Enrong Wang

Magneto-rheological (MR) suspension systems offer meritorious potential for realizing an effective compromise between driving comfort and handling performance. The inherent hysteresis nonlinearity of a magneto-rheological damper (MRD), however, may lead to unpredictable and complex dynamic behavior of the vehicle system. In this study, a pitch-plane half-car model comprising MR suspension with hysteresis nonlinearities was formulated to investigate its dynamic responses as a function of the driving speed. The dynamic stability of the vehicle model was investigated under harmonic excitations through Lyapunov exponents to globally illustrate strong dependencies on the excitation frequency and amplitude. The influences of driving speed, and excitation amplitude and frequency on the nonlinear response characteristics were analyzed through bifurcation diagrams, phase portraits and Poincaré maps. The dynamic evolution of periodic motion to chaotic motion was illustrated through Hopf, saddle node and period-doubling bifurcations, respectively, under low-, mid- and high-speeds. Moreover, the hyperchaotic oscillation of the system was observed for the first time. The results show that the nonlinear response behavior of the half-car MR suspension is mostly concentrated in the medium frequency range for low- as well mid-speeds, which is concerned with ride comfort performance of the vehicle. The results obtained in the study provide essential basis for further investigations on effective controller synthesis and stability analyses of more practical higher order models of vehicles with MR suspension.

Magnetorheological (MR) regenerative suspension system can not only achieve excellent comprehensive suspension performance but also effectively recover and utilize vibration potential energy, which has been a research hotspot in the field of vehicle engineering. In this paper, for the 1/4 vehicle’s MR regenerative suspension system parallel with a tubular permanent magnet linear motor (TPMLM), the dynamic model of the MR semi-active suspension system and the TPMLM finite element model are established separately to form a joint simulation platform. The simulation analysis of the comprehensive suspension performance and regeneration performance under different road excitations is performed. The results show that installing TPMLM does not change the natural resonance frequency of the suspension system, which ensures good driving comfort and handling stability. At the same time, it has considerable regeneration power. This research can provide a reference for the stability analysis and popularization of the vehicle’s MR regenerative suspension system.

Response characteristics of a magneto-rheological (MR) suspension with a modified skyhook control scheme, focusing directly on the command current, were analyzed considering hysteresis nonlinearities. Suspension performance and its dynamic stability were investigated under harmonic excitation at frequencies up to 50 Hz to illustrate highly nonlinear influences of the excitation frequency and magnitude. The nonlinear response characteristics of the system, attributed to damper hysteresis and on-off control, were thoroughly analyzed considering the bifurcation diagrams, Lyapunov exponent spectra, phase portraits and the Poincare maps. These, invariably, showed the presence of quasi-periodic, multi-periodic and chaotic responses of the system under mid- as well as high-frequency excitations. The conducted electromagnetic interference (EMI) due to high frequency variations in the drive current, caused by the nonlinear system responses, were further evaluated using the method described in EN 55022 for the first time. The assessments using the GB9254 guidelines, showed that the EMI levels exceed the recommended limits. The chaos induced EMI may thus be detrimental to the electronic control systems of the automobile, and cannot be ignored. This work is considered to serve as a theoretical foundation for future studies on EMI reduction and nonlinear control of intelligent semi-active suspensions.

Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.

A structure decoupling control strategy of half-car suspension is proposed to fully decouple the system into independent front and rear quarter-car suspensions in this paper. The coupling mechanism of half-car suspension is firstly revealed and formulated with coupled damping force (CDF) in a linear function. Moreover, a novel dual dampers-based controllable quarter-car suspension structure is proposed to realize the independent control of pitch and vertical motions of the half car, in which a newly added controllable damper is suggested to be installed between the lower control arm and connection rod in conventional quarter-car suspension structure. The suggested damper constantly regulates the half-car pitch motion posture in a smooth and steady operation condition meantime achieving the expected completely structure decoupled control of the half-car suspension, by compensating the evolved CDF.

The vehicle semi-active suspension with magneto-rheological damper(MRD) has been a hot topic since this decade, in which the robust control synthesis considering load variation is a challenging task. In this paper, a new semi-active controller based upon the inverse model and sliding mode control (SMC) strategies is proposed for the quarter-vehicle suspension with the magneto-rheological (MR) damper, wherein an ideal skyhook suspension is employed as the control reference model and the vehicle sprung mass is considered as an uncertain parameter. According to the asymptotical stability of SMC, the dynamic errors between the plant and reference systems are used to derive the control damping force acquired by the MR quarter-vehicle suspension system. The proposed modified Bouc-wen hysteretic force-velocity (F-v) model and its inverse model of MR damper, as well as the proposed continuous modulation (CM) filtering algorithm without phase shift are employed to convert the control damping force into the direct drive current of the MR damper. Moreover, the proposed semi-active sliding mode controller (SSMC)-based MR quarter-vehicle suspension is systematically evaluated through comparing the time and frequency domain responses of the sprung and unsprung mass displacement accelerations, suspension travel and the tire dynamic force with those of the passive quarter-vehicle suspension, under three kinds of varied amplitude harmonic, rounded pulse and real-road measured random excitations. The evaluation results illustrate that the proposed SSMC can greatly suppress the vehicle suspension vibration due to uncertainty of the load, and thus improve the ride comfort and handling safety. The study establishes a solid theoretical foundation as the universal control scheme for the adaptive semi-active control of the MR full-vehicle suspension decoupled into four MR quarter-vehicle sub-suspension systems.

