatic suspension system [³⁴[34] Li, H., Li, S., Sun, W., Wang, L., and Lv, D. (2020). The Optimum Matching Control and Dynamic Analysis for Air Suspension of Multi-axle Vehicles with Anti-roll Hydraulically Interconnected System, Mechanical Systems and Signal Processing: 139.

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当车辆配备气动悬架系统时，车辆的振动比传统的被动悬架系统得到更好的控制[ ²⁰ ]。 Kumbhar 等人也通过实验证明了这一点。 [ ²¹ ]。气动悬架系统也可以被认为是主动悬架系统的一种形式。因此，提出将主动悬架系统的控制方法用于气动悬架系统。如果系统被认为是线性的，则可以应用PID和LQR控制方法。在[ ²² ]中，Anh比较了这两种方法的有效性。当LQR控制器与高斯滤波器结合时，就成为LQG控制器[ ²³ ]。此外，许多悬架系统的非线性和智能控制方法也被提出。在[ ²⁴ ]中，赵等人。介绍了气动悬架系统的鲁棒控制方法。该方法有助于稳定地控制车身高度，并且输入参数可以连续改变。与传统的线性控制方法相比，该方法有助于车辆振动接近期望的阈值。此外，主动悬架系统的鲁棒控制方法也可以应用于气动悬架系统[ ²⁵ 、 ²⁶ ]。在[ ²⁷ ]中，Nieto 等人。采用自适应控制方法对主动悬架系统进行控制。 Fu等人的研究中再次使用了该方法。根据[ ²⁸ ]，即使簧上质量不断变化，簧上质量的位移和加速度几乎不变。此外，还提出了智能化、集成化的控制方法。在[ ²⁹ ]中，Rui介绍了一种用于气动悬架系统的非线性自适应滑模控制器。这是两种非线性控制方法的组合。赵等人的论文中也使用了跟踪非线性控制器。 [ ³⁰ ]。气动悬架系统的预测控制模型也已被使用，其效果非常积极[ ³¹ ]。 Chen等人的研究也展示了滑模控制方法。和周等人。 [ ³² ， ³³ ]。此外，其他已经非常有效的主动悬架系统控制方法也可以应用于气动悬架系统[ ³⁴ - ³⁹ ]。

The pneumatic suspension system helps to improve the vehicle's stability and safety when moving on the road. However, this improvement is not much. In many cases, the stability and comfort of the vehicle are still not guaranteed. Therefore, this paper has proposed the use of the pneumatic suspension system, which is integrated with a hydraulic actuator to improve comfort and smoothness. The actuator used in this research is a hydraulic piston, which is widely used on mechatronics systems. According to [⁴⁰[40] Tamburrano, P., Plummer, A. R., Distaso, E., and Amirante, R. (2019). A Review of Electro-hydraulic Servo-valve Research and Development, International Journal of Fluid Power 20(1): 53-98.], the hydraulic piston operates based on the opening and closing of the valve of the servo valve system. The fluid in the system is conveyed by the hydraulic pump. In [⁴¹[41] Lee, J., Oh, K., and Yi, K. (2020). A Novel Approach to Design and Control of an Active Suspension Using Linear Pump Control-based Hydraulic System, Journal of Automobile Engineering 234(5): 1224-48.], Lee et al. introduced a new method to control the operation of the hydraulic pump. The opening and closing of the actuator's valves are controlled based on the voltage signal that is sent from the controller. Shafie et al. developed an algorithm to control the hydraulic actuator, they used two PID controllers for each hydraulic piston [⁴²[42] Shafie, A. A., Bello, M. M., and Khan, R. M. (2015). Active Vehicle Suspension Control Using Electro Hydraulic Actuator on Rough Road Terrain, Journal of Advances Research in Applied Mechanics 9(1): 15-30.]. According to [⁴³[43] Bai, R., and Guo, D. (2018). Sliding-mode Control of the Active Suspension System with the Dynamics of a Hydraulic Actuator, Complexity.], the efficiency of the actuator can be improved by using the sliding mode controller. Similarly, this method has also been mentioned in the paper of Sam and Osman [⁴⁴[44] Sam, Y. M., and Osman, J. H. S. (2006). Sliding Mode Control of a Hydraulically Actuated Active Suspension, Jurnal Teknologi 44: 37-48.]. In addition, integrated controllers have also been introduced to control the operation of hydraulic actuators [⁴⁵[45] Sam, Y. M., Hudha, K., and Osman, J. H. S. (2007). Proportional-integral Sliding Mode Control of a Hydraulically Actuated Active Suspension System: Force Tracking and Disturbance Rejection Control on Non-linear Quarter Car Model, International Journal of Vehicle Systems Modelling and Testing 2(4): 391-410.]. In general, the above control methods bring positive effects to the system.
气动悬架系统有助于提高车辆在道路上行驶时的稳定性和安全性。不过，这种改善并不大。很多情况下，车辆的稳定性和舒适性仍然得不到保证。因此，本文提出采用气动悬架系统，与液压执行器集成，以提高舒适性和平顺性。本研究中使用的执行器是液压活塞，广泛应用于机电一体化系统中。根据[ ⁴⁰ ]，液压活塞基于伺服阀系统的阀门的打开和关闭进行操作。系统中的流体由液压泵输送。在[ ⁴¹ ]中，Lee等人。介绍了一种控制液压泵运行的新方法。执行器阀门的打开和关闭是根据控制器发送的电压信号进行控制的。沙菲等人。开发了一种控制液压执行器的算法，他们为每个液压活塞使用了两个 PID 控制器 [ ⁴² ]。根据[ ⁴³ ]，使用滑模控制器可以提高执行器的效率。同样，Sam和Osman的论文[ ⁴⁴ ]中也提到了这种方法。此外，还引入了集成控制器来控制液压执行器的操作[ ⁴⁵ ]。总的来说，上述控制方法都给系统带来了积极的效果。

