scholarly journals DYNAMIC CHARACTERISTICS OF NON-SMOOTH SUSPENSION SYSTEM UNDER FRACTIONAL-ORDER DISPLACEMENT FEEDBACK

10.6036/10125 ◽  
2021 ◽  
Vol 96 (3) ◽  
pp. 322-328
Author(s):  
JIANCHAO ZHANG ◽  
Zhan Chen ◽  
Jun Wang ◽  
Yufei Hu
Keyword(s):  
Feedback Control ◽  
Analytical Solution ◽  
Fractional Order ◽  
Dynamic Characteristics ◽  
Harmonic Excitation ◽  
Suspension System ◽  
Vehicle Body ◽  
Dynamic Behaviors ◽  
Integer Order ◽  
Suspension Systems

Vehicle suspension systems generally have non-smooth factors, such as clearances, collision, and constraint. The bad dynamic behaviors caused by these non-smooth factors have not been controlled effectively, thus influencing the driving performance and riding comfort of vehicles. To explore the dynamic characteristics of non-smooth suspension systems for controlling the bad dynamic behaviors, an approximate analytical solution to the response of a two-degree of freedom nonlinear suspension system, which has a fractional-order displacement feedback under harmonic excitation, was deduced by the Krylov–Bogoliubov (KB) method. This analytical solution was verified by the numerical solution of the suspension system. Moreover, the response of the suspension system with fractional-order displacement feedback control was compared with those of the systems without feedback control and traditional integer-order control. The influences of the main parameters of the system on the dynamic suspension characteristics were analyzed thoroughly. Finally, the stability of the suspension system was analyzed by plotting the maximum Lyapunov index diagram. Results show that compared with the systems without feedback control and with traditional integer-order control, the nonlinear suspension system with fractional-order displacement feedback control can significantly improve vehicle acceleration, the dynamic deflection of the suspension, and the displacement of the vehicle body. Controlling the nonlinear stiffness coefficient of the suspension system within 103–106 is conducive to decreasing the dynamic deflection of the suspension system of vehicles, while increasing the fractional-order control coefficient and the fractional order is beneficial to controlling the dynamic deflection of the suspension system and the displacement of the vehicle body. Conclusions obtained in the study can provide unique references for the optimal design and control of nonlinear suspension systems with fractional-order displacement feedback control. Keywords: suspension; non-smooth; fractional order; dynamics; analytical solution; nonlinear.

scholarly journals Optimal control and parameters design for the fractional-order vehicle suspension system

2018 ◽  
Vol 37 (3) ◽  
pp. 456-467 ◽  
Author(s):  
Hao You ◽  
Yongjun Shen ◽  
Haijun Xing ◽  
Shaopu Yang
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Suspension System ◽  
Least Square ◽  
Vehicle Body ◽  
Vehicle Suspension ◽  
Vertical Acceleration ◽  
Control Force ◽  
Suspension Systems ◽  
Vehicle Suspension System

In this paper the optimal control and parameters design of fractional-order vehicle suspension system are researched, where the system is described by fractional-order differential equation. The linear quadratic optimal state regulator is designed based on optimal control theory, which is applied to get the optimal control force of the active fractional-order suspension system. A stiffness-damping system is added to the passive fractional-order suspension system. Based on the criteria, i.e. the force arising from the accessional stiffness-damping system should be as close as possible to the optimal control force of the active fractional-order suspension system, the parameters of the optimized passive fractional-order suspension system are obtained by least square algorithm. An Oustaloup filter algorithm is adopted to simulate the fractional-order derivatives. Then, the simulation models of the three kinds of fractional-order suspension systems are developed respectively. The simulation results indicate that the active and optimized passive fractional-order suspension systems both reduce the value of vehicle body vertical acceleration and improve the ride comfort compared with the passive fractional-order suspension system, whenever the vehicle is running on a sinusoidal surface or random surface.

Chaotic Behavior and Feedback Control of Magnetorheological Suspension System With Fractional-Order Derivative

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Chengyuan Zhang ◽  
Jian Xiao
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Suspension System ◽  
Suspension Systems ◽  
Chaotic Vibration ◽  
Nonlinear Dynamic Characteristics ◽  
Magnetorheological Suspension ◽  
Time Domain Response ◽  
Predictor Corrector

The fractional differential equations of the single-degree-of-freedom (DOF) quarter vehicle with a magnetorheological (MR) suspension system under the excitation of sine are established, and the numerical solution is acquired based on the predictor–corrector method. The analysis of phase trajectory, time domain response, and Poincaré section shows that the nonlinear dynamic characteristics between fractional and integer-order suspension systems are quite different, which proves the superiority of using fractional order to describe the physical properties. By discussing the influence of each parameter on the vibration, the range of parameters to avoid the chaotic vibration is obtained. The variable feedback control is used to control the chaotic vibration effectively.

