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This study proposes a modified energy-saving skyhook consisting of active control, energy regeneration, and switch. The modified skyhook coordinates the contradiction between dynamic performance and energy consumption of electromagnetic active suspension. The control principle is analyzed, the switch condition between active control and energy reco...
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Citations
... Therefore, if the matrix Q 1 is given, matrix P 1 can be determined by equation (21). Finally, the optimal control force can be determined by equation (14). ...
The present paper proposes an optimal polynomial control strategy for a quarter-vehicle suspension system based on dynamic programming. The optimal control objective is to decrease the responses of sprung mass acceleration, suspension deformation and road excitation, which are reflected in the performance index. The optimal control force is obtained through the principle of dynamic programming, and the form of the optimal control force mainly depends on the form of the cost function. The optimal nonlinear polynomial control (NPC) force is derived by selecting the cost function in polynomial form. The linear feedback matrix and nonlinear feedback matrix in the NPC force are determined by the Riccati equation and Lyapunov equation, respectively. The root mean square (RMS) responses of the sprung mass acceleration, suspension deformation and road load of driving vehicles under deterministic and random road surfaces are calculated. The numerical results showed that the proposed NPC strategy has a better control effect over the traditional linear quadratic regulator (LQR), especially on the peak reduction of sprung mass acceleration. Finally, the optimal control force is divided into active control force and passive control force. The energy input of the optimal control force can be reduced by only inputting the active control force.
... Therefore, the QZSAS system needs to match the appropriate equivalent damping ratio, and its damping coefficient is much smaller than that of the traditional air suspension system. In the field of semi-active suspension control, various strategies have been applied [17][18][19][20][21][22][23][24][25][26]. Notably, the robust algorithm is outstanding in solving parameter disturbance and suppressing external disturbance input. ...
To further improve the multi-objective comprehensive vibration isolation performance of commercial vehicles and save network resource occupation, this paper proposes a new configuration of semi-active quasi-zero stiffness air suspension (QZSAS) with network communication architecture, and a matching dynamic output feedback control (DOFC) strategy considering event-triggered mechanism. The semi-active QZSAS is mainly composed of a positive stiffness air spring, a pair of negative stiffness double-acting cylinders and two continuous damping controlled (CDC) dampers. Event-triggered mechanism determines whether the control signal is updated by judging the measured signal to save communication resources. Firstly, the nonlinear stiffness of the suspension system is regarded as an uncertain parameter and processed by constructing a Takagi–Sugeno (T-S) fuzzy controller model. Then, the Lyapunov–Krasovskii functional method is employed to design the dynamic output feedback controller under the linear matrix inequality constraint to ensure system stability with H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_\infty }$$\end{document} performance index. Finally, the co-simulation and hardware-in-the-loop (HiL) test results show that the presented new semi-active QZSAS structure and the DOFC method considering event-triggered mechanism can significantly improve the multi-objective performance of commercial vehicles under different driving conditions with significantly reducing the network communication burden.
... In the open literatures, much research effort has been devoted to the control synthesis of Skyhook control suspension systems, For instance, an ideal skyhook suspension model is employed as the reference model in the design of the model reference controller. [24][25][26] However, in order to reduce the complexity of the control system, the suspension control method with simplified skyhook model is still a challenge and motivates this work. To this end, the objective of this work is to propose a backstepping controller based on the improved skyhook reference model for damping force control. ...
... The skyhook damper configuration attempts to alleviate the design difficulty in regard to trade-off between resonance control and high frequency isolation for passive suspensions, which is an ideal solution for isolating the sprung mass from road excitations. 26,31,32 However, it is very difficult to obtain the road excitation as the input while using the ideal skyhook model as reference model in practice. To overcome the above difficulty, this work designs an improved skyhook model as the reference model. ...
The electronically controlled semi-active air suspension systems have been widely used to improve the vehicle ride comfort and road holding performance by adjusting the damper stiffness. This work focuses on the design of a damping force controller to enhance the ride comfort, road holding and stability under the presence of unknown air spring pressure. Firstly, an improved skyhook suspension reference model is developed to generate the desired dynamic criteria (i.e. vehicle body acceleration, pitch and roll angles). Secondly, by employing the backstepping technique, a novel damping force controller is proposed to approach the desired dynamic criteria. Thirdly, a parameter estimation method is also designed to estimate the air spring pressure to obtain the air spring force. Comparative studies are carried out among passive suspension systems, and the semi-active air suspension systems with the proposed model reference damping force control, traditional backstepping control and existing sliding mode control. Numerical results show that a significant improvement of ride comfort can be observed with the semi-active air suspension system based on the proposed model reference backstepping controller.