Previous studies on the pneumatic suspension system often only mentioned the use of the independent pneumatic suspension system. This does not solve the vehicle's vibration problems. Therefore, this paper proposes the use of the pneumatic suspension system that integrates a hydraulic actuator to improve the stability and comfort of the vehicle when moving on the road. The combination of the pneumatic spring and the hydraulic actuator is a novel and unique solution. They can operate independently from each other. Besides, they can also support each other. It enhances the vehicle's safety and comfort more than other conventional solutions. This research analyzes, simulates, and evaluates the efficiency of the integrated pneumatic suspension system. Simulation is performed in the Matlab-Simulink environment. The method and control model are detailed in the content below.
以往对气动悬架系统的研究往往只提到独立气动悬架系统的使用。这并不能解决车辆的振动问题。因此，本文提出采用集成液压执行器的气动悬架系统来提高车辆在道路上行驶时的稳定性和舒适性。气动弹簧和液压执行器的组合是一种新颖且独特的解决方案。它们可以相互独立运行。除此之外，他们还可以互相支持。与其他传统解决方案相比，它更能提高车辆的安全性和舒适性。本研究对集成气动悬架系统的效率进行了分析、模拟和评估。仿真是在Matlab-Simulink 环境中进行的。下面详细介绍该方法和控制模型。

2 MATERIAL AND METHOD
2 材料与方法

2.1 Pneumatic Suspension Model
2.1 气压悬架模型

The physical model of the pneumatic spring is given as shown in Figure 1. Equation (1) shows the balance of the force acting on the pneumatic spring.
气动弹簧的物理模型如图1所示。方程（1）显示了作用在气动弹簧上的力的平衡。

F_{z} = A_{e} p_{b} = A_{e} (p_{0} - p_{a t})

(1)

Figure 1 图1
The physical model of the pneumatic spring.
气动弹簧的物理模型。

When the spring is subjected to a static load F_z, the pressure between the two chambers changes. Therefore, the force F_p appears, which pushes the gas's mass to move along the pipe. As this mass moves, it generates a frictional force F_f, which is a nonlinear frictional force. This shift is described through equation (2):
当弹簧承受静载荷F _z 时，两个腔室之间的压力发生变化。因此，出现了力F _p ，推动气体质量沿着管道移动。当该质量移动时，会产生摩擦力 F，这是一种非线性摩擦力。这种转变通过等式（2）描述：

m_{a} {\ddot{z}}_{a} = F_{p} - F_{f} = (p_{b} - p_{r}) A_{s} - C_{a} {\dot{z}}_{a}^{2}

(2)

Based on this principle, many dynamic models of pneumatic springs have been proposed. In this paper, the GENSYS model is used. This is a novel model, and it has high accuracy and is suitable for the vibration simulation problems of the vehicle [⁸[8] Abid H. J., Chen J., and Nassar, A. A. (2015). Equivalent Air Spring Suspension Model for Quarter Passive Model of Passenger Vehicles, International Scholarly Research Notices.].
基于这一原理，人们提出了许多气动弹簧的动力学模型。本文采用GENSYS模型。该模型新颖，精度高，适用于车辆振动仿真问题[ ⁸ ]。

The pneumatic spring is converted equivalently to the oscillating system in Figure 2. This system consists of the main spring K_e, the auxiliary spring K_v, these are two linear springs. The compressed air in the spring is converted to mass ma. As air moves through the pipes, they create friction. This friction process is shown through C_a nonlinear damping.
气动弹簧等效转换为图2中的振荡系统。该系统由主弹簧K _e 、辅助弹簧K _v 组成，这是两个线性弹簧。弹簧中的压缩空气转换为质量ma。当空气通过管道时，会产生摩擦。这个摩擦过程通过C _a 非线性阻尼来表现。

