Performance Analysis of Nonlinear Stiffness Suspension Based on Multi-Objective Optimization

This paper concerns the dynamic performance analysis of the vehicle ISD (inerter-spring-damper) suspension employing an eccentric inerter. Firstly, the quarter car model of the two basic vehicle suspension layouts involving an eccentric inerter, namely, the series-connected layout and the parallel-connected layout, is established. Then, by considering the overall performance such as the vehicle body acceleration, the suspension working space, and the dynamic tire load, the key parameters of the two suspensions are optimized by using the genetic algorithm. Simulation analysis results indicate that the series-connected vehicle ISD suspension is superior to the parallel-connected one, and all of the RMS values of the body acceleration, the suspension working space, and the dynamic tire load are decreased significantly by comparing to the conventional suspension, while the improvement of the parallel-connected vehicle ISD suspension is relatively poor. At last, the impact of the flywheel eccentricity and the screw pitch on the dynamic performance indices of the two suspensions is discussed, and the trade-offs among the three performances are analyzed, which will provide a guide method for the suspension design when considering the eccentric factor.

Energy consumption sensitivity analysis and energy-reduction control of hybrid electromagnetic active suspension

In this study, a new hybrid electromagnetic actuator (HEMA) that integrates a cylindrical permanent magnet linear synchronous motor and a hydraulic damper is proposed and designed to solve the problem of poor reliability of a linear electromagnetic actuator. A modified skyhook control that matches the structure of the HEMA is adopted, and the performance parameters are optimized. Then, the relationships among structural parameters of the HEMA are analyzed using equivalent magnetic circuit method. On the basis of these relationships, multiple alternative groups of structural parameters are obtained. Moreover, finite element models are established in Ansoft Maxwell software. The structural parameters of the HEMA are optimized and determined to produce the peak electromagnetic thrust force that the linear motor requires. Finally, a prototype is developed on the basis of the optimized results for the bench test. Test results show that the linear motor tracks the desired force effectively. In contrast to the passive damper, the body acceleration and suspension working space of HEMA are decreased by 20.6% and 13.3%, respectively. The dynamic tire load is increased by 16%, which is in a reasonable range. And compared with LEMA, the body acceleration is increased by 2.73%, but the suspension working space and dynamic tire load are reduced by 1.1% and 38.1%. All the results above mentioned demonstrate that the HEMA can considerably improve the vehicle dynamic performance.

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.

This paper concerns the impact of inerter element on the vehicle suspension system. On the basis of the analysis of three simple elements’ networks including one inerter, one spring and one damper, the improved networks are further proposed. A quarter-vehicle model is considered, and the three performance indexes, namely the body acceleration, suspension working space and dynamic tire load are taken into account. With the increase of the inertance value, numerical simulations are carried out and the influences on the performance indexes, the partial frequencies and the dominant frequencies are discussed in detail. Results indicate that the value of the partial frequencies and the dominant frequencies will reduce effectively by increasing the inertance value of the suspension system. At last, two type suspension layouts are analysed by comparing to a passive suspension, and their performance advantages are also validated.

<div>The usage of the inerter and its studies has greatly developed in recent years as it offers better performance compared to passive systems and has lower cost and power consumption than active and semi-active systems. This article focuses on studying a half-vehicle model to obtain the optimal layout of the mechatronic inerter, spring, and damper suspension system (ISD) for comfort enhancement with the aid of the structure-immittance approach, ensuring structural simplicity.</div> <div>The mechatronic inerter, which consists of a single capacitance, resistance, and inductance, is added to a half-vehicle model composed of an inerter, spring, and damper. All possible layouts are studied to achieve the optimal design layout. Evaluation criteria such as the performance index, system peak-to-peak value, and settling time are utilized to assess body acceleration, thereby improving passenger comfort. Furthermore, the system’s impact on dynamic tire load and suspension working space under diverse road conditions is analyzed. Theoretical analyses conducted using MATLAB/Simulink demonstrate that the novel mechatronic ISD layout significantly enhances body acceleration performance compared to conventional passive systems, switchable hydraulic ISD systems, and fuzzy logic-controlled three-setting switchable dampers.</div>