... The permanent magnet linear synchronous motor (PMLSM) cancels the intermediate transmission link, which has the advantages of high thrust density, fast speed, high precision, etc. [1][2][3][4]. Together with the rapid development of rare earth materials, this further improves performance and minimizes the cost of PMLSMs, making them widely used in industrial automation and in other fields [5,6]. However, the structural defects of the linear motor itself (discontinuity of the primary core) produce end effects and lead to increased thrust ripple, limiting its development to the field of high precision [7]. ...
In response to the end effect of the permanent magnet linear synchronous motor, this paper proposes an improved modular motor structure. To compute its electromagnetic characteristics, a subdomain model that converts the Cartesian coordinate system into a polar coordinate system through coordinate transformation is further formulated, thus significantly reducing programming difficulty. The analytical results are compared with those of the finite element method and indicate that the subdomain model can accurately consider the effects of end and flux barriers. Moreover, the magnetic field distribution inside the motor is applied to explain the end force abatement, and the suggested flux barrier width is obtained. Finally, the modular structure is applied to a 9-slot, 10-pole permanent magnet linear synchronous motor. The simulation results show that the modular structure can effectively suppress the end effect of the linear motor, and the proposed subdomain model applies to the design of the modular motor.
... The skyhook control algorithm was first proposed by Karnopp in the United States and was originally used for the control of semi-active suspension [154]. With the development of the suspension system and the deepening of control research, it has been developed into ideal skyhook control [155], skyhook active control [156], and skyhook on-off control [157]. ...
The active suspension has undoubtedly improved the performance of the vehicle, however, the trend of “low-carbonization, intelligence, and informationization” in the automotive industry has put forward higher and more urgent requirements for the suspension system. The automotive industry and researchers favor active energy regeneration suspension technology with safety, comfort, and high energy regenerative efficiency. In this paper, we review the research progress of the structure form, optimization method, and control strategy of electromagnetic energy regenerative suspension. Specifically, comparing the pros and cons of the existing technology in solving the contradiction between dynamic performance and energy regeneration. In addition, the development trend of electromagnetic energy regenerative suspension in the field of structure form, optimization method, and control technology prospects.
... Tubular permanent magnet synchronous linear motor (TPMSLM) has the advantages of slight armature reaction, high positioning accuracy, and good reliability, which has been applied in the needle-free jet injection and linear electromagnetic actuators [1][2][3][4][5][6]. However, the large thrust ripple of linear motors still restricts their development in highprecision applications. ...
The limitation of the primary core length of the tubular permanent magnet synchronous linear motor (TPMSLM) causes large thrust ripples during operation. To end this, a modular TPMSLM with two units is proposed. The principle of its suppression of end effects is derived, and utilization of the three-phase winding is improved using the star vectograms of the back electromotive force (EMF). Afterward, an equivalent subdomain method is adopted to analyze the above structure. This method combines the subdomain and the equivalent magnetic circuit (EMC) model, and the comparison with nonlinear FEM verifies its effectiveness. Using this integrated approach, reasonable structure parameters are selected. Finally, the experimental platform of the two-unit modular TPMSLM prototype is built with the selected structural parameters. Good agreement between the simulation and the experiment on the back EMF, detent force, and the prototype's static thrust verifies the new structure's feasibility.
... Control algorithms [5][6][7][8] based on closed-loop PID have been proposed. Most of these methods are aimed at achieving the ideal dynamic capability of skyhook damping while balancing the robustness and stability of the system. ...
Although many adaptive techniques for active vibration reduction have been designed to achieve optimal performance in practical applications, few are related to reinforcement learning (RL). To explore the best performance of the active vibration reduction system (AVRS) without prior knowledge, a self-adaptive parameter regulation method based on the DDPG algorithm was examined in this study. The DDPG algorithm is unsuitable for a random environment and prone to reward-hacking. To solve this problem, a reward function optimization method based on the integral area of the decibel (dB) value between transfer functions was investigated. Simulation and graphical experimental results show that the optimized DDPG algorithm can automatically track and maintain optimal control performance of the AVRS.