The stiffness of the main spring K_e depends on the initial absolute pressure p₀, the effective area of the spring A_e, the initial volumes of the balloon and reservoir V_b0 and V_r0, and multivariable coefficient n.
主弹簧的刚度 K _e 取决于初始绝对压力 p ₀ 、弹簧的有效面积 A _e 、气球的初始体积和储层V _b0 和V _r0 以及多变量系数n。

K_{e} = \frac{p_{0} n A_{e}^{2}}{V_{b 0} + V_{r 0}}

(3)

The stiffness of the auxiliary spring K_v is proportional to the stiffness of the main spring K_e through the ratio between the initial volumes.
辅助弹簧的刚度K _v 与主弹簧的刚度K _e 通过初始体积之比成正比。

K_{v} = \frac{p_{0} n A_{e}^{2}}{V_{r 0} + V_{b 0}} \frac{V_{r 0}}{V_{b 0}} = K_{e} \frac{V_{r 0}}{V_{b 0}}

(4)

Figure 2 图2
GENSYS model. GENSYS 模型。

To simplify the model, the compressed air is equivalently converted to mass m_a. This is a nonlinear function, and it depends on the characteristics of the air and the size of the pneumatic spring.
为了简化模型，将压缩空气等价转换为质量 m _a 。这是一个非线性函数，它取决于空气的特性和气动弹簧的尺寸。

m_{a} = ρ A_{s} l_{s} {(\frac{A_{e}}{A_{s}} \frac{V_{r 0}}{V_{r 0} + V_{b 0}})}^{2}

(5)

The damping coefficient C_a of the pneumatic spring is nonlinear. In order to calculate this value, the parameters of the size of the spring A_e, the size of the pipe A_s, the initial volume of balloon and reservoir V_r0, V_b0, the density of the air ρ, and the total loss coefficient of the connection pipes k need to be determined before.
气动弹簧的阻尼系数C _a 是非线性的。为了计算该值，弹簧尺寸A _e 、管道尺寸A _s 、气球和储液器初始体积V _r0 、空气密度ρ以及连接管道的总损失系数k。

C_{a} = \frac{1}{2} A_{s} ρ k {(\frac{A_{e}}{A_{s}} \frac{V_{r 0}}{V_{r 0} + V_{b 0}})}^{1 + b}

(6)

After the necessary coefficients have been determined, the vehicle dynamics model can be established. In the oscillation and control problems of vehicles, the quarter dynamic model is often used (Figure 3). This model consists of the linear damper C, the pneumatic spring (K_e, K_v, C_a), and the hydraulic actuator A. Instead of the usual two degrees of freedom, this model uses three degrees of freedom (z₁, z₂, and z_a). The vehicle's oscillation is generated from the excitation from the road surface h.
确定必要的系数后，即可建立车辆动力学模型。在车辆的振荡与控制问题中，经常使用四分之一动态模型（图3）。该模型由线性阻尼器C、气动弹簧（K _e 、K _v 、C _a ）和液压执行器A组成。通常为两个自由度，此模型使用三个自由度（ z ₁ 、 z ₂ 和 z _a ）。车辆的振动是由路面h的激励产生的。

Figure 3 图3
The quarter dynamic model.
季度动态模型。

The vertical displacement of the sprung mass m₁, the unsprung mass m₂, and the mass of the air m_a are expressed by the following equations:
簧上质量 m ₁ 、簧下质量 m ₂ 和空气质量 m _a 的垂直位移由以下方程表示：

m_{1} {\ddot{z}}_{1} = F_{C} + F_{K e} + F_{K v} + F_{S} + F_{A}

(7)

m_{2} {\ddot{z}}_{2} = F_{K T} - F_{C} - F_{K e} - F_{C a} - F_{A}

(8)

m_{a} {\ddot{z}}_{a} = F_{C a} - F_{K v}

(9)

Where: 在哪里：

Pneumatic force: 气压：

F_{S} = p_{b} A_{e} = p_{0} [{(\frac{V_{b 0}}{V_{b 0} - A_{e} (z_{2} - z_{1})})}^{n} - 1] A_{e}

(10)

Linear damping force: 线性阻尼力：

F_{C} = C ({\dot{z}}_{2} - {\dot{z}}_{1})

(11)

Main spring force: 主弹簧力：

F_{K e} = K_{e} (z_{2} - z_{1})

(12)

Auxiliary spring force: 辅助弹簧力：

F_{K v} = K_{v} (z_{a} - z_{1})

(13)

Nonlinear damping force:
非线性阻尼力：

F_{C a} = C_{a} {({\dot{z}}_{2} - {\dot{z}}_{a})}^{2}

(14)

Tire force: 轮胎受力：

F_{K T} = K_{T} (h - z_{2})

(15)

The value of force F_A that is generated from the controller needs to be calculated through the control model.
控制器产生的力F _A 的值需要通过控制模型计算出来。