The active suspension system (ASS) is considered a highly promising solution for effectively addressing the inherent conflicts between ride comfort, vehicle stability, and driving safety. However, its performance is significantly influenced by the control strategies employed. To address this, the present study investigates the effectiveness of various control strategies applied to the ASS of an electric vehicle (EV). For this purpose, a half-car EV model with five degrees of freedom is developed for the deployment of the ASS. Several control strategies are proposed for the ASS, including the classical Proportional-Integral-Derivative (PID) controller, a Type-2 Fuzzy Logic Controller (T2FLC), a hybrid controller that combines PID and T2FLC referred to as HT2FLCPID, and an adaptive type of the controller called AT2FLCPID. The Particle Swarm Optimization (PSO) algorithm is selected to optimize the parameters of these control strategies. The ASS with the proposed control strategies is developed in the MATLAB/Simulink environment. The results show that the root mean square (RMS) values of seat acceleration ( a zs ), body acceleration ( a zb ), pitching body acceleration ( a φb ), suspension working space ( SWS ), and dynamic tire load ( DTL ) in the ASS with the proposed control strategies demonstrate significantly improved vibration absorption compared to the passive suspension system (PSS). Among these strategies, the AT2FLCPID controller demonstrates the best performance in comparison to the other control strategies. The findings of this study provide valuable insights into the advantages and limitations of each control strategy, offering a solid foundation for the development of smarter and more efficient suspension systems for future electric vehicle applications.

To address the challenge of physically realizing fractional-order electrical networks, this study proposes an implementation method for a mechatronic inerter–spring–damper (ISD) suspension based on a fractional-order biquadratic transfer function. Building upon a previously established model of a mechatronic ISD suspension, the influence of parameter perturbations on the suspension’s dynamic performance characteristics was systematically investigated. Positive real synthesis was employed to determine the optimal five-element passive network structure for the fractional-order biquadratic electrical network. Subsequently, the Oustaloup filter approximation algorithm was utilized to realize the integer-order equivalents of the fractional-order electrical components, and the approximation effectiveness was analyzed through frequency-domain and time-domain simulations. Bench testing validated the effectiveness of the proposed method: under random road excitation at 20 m/s, the root mean square (RMS) values of the vehicle body acceleration, suspension working space, and dynamic tire load were reduced by 7.86%, 17.45%, and 2.26%, respectively, in comparison with those of the traditional passive suspension. This research provides both theoretical foundations and practical engineering solutions for implementing fractional-order transfer functions in vehicle suspensions, establishing a novel technical pathway for comprehensively enhancing suspension performance.

The aim of the present work is to illustrate the application of mixed H2/H∞ control theory with Pole-Placement in de- signing controller for semi-active suspension system. It is well known that the ride comfort is improved by reducing vehicle body acceleration generated by road disturbance. In order to study this phenomenon, Two Degrees of Freedom (DOF) in state space vehicle model was built in. However, the role of H is to minimize the disturbance effect on the output while H2 is used to improve the input of controller. Linear Matrix Inequality (LMI) technique is used to calculate the dynamic controller parameters. The simulation results show that the H2 and H techniques can effectively control the vibration of vehicle system where the reduction of suspension working space, dynamic tire load and body acceleration. Moreover, the simulation results show that the (RMS) of suspension working space was reduced by 44.5%, body acceleration and dynamic tire load are reduced by 18.5% and 20% respectively.

To address the limited capability of conventional hydro-pneumatic suspensions in coordinated damping–stiffness regulation, this paper proposes a new semi-active hydro-pneumatic suspension (SAHPS) system based on a dual-valve shock absorber. A damping valve architecture composed of a spring check valve–solenoid proportional valve–spring check valve is arranged between the rod and rodless chambers of the hydraulic cylinder, enabling coordinated adjustment of suspension damping and equivalent stiffness. Furthermore, a genetic algorithm optimization with model predictive control (GA-MPC) is designed to enhance the overall dynamic performance of the suspension while effectively reducing the operating frequency of the solenoid proportional valve. Finally, AMESim–Simulink co-simulations and hardware-in-the-loop (HIL) experiments are conducted under bumpy road excitation and Class C random road conditions. Under Class C random road conditions, compared with passive hydro-pneumatic suspension and semi-active suspension with conventional MPC, the proposed method achieves maximum reductions of 11%, 25%, and 12.9% in the root mean square values of body acceleration, suspension working space, and dynamic tire load, respectively. The discrepancies between experimental and simulation results remain below 7%, confirming the effectiveness of the proposed system and control strategy. This study provides a new technical guidance for low-frequency vibration suppression in vehicle suspension systems.