scholarly journals Feedback control for two-degree-of-freedom vibration system with fractional-order derivative damping

2017 ◽  
Vol 37 (3) ◽  
pp. 554-564
Author(s):  
Canchang Liu ◽  
Chicheng Ma ◽  
Jilei Zhou ◽  
Lu Liu ◽  
Shuchang Yue ◽  
...  
Keyword(s):  
Feedback Control ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Suspension System ◽  
Degree Of Freedom ◽  
Vehicle Suspension ◽  
Vibration System ◽  
Fractional Order Derivative ◽  
Vehicle Suspension System ◽  
Two Degree Of Freedom

A two-degree-of-freedom nonlinear vibration system of a quarter vehicle suspension system is studied by using the feedback control method considered the fractional-order derivative damping. The nonlinear dynamic model of two-degree-of-freedom vehicle suspension system is built and linear velocity and displacement controllers are used to control the nonlinear vibration of the vehicle suspension system. A case of the 1:1 internal resonance is considered. The amplitude–frequency response is obtained with the multiscale method. The asymptotic stability conditions of the nonlinear system can be gotten by using the Routh–Hurwitz criterion and the ranges of control parameters are gained in the condition of stable solutions to the system. The simulation results show that the feedback control can effectively reduce the amplitude of primary resonance, weaken or even eliminate the nonlinear vibration characteristics of the suspension system. Fractional orders have an impact on control performance, which should be considered in the control problem. The study will provide a theoretical basis and reference for the optimal design of the vehicle suspension system.

scholarly journals Modelling and Sensitivity Analysis of Influencing Parameters in Displacement of Dynamic Bodies

2021 ◽  
Vol 06 (05) ◽  
Author(s):  
Yokesh K.S ◽  
Keyword(s):  
Dynamic Characteristics ◽  
Vertical Displacement ◽  
Suspension System ◽  
Damping Coefficient ◽  
Vehicle Body ◽  
Dominant Factor ◽  
Spring Stiffness ◽  
Variation Of Parameters ◽  
Important Challenge ◽  
Influencing Parameters

The mathematical modelling in relation to the Six-degree freedom system of train suspension is developed and simulated for their dynamic characteristics. The important challenge in the suspension system is vertical displacement obtained from the vehicle body. To reduce vertical displacement, an analysis of the model is done by variation of parameters such as stiffness of spring and damping coefficient. The model has been created by deriving the equations of a system using Newton’s law. The developed model has the potential to analyse the dynamic characteristics of the suspension system for both displacement of the vehicle body and displacement of the wheel. The outcome of this research revealed that Secondary spring stiffness is the most dominant factor to influence the displacement of the vehicle body; Primary damping coefficient is the most dominant factor to influence displacement of the wheel.

An optimal control method for time-delay feedback control of 1/4 vehicle active suspension under random excitation

2021 ◽  
pp. 146134842110592
Author(s):  
Kaiwei Wu ◽  
Chuanbo Ren ◽  
Yuanchang Chen
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Control Method ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
Vehicle Body ◽  
Vehicle Suspension ◽  
Control Parameters ◽  
Damping Effect ◽  
Delay Feedback Control

Time-delay feedback control can effectively broaden the damping frequency band and improve the damping efficiency. However, the existing time-delay feedback control strategy has no obvious effect on multi-frequency random excitation vibration reduction control. That is, when the frequency of external excitation is more complicated, there is no better way to obtain the best time-delay feedback control parameters. To overcome this issue, this paper is the first work of proposing an optimal calculation method that introduces stochastic excitation into the process of solving the delay feedback control parameters. It is a time-delay control parameter with a better damping effect for random excitation. In this paper, a 2 DOF one-quarter vehicle suspension model with time-delay is studied. First, the stability interval of time-delay feedback control parameters is solved by using the Lyapunov stability theory. Second, the optimal control parameters of the time-delay feedback control under random excitation are solved by particle swarm optimization (PSO). Finally, the simulation models of a one-quarter vehicle suspension simulation model are established. Random excitation and harmonic excitation are used as inputs. The response of the vehicle body under the frequency domain damping control method and the proposed control method is compared and simulated. To make the control precision higher and the solution speed faster, this paper simulates the model by using the precise integration method of transient history. The simulation results show that the acceleration of the vehicle body in the proposed control method is 13.05% less than the passive vibration absorber under random excitation. Compared with the time-delay feedback control optimized by frequency response function, the damping effect is 12.99%. The results show that the vibration displacement, vibration velocity, and vibration acceleration of the vehicle body are better than the frequency domain function optimization method, whether it is harmonic excitation or random excitation. The ride comfort of the vehicle is improved obviously. It provides a valuable tool for time-delay vibration reduction control under random excitation.