2.2 Control model 2.2 控制模型

Different from other common research which only uses pneumatic springs in the suspension system, this research has integrated the hydraulic actuator with the pneumatic suspension system. When the vehicle's body oscillates, the hydraulic actuator will generate a force F_A acting on the sprung mass m₁ and the unsprung mass m₂. The actuator is automatically controlled through the previously established controller (Figure 4).
与其他仅在悬架系统中使用气动弹簧的研究不同，本研究将液压执行器与气动悬架系统集成在一起。当车体摆动时，液压执行器将产生作用在簧上质量m ₁ 和簧下质量m ₂ 上的力F _A 。执行器通过先前建立的控制器自动控制（图4）。

Figure 4 图4
The hydraulic actuator.
液压执行器。

The actuator force F_A depends on the change in hydraulic pressure inside the system:
执行器力 F _A 取决于系统内部液压的变化：

F_{A} = S_{p} Δ P

(16)

The difference in hydraulic pressure inside the actuator is expressed through the piston's displacement and liquid's flow:
执行器内部的液压差通过活塞的位移和液体的流量来表示：

Δ P = γ_{1} \int (Q - \frac{γ_{2}}{γ_{1}} P - S_{p} {\dot{x}}_{s}) d t

(17)

Q = \frac{γ_{3}}{γ_{1}} x_{s v} \sqrt{P_{s} - sgn (x_{s v}) Δ P}

(18)

The flow of liquid through the valve depends on the opening and closing of the valve. The valves are opened and closed by the control voltage signal u(t), which is generated from the controller.
通过阀门的液体流量取决于阀门的打开和关闭。阀门由控制器产生的控制电压信号 u(t) 打开和关闭。

x_{s v} = \frac{1}{τ} \int (k_{s v} u (t) - x_{s v}) d t

(19)

Where: γ: Actuator coefficient
其中： γ：执行器系数

τ: Time coefficient τ：时间系数

S_p: Piston cross section
S _p ：活塞横截面

k_sv: Servo valve gain
k _sv ：伺服阀增益

P_s: Supply pressure
P _s : 供给压力

x_sv: Displacement of the servo valve
x _sv ：伺服阀的位移

This paper uses the PI controller to control the operation of the hydraulic actuator. Compared with other controllers, the PI controller has many advantages such as low cost, high reliability, easy control. Besides, this controller works stably with the SISO control object.
本文采用PI控制器来控制液压执行机构的运行。与其他控制器相比，PI控制器具有成本低、可靠性高、控制方便等优点。此外，该控制器与SISO控制对象配合工作稳定。

Although the established dynamics model has three degrees of freedom, the control object here is only the acceleration of the sprung mass. When the acceleration of the sprung mass is controlled, the value of displacement of the sprung mass can also be improved. Therefore, it is perfectly appropriate to use a PI controller.
虽然建立的动力学模型具有三个自由度，但这里的控制对象只是簧上质量的加速度。当控制簧上质量的加速度时，也可以改善簧上质量的位移值。因此，使用 PI 控制器是非常合适的。

The PID controller consists of three stages: Proportional (P), Integral (I), and Derivative (D). The mathematical model of this controller is given as (20). If the Derivative stage (D) is eliminated (T_D = 0), it becomes a PI controller, which consists of only two stages.
PID 控制器由三个阶段组成：比例 (P)、积分 (I) 和微分 (D)。该控制器的数学模型如(20)所示。如果微分阶段 (D) 被消除 (T _D = 0)，它就成为一个 PI 控制器，仅由两个阶段组成。

u (t) = k_{p} [e (t) + \frac{1}{T_{I}} \int_{0}^{t} e (τ) d τ + T_{D} \dot{e} (t)]

(20)

Where: 在哪里：

e(t): input signal of the controller.
e(t)：控制器的输入信号。

u(t): output signal of the controller.
u(t)：控制器的输出信号。

k_p: proportional coefficient.
k _p ：比例系数。

T_I: integral coefficient. T：积分系数。

T_D: derivative coefficient.
T _D ：导数系数。

There are many methods used to determine the parameters of the PI controller. In this paper, the controller's parameters are determined by the second Ziegler-Nichols method [⁴⁶[46] Patel, V. V. (2020). Ziegler-Nichols Tuning Method, Resonance 25: 1385-97.]. The transfer function of the controller is given as (21).
有多种方法可用于确定 PI 控制器的参数。本文采用第二种Ziegler-Nichols方法确定控制器的参数[ ⁴⁶ ]。控制器的传递函数如(21)所示。

R (s) = k_{p} (1 + \frac{1}{T_{I} s}) = δ k_{t h} (1 + \frac{1}{λ T_{t h} s})

(21)

3 RESULTS AND DISCUSSIONS
3 结果与讨论

3.1 Simulation conditions
3.1 模拟条件

After the vehicle dynamics model has been established, simulation is done. The specifications of the vehicle and hydraulic actuator are given in Tables 1 and 2 respectively [⁴⁷[47] Nguyen, T. A. (2021). Improving the Comfort of the Vehicle Based on Using the Active Suspension System Controlled by the Double-Integrated Controller, Shock and Vibration.].
建立车辆动力学模型后，进行仿真。车辆和液压执行器的规格分别见表1和表2[ ⁴⁷ ]。