This paper proposes an adaptive robust sliding mode control (SMC) strategy based on radial basis function neural networks (RBF-NNs) to address nonlinear issues in semi-active suspension system (SASS), such as external disturbances and uncertain parameters. Firstly, the Dahl model is selected for the parameters identification of the magnetorheological (MR) damper, followed by the establishment of a model for the SASS. Secondly, this paper proposes a control strategy that integrates robust control with SMC. The RBF-NNs are utilized to estimate the system’s uncertain parameters, thereby enhancing the robustness of the suspension system against external disturbances and ensuring its stability. The stability and controllability of the closed-loop SASS are rigorously verified through the application of Lyapunov theory.1 Under the road excitations of B-Class and speed bump, the dynamic characteristics of the passive control, the robust SMC, and the adaptive robust SMC based on RBF-NNs applied to the MR-SASS are analyzed. The vertical acceleration of the automobile body, the suspension working space and the tire dynamic load are selected as the evaluation indices. The results demonstrate that the adaptive robust SMC significantly improves the ride comfort and handling stability of the vehicle.

This paper designs a quasi-zero stiffness suspension with an air spring and a magnetic spring in parallel to improve the vehicle ride comfort. The proposed new suspension does not change the overall layout of the air suspension or affect the handling stability, reducing the system’s natural frequency by a sound vibration isolation effect for a low-frequency vibration and finally improving ride comfort. The feasibility of quasi-zero stiffness suspension is verified by mathematical modeling of air spring and magnetic spring, and reasonable structural parameters are set for the simulation experiment. The 1/4 vehicle model with two degrees of freedom is built in MATLAB / Simulink. Select body acceleration, suspension working space, and tire dynamic load as evaluation indexes to test the comfort performance of the proposed suspension. The result shows that the proposed new suspension has a noticeable effect on reducing the acceleration of the vehicle body and significantly improves the vehicle ride comfort.

To study the application effect of linear motor energy regenerative suspension in semi-active suspension of automobiles, a 1/4 two degrees of freedom semi-active suspension dynamic model, energy regenerative circuit, and current hysteresis loop control model were established. Establish an integer order skyhook control semi-active suspension, use an improved Oustaloup filter algorithm to establish a fractional order skyhook control semi-active suspension based on fractional calculus, and compare and analyze it with a composite fractional order skyhook control semi-active suspension based on fractional order skyhook control. The simulation results show that when the vehicle is driving at a constant speed of 60 km/h on a C-grade road, compared with passive suspension, semi-active suspension has a significant improvement in sprung mass acceleration, suspension working space, and dynamic tire load. Among them, fractional order skyhook control semi-active suspension and composite fractional order skyhook control suspension have better sprung mass acceleration and dynamic tire load than integer order skyhook control semi-active suspension. However, suspension working space deteriorates to some extent compared to integer order skyhook controlled semi-active suspension. When there is a time delay in the system, as time delay increases, the control effect gradually deteriorates. When the time delay is within a certain range, the composite fractional order skyhook control suspension performs better than the other two control methods. In summary, while maintaining the control performance of fractional order semi-active suspension, the composite fractional order skyhook control has certain improvements and improvements in various aspects compared to integer order skyhook control semi-active suspension, especially when there is a certain range time delay in the system.

Integrated optimization for mechanical elastic wheel and suspension based on an improved artificial fish swarm algorithm

Reducing vibrations for the hub motor driven vehicle (HMDV) under the adverse effects of the unbalanced radial force of the switched reluctance motor (SRM) and road surface excitation is essential to enhance the overall performance of electric vehicles. To address this issue, a quarter dynamic model of the HMDV is established. Subsequently, four structures of the inertial suspension system are proposed to improve vibration isolation for the HMDV. To achieve this, the Particle Swarm Optimization (PSO) algorithm is employed to optimize the parameters of the inertial suspension system. The root mean square (RMS) values of body acceleration, suspension working space, and dynamic tire load are chosen as the objective functions. Finally, two representative structures of the inertial suspension system are selected and developed into semi-active inertial suspension systems to further enhance vibration isolation performance for the HMDV. Fuzzy logic control (FLC) is then applied to control the damping coefficient of the semi-active inertial suspension system. To improve the effectiveness of the FLC, the PSO algorithm is used to optimize the input and output ranges of the FLC. The performance of the semi-active inertial suspension system is thoroughly evaluated in both the time and frequency domains. The results show that the semi-active inertial suspension system significantly improves ride comfort, driving safety, and road friendliness compared to the conventional suspension system. These findings underscore the potential of semi-active inertial suspension systems to significantly enhance vibration isolation for the HMDV.