... Therefore, the QZSAS system needs to match the appropriate equivalent damping ratio, and its damping coefficient is much smaller than that of the traditional air suspension system. In the field of semi-active suspension control, various strategies have been applied, such as such as the skyhook control [16,17], sliding mode control [18,19], adaptive backstepping control [20,21], robust control [22,23], hybrid control [24,25]. Notably, the robust algorithm is outstanding in solving parameter disturbance and suppressing external disturbance input. ...
To further improve the multi-objective comprehensive vibration isolation performance of commercial vehicles and save network resource occupation, this paper proposes a new configuration of semi-active quasizero stiffness air suspension (QZSAS) with network communication architecture, and a matching dynamic output feedback control (DOFC) strategy considering eventtriggered mechanism. The semi-active QZSAS is mainly composed of a positive stiffness air spring, a pair of negative stiffness double-acting cylinders and two CDC dampers. Event-triggered mechanism determines whether the control signal is updated by judging the measured signal to save communication resources. Firstly, The nonlinear stiffness of the suspension system is regarded as an uncertain parameter and processed by constructing a Takagi-Sugeno (T-S) fuzzy controller model. Then, the Lyapunov-Krasovskii functional method is employed to design the dynamic output feedback controller under the linear matrix inequality (LMI) constraint to ensure system stability with H ∞ performance index. Finally, the co-simulation and hardware-in-the-loop (HiL) test results show that the presented new semi-active QZSAS structure and the DOFC method considering eventtriggered mechanism can significantly improve the multiobjective performance of commercial vehicles under different driving conditions with significantly reducing the network communication burden.
... As one of the linchpins of the vehicle chassis system, the suspension system can exert significant influences on ride comfort and vehicle handling performance. Until now, semiactive suspension [1][2][3][4][5] and active suspension [6][7][8][9][10][11] systems are widely known for their versatility. For the semiactive suspension system, it can adjust the damping force by changing the command current, which generates advantages such as lower consumption, rapid response, and simplicity. ...
This paper concerns the optimal problem of the vehicle ISD (inerter-spring-damper) suspension based on the asymmetric-damping effect. In order to explore the benefits of the asymmetric damping, a quarter car model of the four-element ISD suspension is built by considering the symmetric and asymmetric reciprocating damping factors. The parameters of the proposed vehicle ISD suspension with symmetric-damping and asymmetric-damping features are optimized by means of the genetic algorithm in single-objective scenario and multiobjective scenario, respectively. The dynamic performances are analyzed through simulations in time and frequency domains, and the impacts of the compression and tensile damping on the body acceleration, the suspension working space, and the dynamic tire load are discussed. Results indicate that, compared with the conventional passive suspension, the proposed ISD suspensions manifest excellent vibration isolation performance, and the asymmetric reciprocating damping ISD suspension even showcases extra improving space of the dynamic performances except for the dynamic tire load in the impulse input condition. It seems that the dynamic performance of the vehicle ISD suspension will be much superior when considering the asymmetric reciprocating damping factors.
... In case of semiactive dampers, similarly as in dampers of vehicle suspensions, damping coefficient is changed during the operation of the system [11,12]. However, in the case of active systems of vibration reduction, additional energy used to react to variable load is supplied to the system [9,13]. Although active systems seem to be more effective, due to the necessity to supply significant energy to the system, semi-active systems are more often used [14][15][16]. ...
In this work an original construction of a vibration damper controlled by means of a valve with a short time of operation lag is presented. The valve-controlling properties of the damper regulates the flow of fluid between the chambers of the damper and was constructed using piezoelectric actuators, whose characteristic feature is the possibility to change dimensions, e.g., length, under the influence of voltage. As a result, by changing voltage it is possible to control the throttle of the flow by changing the width of a gap, which influences a change of damping forces. Such a solution enables a quicker change of damping forces than in other kinds of controlled damper. Due to the obtained properties, the damper may be applied to reduce the vibrations of vehicles and machines that undergo quick-change loads. In the article, the results of experimental studies of the aforementioned damper are presented. Based on the results, dissipative characteristics were determined. Also, results of numerical studies comprising the development of a numerical model of a controlled piezoelectric damper are shown. Results of numerical studies, as well as experimental studies, are presented in the form of dissipative characteristics. Comparison of results of numerical and experimental studies confirms the possibility to apply this kind of construction in semi-active systems of vibration reduction of vehicles and machines.