Thumbnail 缩略图

Table 1 表格1
The specifications of the vehicle.
车辆的规格。

Thumbnail 缩略图

Table 2 表2
The specifications of the hydraulic actuator.
液压执行器的规格。

The results of the simulation process are the displacement of the sprung mass, the acceleration of the sprung mass, and the change in pressure of the pneumatic suspension. These are the parameters that characterize the vehicle's oscillation. The maximum value and changing trend of these parameters are interesting objects. Besides, the average value is also calculated to be able to determine the stable oscillation threshold of the system. The average value of the oscillation is calculated by the Root Mean Square method (RMS).
仿真过程的结果是簧载质量的位移、簧载质量的加速度以及气动悬架的压力变化。这些是表征车辆振动的参数。这些参数的最大值和变化趋势是有趣的对象。此外，还计算平均值以确定系统的稳定振荡阈值。振荡的平均值通过均方根法（RMS）计算。

R M S = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} x_{i}^{2}}

(22)

Stimulation from the road surface is a factor that directly affects the smoothness and comfort of the vehicle. In this paper, three types of the excitation are used, including sine wave, random, and step. The values of displacement of the sprung mass and the acceleration of the sprung mass will be determined corresponding to the simulation cases, including:
来自路面的刺激是直接影响车辆行驶平稳性和舒适性的因素。本文使用了三种类型的激励，包括正弦波、随机和阶跃。根据仿真情况确定簧载质量的位移值和簧载质量的加速度值，包括：

+ Vehicles using passive suspension system (Pa)
+ 采用被动悬架系统的车辆 (Pa)

+ Vehicles using conventional pneumatic suspension system (Pn)
+ 使用传统气动悬架系统（Pn）的车辆

+ Vehicles using integrated pneumatic suspension system (I-Pn)
+ 采用集成气动悬架系统 (I-Pn) 的车辆

3.2 Results 3.2 结果

Case 1: Sine wave type
情况1：正弦波型

In this case, the excitation from the road surface takes the form of a periodic sine wave function. This type is often used in control problems. The graph in Figure 5 shows the change of displacement of the sprung mass over time. If the vehicle uses only the conventional passive suspension system, the value of the displacement of the sprung mass is quite large, reaching about 50.10 (mm). Its trajectory closely matches that of the excitation signal from the road surface. When the vehicle uses the pneumatic suspension system, this value may decrease. However, the change is small. If the vehicle is equipped with a pneumatic suspension system integrated with the hydraulic actuator, the displacement value of the sprung mass is significantly reduced. The maximum amplitude of vibration is only about 27.55 (mm), it is much smaller than the two cases mentioned above. According to equation (22), the mean value of oscillation in this case reaches RMS_Pa = 34.69 (mm), RMS_Pn = 34.63 (mm), and RMS_I-Pn = 20.79 (mm), respectively.
在这种情况下，来自路面的激励采用周期性正弦波函数的形式。这种类型常用于控制问题。图 5 中的图表显示了簧载质量的位移随时间的变化。如果车辆仅采用传统的被动悬架系统，簧上质量的位移值相当大，达到约50.10(mm)。其轨迹与路面激励信号的轨迹非常匹配。当车辆使用气动悬架系统时，该值可能会减小。不过，变化很小。如果车辆配备与液压执行器集成的气动悬架系统，簧载质量的位移值将显着减小。最大振动幅度仅为27.55（mm）左右，比上述两种情况要小得多。根据式(22)，此时的振荡平均值达到RMS _Pa = 34.69 (mm)、RMS _Pn = 34.63 (mm)、RMS _I-Pn

