Semi-active Sliding Mode Control of Vehicle Suspension with Magneto-rheological Damper

The vehicle semi-active suspension with magneto-theological 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.

SEMI-ACTIVE CONTROL OF VEHICLE SUSPENSION WITH MAGNETO-RHEOLOGICAL DAMPERS PARTⅡ——EVALUATION OF SUSPENSION PERFORMANCE

The design and analysis of an intelligent vehicle suspension with MR dampers should address hybrid semi-active control goals, such as rejection of current-switching discontinuity and MR-damper hysteresis, asymmetric damping from the symmetric MR-damper design, robustness on the vehicle operation parameter uncertainties and consideration of essential multiple suspension goals. Following the proposed skyhook-based asymmetric semi-active controller （Part I ） for achieving the above goals, herein, a set of suspension performance measures and three kinds of varying amplitude harmonic, rounded pulse and really measured random excitations are systematically defined, and the sensitivity of quarter-vehicle MR-suspension performance to variations in operating conditions is thoroughly analyzed. The results illustrate that the proposed skyhook-based semi-active MR-suspension in the asymmetric mode yields relatively superior dynamic responses to meet the multiple suspension performances of ride, rattle space, road-holding and dynamic tire force transmitted to the pavement, and has desirable robustness on variations in operating conditions of vehicle load and speed and the road roughness.

SEMI-ACTIVE CONTROL OF VEHICLE SUSPENSION WITH MAGNETO-RHEOLOGICAL DAMPERS:PART Ⅰ——CONTROLLER SYNTHESIS AND EVALUATION

A modified skyhook-based semi-active controller is proposed for implementing an asymmetric control suspension design with symmetric magneto-rheological （MR） dampers. The controller is formulated in current form, which is modulated by integrating a continuous modulation and an asymmetric damping force generation algorithms, so as to effectively minimize switching and hysteretic effects from the MR-damper. The proposed controller is implemented with a quarter-vehicle MR-suspension model, and its relative response characteristics are thus evaluated in terms of defined performance measures under varying amplitude harmonic, rounded pulse and random excitations. The sensitivity of the semi-active suspension performance to variations in controller parameters is thoroughly evaluated. The results illustrate that the proposed skyhook-based asymmetric semi-active MR-suspension controller has superior robustness on the system parameter variations, and can achieve desirable multi-objective suspension performance.

SEMI-ACTIVE CONTROL OF VEHICLE SUSPENSION WITH MAGNETO-RHEOLOGICAL DAMPERS:PART III—EXPERIMENTAL VALIDATION

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.

Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension

A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established. Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory. Transition sets of the system and 40 groups of bifurcation diagrams are obtained. The local bifurcation is found, and shows the overall character- istics of bifurcation. Based on the. relationship between parameters and the topological bifurcation solutions, motion characteristics with different parameters are obtained. The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.

Vibration Control of Vehicle Suspension System by Electrorheological Damper

An overview of electrorheological （ER） fluid characteristics is given. Based on the Bingham plasticity model and a simple parallel-plate model, the operation principle of ER damper is presented and a four-DOF dynamic model of a vehicle suspension is constructed. Then a semi-active control of vehicle suspension system by ER damper is obtained. According to the semi-active control theory, the acceleration frequency characteristic is achieved with Matlab toolbox. Simulation results show that the vibration of the suspension system is well controlled.

Basic Problems in Design and Inverse Engineering Solution for Outer Characteristic of Vehicle Suspension Shock Absorbers

Based on the theory and the practical experiences of linearity design of feasible design area and inverse solution of non linear outer characteristic of suspension shock absorber, in accordance with non linearity outer characteristic formed by open up damping coefficient, full open damping coefficient and smoothness to safety ratio of suspension shock absorber, a method and a research conclusion of the feasible design and inverse solution for the basic problems of designing and inverse solution of non linear outer characteristic of suspension damping components are provided.