Research on vibration reduction of semi-active suspension system of quarter vehicle based on time-delayed feedback control with body acceleration

2021 ◽  
pp. 146134842110518
Author(s):  
Yong Guo ◽  
Chuanbo Ren
Keyword(s):  
Feedback Control ◽  
Delayed Feedback ◽  
Suspension System ◽  
Delayed Feedback Control ◽  
Vehicle Body ◽  
Vehicle Suspension ◽  
Vertical Acceleration ◽  
Control Parameters ◽  
Vehicle Suspension System ◽  
Time Delayed Feedback

In this paper, the mechanical model of two-degree-of-freedom vehicle semi-active suspension system based on time-delayed feedback control with vertical acceleration of the vehicle body was studied. With frequency-domain analysis method, the optimization of time-delayed feedback control parameters of vehicle suspension system in effective frequency band was studied, and a set of optimization method of time-delayed feedback control parameters based on “equivalent harmonic excitation” was proposed. The time-domain simulation results of vehicle suspension system show that compared with the passive control, the time-delayed feedback control based on the vertical acceleration of the vehicle body under the optimal time-delayed feedback control effectively broadens the vibration absorption bandwidth of the vehicle suspension system. The ride comfort and stability of the vehicle under random road excitation are significantly improved, which provides a theoretical basis for the selection of time-delayed feedback control strategy and the optimal design of time-delayed feedback control parameters of vehicle suspension system.

scholarly journals Performance Comparison of Various controllers on Semi-Active Vehicle Suspension System

2021 ◽  
Vol 40 ◽  
pp. 01001
Author(s):  
Sarvesh Walavalkar ◽  
Viraj Tandel ◽  
Rahul Sunil Thakur ◽  
V.V Pramod Kumar ◽  
Supriya Bhuran
Keyword(s):  
Active Suspension ◽  
Suspension System ◽  
Internal Model Control ◽  
Vehicle Body ◽  
Vehicle Suspension ◽  
Inference System ◽  
Proportional Integral ◽  
Suspension Systems ◽  
Model Control ◽  
Vehicle Suspension System

The value of a self-tuning adaptive semi-active control scheme for automotive suspension systems is discussed in this paper. The current vehicle suspension system uses fixed-coeffcient springs and dampers. The ability of vehicle suspension systems to provide good road handling and improve passenger comfort is usually valued. Passive suspension allows you to choose between these two options. Semi-Active suspension(SAS), on the other hand, can provide both road handling and comfort by manipulating the suspension force actuators directly. The semi-active suspension system for a quarter car model is compared to passive and various controllers such as Proportional-Integral, Proportional-Integral-Derivative, Internal model control (IMC)-PID, IMC-PID with filter, FUZZY, and Adaptive-network-based fuzzy inference system(ANFIS) in this analysis. This research could be relevant in the future for designing better car suspension adjustments to eliminate vertical jerks and rolling motion experienced by the vehicle body on bumps and humps.

Study of Dynamic Performance of a Vehicle With Planar Suspension Systems in a Split-µ Braking-in-Turning

2010 ◽  
Author(s):  
Jian Jun Zhu ◽  
Amir Khajepour ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Transient Response ◽  
Ride Comfort ◽  
Dynamic Performance ◽  
Suspension System ◽  
Dynamic Behaviors ◽  
Conventional Vehicle ◽  
Suspension Systems ◽  
Simulation Results ◽  
Different Characteristics ◽  
Better Than

A planar suspension system (PSS) has spring-damping struts in both the vertical and longitudinal directions so that the vibrations and shocks caused by road obstacles in any direction within the wheel plane can be effectively absorbed. Consequently, the ride comfort of a PSS vehicle can be improved considerably compared to a conventional vehicle. For a vehicle with such suspension systems, however, the wheels can move forth and back with respect to the chassis. The dynamic behaviors of a PSS vehicle under some special conditions, such as a split-μ turning combined with braking operation, may exhibit different characteristics. This paper presents the study of the transient response of a vehicle with PSS in such a case. The simulation results are also compared with those of a similar vehicle with conventional suspension under the same operational condition. The study demonstrates that the handling behavior of a PSS vehicle is generally comparable with, and in some conditions, even better than that of a conventional vehicle.

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