Figure 5 图5
Displacement of the sprung mass.
簧载质量的位移。

Figure 6 图6
Acceleration of the sprung mass.
簧载质量的加速度。

Acceleration of the sprung mass is a characteristic parameter for the smoothness and comfort of the vehicle when moving on the road. Figure 6 shows the change of this value in the case of excitation from the road surface having a sine form. If the vehicle uses only the passive suspension system, the maximum value of acceleration is quite large, reaching about 0.44 (m/s²). This value tends to decrease gradually and fluctuates stably around the threshold of 0.05 (m/s²). When the pneumatic suspension system is used to replace the passive suspension system, the change of this value is also not much. Therefore, the smoothness and comfort of the vehicle cannot be improved. If the pneumatic suspension system is integrated with a hydraulic actuator, the vehicle's stability and comfort can be further improved. Its maximum value reaches 0.22 (m/s²), only half that of the vehicle using the passive suspension system. After reaching the maximum value, its amplitude of oscillation gradually decreases. The value fluctuates steadily between -0.023 (m/s²) to 0.023 (m/s²). Besides, the average value of acceleration in this case is RMS_Pa = 0.052 (m/s²), RMS_Pn = 0.043 (m/s²), and RMS_I-Pn = 0.025 (m/s²), respectively. In general, if the vehicle is equipped with an integrated pneumatic suspension system, the vehicle's stability and comfort can be significantly improved.
簧载质量的加速度是车辆在道路上行驶时的平稳性和舒适性的特征参数。图6显示了在路面激励为正弦形式的情况下该值的变化。如果车辆仅采用被动悬架系统，加速度的最大值相当大，达到约0.44（m/s ² ）。该值呈逐渐减小的趋势，并在阈值0.05（m/s ² ）附近稳定波动。当用气动悬架系统取代被动悬架系统时，这个值的变化也并不大。因此，无法提高车辆的平稳性和舒适性。如果气动悬架系统与液压执行器集成，则可以进一步提高车辆的稳定性和舒适性。其最大值达到0.22（m/s ² ），仅为采用被动悬架系统车辆的一半。达到最大值后，其振荡幅度逐渐减小。该值在 -0.023 (m/s ² ) 到 0.023 (m/s ² ) 之间稳定波动。另外，此时的加速度平均值为 RMS _Pa = 0.052 (m/s ² )，RMS _Pn = 0.043 (m/s ² ) 和 RMS _I-Pn = 0.025 (m/s ² )。一般来说，如果车辆配备了集成式气动悬架系统，则车辆的稳定性和舒适性可以显着提高。

The pressure of the pneumatic suspension system changes continuously depending on the stimulus from the road surface. This change is shown graphically in Figure 7. The change in pressure when the vehicle is equipped with an integrated pneumatic suspension system is larger than when the vehicle is used with the conventional pneumatic suspension system, this is a perfect fit. The pressure in the system can change continuously in response to the fluctuations of the stimuli from the road surface.
气动悬架系统的压力根据路面的刺激而不断变化。这种变化如图7所示。车辆配备集成气动悬架系统时的压力变化比车辆配备传统气动悬架系统时的压力变化更大，这是完美的配合。系统中的压力会随着路面刺激的波动而不断变化。

Figure 7 图7
Changing of the pressure of the pneumatic spring.
改变气动弹簧的压力。

Case 2: Random type
情况2：随机型

In this case, random excitation is used. This is the actual pavement type, and it gives more accurate results than the sine form. In Figure 8, the change of displacement of the sprung mass over time is clearly shown. This value changes continuously, and it does not follow any rules because the excitation from the road surface is random. Although the maximum amplitude of the stimulus from the road surface is only 50.00 (mm), the displacement value can reach 70.12 (mm) and 39.70 (mm) respectively in the case of the vehicle using the passive suspension system and the conventional pneumatic suspension system. If the integrated pneumatic suspension system is equipped, this value is further reduced. Besides, the difference in displacement at different times is not large. The average value of vehicle body's displacement in this case, respectively, reaches RMS = {30.70; 17.06; 12.56} (mm).
在这种情况下，使用随机激励。这是实际的路面类型，它给出的结果比正弦形式更准确。在图 8 中，清楚地显示了簧载质量随时间的位移变化。这个值是连续变化的，并且不遵循任何规则，因为路面的激励是随机的。虽然路面刺激的最大振幅仅为50.00（mm），但采用被动悬架系统和传统气动悬架系统的车辆的位移值可分别达到70.12（mm）和39.70（mm）。如果配备集成式气动悬挂系统，这个值还会进一步降低。此外，不同时间的位移差异并不大。此时车体位移平均值分别达到RMS={30.70； 17.06； 12.56}（毫米）。

Figure 8 图8
Displacement of the sprung mass.
簧载质量的位移。

Figure 9 图9
Acceleration of the sprung mass.
簧载质量的加速度。

The acceleration of the vehicle body in this case fluctuates continuously (Figure 9). Besides, its maximum value is also very large, can reach 25.51 (m/s²) if the vehicle only uses the passive suspension system. This is a huge value, and it can affect the smoothness and comfort of the vehicle. If the vehicle uses the conventional pneumatic suspension system, the maximum value of acceleration can reach 23.12 (m/s²), the difference is not too large. Otherwise, if the integrated pneumatic suspension system is equipped to replace the other suspension systems, stability and comfort can be further improved. The maximum value of the acceleration of the sprung mass, in this case, is only 15.72 (m/s²), which is much smaller than the other two cases. This stability is also shown through the average value of acceleration RMS_Pa = 6.53 (m/s²), RMS_Pn = 6.18 (m/s²), and RMS_I-Pn = 3.78 (m/s²).
这种情况下车体的加速度连续波动（图9）。另外，其最大值也很大，如果车辆仅采用被动悬架系统，可以达到25.51（m/s ² ）。这是一个巨大的数值，它会影响车辆的平稳性和舒适性。如果车辆采用常规气动悬架系统，加速度最大值可达23.12（m/s ² ），相差并不算太大。另外，如果配备集成气动悬架系统来替代其他悬架系统，则可以进一步提高稳定性和舒适性。在这种情况下，簧载质量的加速度最大值仅为15.72（m/s ² ），远小于其他两种情况。这种稳定性还通过加速度平均值 RMS _Pa = 6.53 (m/s ² )、RMS _Pn = 6.18 (m/s ² ），RMS _I-Pn = 3.78（m/s ² ）。