Active suspension with optimal control based on a full vehicle model

The 7-DOF model of a full vehicle with an active suspension is developed in this paper.The model is written into the state equation style.Actuator forces are treated as inputs in the state equations.Based on the basic optimal control theory,the optimal gains for the control system are figured out.So an optimal controller is developed and implemented using Matlab/Simulink,where the Riccati equation with coupling terms is deduced using the Hamilton equation.The all state feedback is chosen for the controller.The gains for all vehicle variables are traded off so that majority of indexes were up to optimal.The active suspension with optimal control is simulated in frequency domain and time domain separately,and compared with a passive suspension.Throughout all the simulation results,the optimal controller developed in this paper works well in the majority of instances.In all,the comfort and ride performance of the vehicle are improved under the active suspension with optimal control.

Finite Frequency Fuzzy H∞Control for Uncertain Active Suspension Systems With Sensor Failure

This paper investigates the problem of finite frequency fuzzy H_∞ control for uncertain active vehicle suspension systems, in which sensor failure is taken into account. TakagiSugeno(T-S) fuzzy model is established for considered suspension systems. In order to describe the sensor fault effectively, a corresponding model is introduced. A vital performance index,H_∞ performance, is utilized to measure the drive comfort. In the framework of Kalman-Yakubovich-Popov theory, the H_∞ norm from external perturbation to controlled output is optimized effectively in the frequency domain of 4 Hz-8 Hz to enhance ride comfort level. Meanwhile, three suspension constrained requirements, i.e., ride comfort level, manipulation stability,suspension deflection are also guaranteed. Furthermore, sufficient conditions are developed to design a fuzzy controller to guarantee the desired performance of active suspension systems. Finally, the proposed control scheme is applied to a quarter-vehicle active suspension, and simulation results are given to illustrate the effectiveness of the proposed approach.

Influence of Vehicle Parameters on Critical Hunting Speed Based on Ruzicka Model

While introducing foreign advanced technology and cooperating with Chinese famous research institutes,the high-speed vehicles are designed and take the major task of passenger transport in China.In high-speed vehicle,the characteristic of shock absorber is an important parameter which determines overall behavior of the vehicle.The most existing researches neglect the influence of the series stiffness of the shock absorber on the vehicle dynamic behavior and have one-sided views on the equivalent conicity of wheel tread.In this paper,a high speed passenger vehicle in China is modeled to investigate the effect of the parameters taking series hydraulic shock absorber stiffness into consideration on Ruzicka model.Using the vehicle dynamic model,the effect of main suspension parameters on critical speed is studied.In order to verify the reasonableness of shock absorber parameter settings,vibration isolation characteristics are calculated and the relationship between suspension parameters and the vehicle critical hunting speed is studied.To study the influence of equivalent conicity on vehicle dynamic behavior,a series of wheel treads with different conicities are set and the vehicle critical hunting speeds with different wheel treads are calculated.The discipline between the equivalent conicity of wheel tread and critical speed are obtained in vehicle nonlinear system.The research results show that the critical speed of vehicle much depends on wheelset positioning stiffness and anti-hunting motion damper,and the series stiffness produces notable effect on the vehicle dynamic behavior.The critical speed has a peak value with the equivalent conicity increasing,which is different from the traditional opinion in which the critical speed will decrease with the conicity increasing.The relationship between critical speed and conicity of wheel tread is effected by the suspension parameters of the vehicle.The study results obtained offer a method and useful data to designing the parameters of the high speed vehicle and simulation study.