The control study of vehicle semi-active suspension with magneto-rheological (MR) dampers has been attracted much attention internationally. However, a simple, real time and easy implementing semi-active controller has not been proposed for the MR full-vehicle suspension system, and a systematic analysis method has not been established for evaluating the multi-objective suspension performances of MR full-vehicle vertical, pitch and roll motions. For this purpose, according to the 7-degree of freedom (DOF) full-vehicle dynamic system, a generalized 7-DOF MR and passive full-vehicle dynamic model is set up by employing the modified Bouc-wen hysteretic force-velocity (F-v) model of the MR damper. A semi-active controller is synthesized to realize independent control of the four MR quarter-vehicle sub-suspension systems in the full-vehicle, which is on the basis of the proposed modified skyhook damping scheme of MR quarter-vehicle sub-suspension system. The proposed controller can greatly simplify the controller design complexity of MR full-vehicle suspension and has merits of easy implementation in real application, wherein only absolute velocities of sprung and unsprung masses with reference to the road surface are required to measure in real time when the vehicle is moving. Furthermore, a systematic analysis method is established for evaluating the vertical, pitch and roll motion properties of both MR and passive full-vehicle suspensions in a more realistic road excitation manner, in which the harmonic, rounded pulse and real road measured random signals with delay time are employed as different road excitations inserted on the front and rear two wheels, by considering the distance between front and rear wheels in full-vehicle. The above excitations with different amplitudes are further employed as the road excitations inserted on left and right two wheels for evaluating the roll motion property. The multi-objective suspension performances of ride comfort and handling safety of the proposed MR full-vehicle suspension are thus thoroughly evaluated by comparing with those of the passive full-vehicle suspension. The results show that the proposed controller can ideally improve multi-objective suspension performances of the ride comfort and handling safety. The proposed harmonic, rounded pulse and real road measured random signals with delay time and asymmetric amplitudes are suitable for accurately analyzing the vertical, pitch and roll motion properties of MR full-vehicle suspension system in a more realistic road excitation manner. This research has important theoretical significance for improving application study on the intelligent MR semi-active suspension.

A hardware-in-the-loop(HIL) test and simulation platform is developed in the laboratory, so as to validate the performance characteristics of the proposed skyhook-based asymmetric semi-active controller in Part I, and examine the validity of the proposed MR-damper model in a system surrounding. A real-time monitor is designed to assess and monitor the responses of the quarter-vehicle model in the HIL platform, and to select the excitation, controller synthesis, and the output displays. A drive current circuit hardware employing PID feedback technique is developed to compensate for the time delays from the servo-controller and drive current circuit, in which a small resistance is integrated in the current amplifier circuit to provide the feedback signal. The experiments were performed to measure the responses of the quarter-vehicle MR-suspension models with fixed current and the proposed semi-active MR-damping variations, under harmonic, rounded pulse and random road excitations. The measured data were compared with the corresponding model results to examine the model and controller validity, and revealed generally good agreements in the model and tested results and very little sensitivity of the tested responses to variations in the sprung mass. The HIL test results validate the effectiveness of the proposed skyhook-based semi-active asymmetric controller and its high robustness against the vehicle load variations in view of the intelligent vehicle suspension design.

On basis of a modified "on-off" damping law, an inverse model based semi-active damping controller is proposed for implementing an asymmetric control suspension design with symmetric MR dampers. The inverse model control has potential to compensate the hysteresis effects of MR-damper and realize the semi-active force tracking control. The controller is formulated in current form by integrating a continuous modulation and an asymmetric damping force generation algorithms, so as to effectively minimize the switching transient effects and to realize asymmetric damping forces in compression and rebound from the symmetric MR-damper design. The proposed controller is thoroughly evaluated in terms of defined performance measures under varying amplitude harmonic, rounded pulse and really measured random excitations. The results illustrate that the proposed inverse model based asymmetric semi-active MR-suspension has superior robustness against variations of vehicle load and speed, and the road roughness, and can thus achieve desirable multi-body vehicle suspension performance.