To be able to respond well to changes from road surface stimuli, the pressure of the pneumatic suspension system needs to be constantly changing. The change in pneumatic pressure when the vehicle uses the integrated pneumatic suspension system is better and more consistent than with the conventional pneumatic suspension system (Figure 10). As a result, stability and safety issues of the vehicle can be more assured.
为了能够很好地响应路面刺激的变化，气动悬架系统的压力需要不断变化。车辆采用集成式气动悬架系统时气压的变化比传统气动悬架系统更好、更一致（图10）。从而可以更加保证车辆的稳定性和安全性问题。

Figure 10 图10
Changing of the pressure of the pneumatic spring.
改变气动弹簧的压力。

Case 3: Step type
情况3：阶梯式

Figure 11 图11
Displacement of the sprung mass.
簧载质量的位移。

Step stimulation is used in this case. The displacement of the sprung mass was markedly different in the three simulation conditions (Figure 11). The maximum value of amplitude reached 73.42 (mm), 49.53 (mm), and 32.82 (mm) respectively. The acceleration of the sprung mass is also significantly different when the vehicle uses the integrated pneumatic suspension system (Figure 12). Its maximum value is only about 57.3% compared to the vehicle using the passive suspension system. The pneumatic pressure variation of the suspension system is suitable, which response well to changes from external stimuli (Figure 13).
在这种情况下使用步进刺激。簧载质量的位移在三种模拟条件下明显不同（图 11）。振幅最大值分别达到73.42（mm）、49.53（mm）和32.82（mm）。当车辆使用集成气动悬架系统时，簧载质量的加速度也显着不同（图12）。与采用被动悬架系统的车辆相比，其最大值仅为57.3%左右。悬架系统气压变化合适，对外界刺激的变化反应良好（图13）。

Figure 12 图12
Acceleration of the sprung mass.
簧载质量的加速度。

Figure 13 图13
Changing of the pressure of the pneumatic spring.
改变气动弹簧的压力。

In general, when the vehicle was equipped with the pneumatic suspension system that integrated the hydraulic actuator, the displacement and acceleration values of the sprung mass were significantly reduced compared with the other two cases. This has been demonstrated through various excitation conditions from the road surface. Therefore, the smoothness and comfort of the vehicle have been greatly improved. The results of the simulation process are shown in Tables 3 and 4.
总体而言，当车辆配备集成液压执行器的气动悬架系统时，簧载质量的位移和加速度值与其他两种情况相比显着减小。这已经通过路面的各种激励条件得到了证明。因此，车辆的平顺性和舒适性得到了很大的提高。仿真过程的结果如表3和表4所示。

Thumbnail 缩略图

Table 3 表3
The maximum value of the oscillation.
振荡的最大值。

Thumbnail 缩略图

Table 4 表4
The average value of the oscillation.
振荡的平均值。

命名法

F_A: Actuator force, N
F _A ：执行器力，N
F_C: Linear damping force, N
F _C ：线性阻尼力，N
F_Ca: Nonlinear damping force, N
F _Ca ：非线性阻尼力，N
F_f: Friction force, N
F：摩擦力，N
F_Ke: Main spring force, N
F _Ke : 主弹簧力，N
F_Kv: Auxiliary spring force, N
F _Kv ：辅助弹簧力，N
F_p: Push force, N
F _p ：推力，N
F_S: Pneumatic force, N
F _S : 气动力，N
F_z: Static force, N
F _z ：静力，N
h : Bump on the road, m
h : 路上的颠簸，m
m₁: Sprung mass, kg
m ₁ ：簧载质量，kg
m₂: Unsprung mass, kg
m ₂ ：簧下质量，kg
m_a: Pneumatic mass, kg
m _a : 气动质量，kg
z₁: Displacement of the sprung mass, m
z ₁ ：簧载质量的位移，m
z₂: Displacement of the unsprung mass, m
z ₂ ：非簧载质量的位移，m
z_a: Displacement of the pneumatic mass, m
z _a ：气动质量的位移，m

4 CONCLUSION 4。结论

Stability and comfort are very important issues of the vehicle when moving on the road. It directly affects passengers, cargoes, and the durability of the vehicle. The comfort and smoothness are expressed through the vibrations of the sprung mass. Characterizing the main oscillations are the values of displacement and acceleration of the sprung mass (maximum amplitude, stability amplitude, oscillation frequency, etc.). The vehicle's suspension system has the role of regulating and extinguishing the oscillations generated from external stimuli.
稳定性和舒适性是车辆在道路上行驶时非常重要的问题。它直接影响乘客、货物以及车辆的耐用性。舒适性和平稳性通过簧载质量的振动来表达。表征主要振动的是簧载质量的位移和加速度值（最大振幅、稳定振幅、振动频率等）。车辆的悬架系统具有调节和消除外部刺激产生的振动的作用。