Vibration reduction for a new-type maglev vehicle with mid-mounted suspension under levitation failure

Levitation failure occasionally occurs when a maglev vehicle runs on a track. At the moment of levitation failure, the levitation module falls and hits the track, and there is a violent impact on the maglev vehicle-bridge coupled system. In this paper, the response of the maglev vehicle-bridge coupled system at the moment of and after levitation failure is analyzed, and three methods of reducing the vibration are proposed. First, a dynamics model of the maglev vehicle-bridge coupled system, which considers the control system, five flexible bridges, and track irregularity, is established, and the correctness of the model is verified using test data. The system response for different failure cases is then analyzed. Finally, the three methods of reducing vibration under levitation failure are proposed, and their effectiveness is evaluated. The results show that the failure position and speed barely affect the response, whereas the maximum impact forces due to levitation failure reduced by 13%, 63%, and 50% by adopting the three methods, namely connecting the first and third coils in series, coupling the ends of the levitation module vertically, and adopting two sets of anti-roll devices, respectively. When the latter two schemes are combined, the maximum impact force reduced from 133 kN(without vibration-reduction measures) to 9 kN, and the vibration-reduction measure is also effective for failures of the levitation units at the ends of the vehicle.

GENERATION OF ASYMMETRIC F-v CHARACTERISTICS FOR SYMMETRIC MR DAMPERS

An asymmetric damping force generation algorithm is originally proposed to yield the asymmetric force-velocity characteristics for the symmetric magneto-rheological （MR） dampers. The command current is formulated in an asymmetric manner to excite the symmetric MR dampers by employing the “on-off” control law in response to the direction of velocity, and a smooth modulation function is developed without phase shift to suppress strong transients in the damping forces caused by the current-switching discontinuity. The effectiveness of the proposed algorithm is evaluated by analyzing the dynamic responses of a quarter-vehicle suspension system with a symmetric MR-damper by modulating the command current into the asymmetric manner. The simulation results show that the proposed algorithm could achieve a better compromise between the conflicting requirements of the asymmetric damping force ratio and the force-velocity curve smoothness, and the asymmetric damping MR-suspension design can ideally improve the road holding and ride performances of vehicle motion. The proposed algorithm can be generally incorporated with a controller synthesis to realize an intelligent vehicle suspension design with the symmetric MR dampers.

Proportional-integral-derivative control of nonlinear half-car electro-hydraulic suspension systems

This paper presents the development of a proportional-integral-derivative (PID)-based control method for application to active vehicle suspension systems (AVSS). This method uses an inner PID hydraulic actuator force control loop, in combination with an outer PID suspension travel control loop, to control a nonlinear half-car AVSS. Robustness to model uncertainty in the form of variation in suspension damping is tested, comparing performance of the AVSS with a passive vehicle suspension system (PVSS), with similar model parameters. Spectral analysis of suspension system model output data, obtained by performing a road input disturbance frequency sweep, provides frequency response plots for both nonlinear vehicle suspension systems and time domain vehicle responses to a sinusoidal road input disturbance on a smooth road. The results show the greater robustness of the AVSS over the PVSS to parametric uncertainty in the frequency and time domains.

Dynamic Event-triggered Control and Estimation: A Survey

The efficient utilization of computation and communication resources became a critical design issue in a wide range of networked systems due to the finite computation and processing capabilities of system components(e.g., sensor, controller) and shared network bandwidth. Event-triggered mechanisms(ETMs) are regarded as a major paradigm shift in resource-constrained applications compared to the classical time-triggered mechanisms, which allows a trade-off to be achieved between desired control/estimation performance and improved resource efficiency. In recent years, dynamic event-triggered mechanisms(DETMs) are emerging as a promising enabler to fulfill more resource-efficient and flexible design requirements. This paper provides a comprehensive review of the latest developments in dynamic event-triggered control and estimation for networked systems. Firstly, a unified event-triggered control and estimation framework is established, which empowers several fundamental issues associated with the construction and implementation of the desired ETM and controller/estimator to be systematically investigated. Secondly, the motivations of DETMs and their main features and benefits are outlined. Then, two typical classes of DETMs based on auxiliary dynamic variables(ADVs) and dynamic threshold parameters(DTPs) are elaborated. In addition, the main techniques of constructing ADVs and DTPs are classified, and their corresponding analysis and design methods are discussed. Furthermore, three application examples are provided to evaluate different ETMs and verify how and under what conditions DETMs are superior to their static and periodic counterparts. Finally, several challenging issues are envisioned to direct the future research.