In order to improve the efficiency of the suspension system, the stiffness of the spring and damper needs to be changed continuously. The method of equipping the conventional pneumatic suspension system to replace the passive suspension system has been proposed and used. However, the results it brings are still not great. This paper has introduced a method of using the pneumatic suspension system integrated with the hydraulic actuator instead of just using the conventional pneumatic suspension system. The hydraulic actuator is controlled through the established linear controller. Based on the basic parameters of the system, the simulation process was performed for different excitation conditions from the road surface. The results of the research show that when the vehicle is equipped with the integrated pneumatic suspension system, the values of displacement and acceleration of the sprung mass are greatly reduced compared to the other two cases. To be able to do this, the system's compressed pneumatic pressure changes are continuous.
为了提高悬架系统的效率，需要不断改变弹簧和阻尼器的刚度。已经提出并使用了配备传统气动悬架系统来替代被动悬架系统的方法。然而，它带来的结果仍然不是很好。本文介绍了一种使用与液压执行器集成的气动悬架系统的方法，而不是仅仅使用传统的气动悬架系统。液压执行机构通过既定的线性控制器进行控制。根据系统的基本参数，对路面不同的激励条件进行了仿真过程。研究结果表明，当车辆配备集成气动悬架系统时，簧载质量的位移和加速度值相比其他两种情况均大大减小。为了做到这一点，系统的压缩气动压力是连续变化的。

The method of using the integrated pneumatic suspension system is completely novel. Its results are also very positive. However, the investment cost is quite expensive. In the future, nonlinear control and intelligent control methods can be used to control this system to improve its efficiency. Besides, the experimental process is necessary to be able to demonstrate the effectiveness of the integrated pneumatic suspension system.
使用集成气动悬架系统的方法是完全新颖的。其结果也非常积极。然而，投资成本相当昂贵。未来可以采用非线性控制和智能控制方法来控制该系统，以提高其效率。此外，实验过程对于证明集成气动悬架系统的有效性是必要的。

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Edited by 编辑者

Editor: 编辑：

Marcílio Alves. 马西利奥·阿尔维斯。

Publication Dates 出版日期

Publication in this collection
出版于本集
01 Nov 2021 2021 年 11 月 1 日
Date of issue 签发日期
2021

History 历史

Received 已收到
20 June 2021 2021 年 6 月 20 日
Reviewed 已审核
14 Sept 2021 2021 年 9 月 14 日
Accepted 公认
18 Sept 2021 2021 年 9 月 18 日
Published 已发表
20 Sept 2021 2021 年 9 月 20 日

This is an open-access article distributed under the terms of the Creative Commons Attribution License
这是根据知识共享署名许可条款分发的开放获取文章

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Symbol	Description	Value	Unit
m₁	Sprung mass	400	kg
m₂	Unsprung mass	40	kg
C	Damper coefficient	3000	Ns/m
K_T	Tire coefficient	180000	N/m

Symbol	Description	Value	Unit
A_e	Effective area of the pneumatic spring	0.002	m²
A_s	Connecting pipe cross section	3×10^-4	m²
l_s	Connecting pipe length	2	m
p_at	Atmospheric pressure	1×10⁵	N/m²
p₀	Initial absolute pneumatic spring pressure	4×10⁵	N/m²
V_r0	Initial volumes of the reservoir	0.004	m³
V_b0	Initial volumes of the balloon	0.008	m³
ρ	Density of the air at initial condition	1.29	kg/m³
β	Constant	2
k	Total loss coefficient of the connection pipes	3.5
n	Multivariable coefficient	1.4
γ₁	Actuator coefficient	4.5×10¹³	N/m⁵
γ₂	Actuator coefficient	1	s^-1
γ₃	Actuator coefficient	1.5×10⁹	N/kg^1/2m^5/2
τ	Time coefficient	2.5×10^-3	s
S_p	Piston cross section	3.5×10^-4	m²
P_s	Supply pressure	1056240	N/m²
k_sv	Servo valve gain	1×10^-3	m/V

Brasil 巴西

Brasil 巴西

Advance the stability of the vehicle by using the pneumatic suspension system integrated with the hydraulic actuator
使用集成液压执行器的气动悬架系统提高车辆的稳定性

Abstract 抽象的

Graphical Abstract 图形概要

1 INTRODUCTION 1 简介

2 MATERIAL AND METHOD
2 材料与方法

2.1 Pneumatic Suspension Model
2.1 气压悬架模型

2.2 Control model 2.2 控制模型

3 RESULTS AND DISCUSSIONS
3 结果与讨论

3.1 Simulation conditions
3.1 模拟条件