Vehicle Suspension Control Research Articles

A new approach to optimal control of nonlinear vehicle suspension system with input constraint

The vehicle active suspension system is a multi-objective control system with the input constraint. In this paper, a new effective method is proposed for constrained optimal control of a vehicle suspension system including nonlinear characteristics for elasto-damping elements. In the proposed method, an equivalent constrained optimization problem is firstly formulated by performing a performance index which is defined as a weighted combination of predicted responses of nonlinear suspension system and control signal. Then, the constrained optimization problem is analytically solved by the Kerush–Kuhn–Tucker (KKT) theorem to find the control law. The proposed constrained controller is compared with the unconstrained optimal controller for which the limitation of control force is satisfied by regulation of its weighting factor in the performance index. Simulation studies are conducted to show the effectiveness of two controllers. The results indicate that the constrained controller utilizes the maximum capacity of external forces and consequently attains a better performance in the presence of force limitations.

Research on Multi-objective Topology Optimization of Vehicle Suspension Control Arm

Research on Multi-objective Topology Optimization of Vehicle Suspension Control Arm

Modeling and control of rail vehicle suspensions: A comparative study based on the passenger comfort

This paper deals with the modeling and control of rail vehicle suspensions. The analytical models of the quarter rail vehicle with a passenger seat, describing the vertical dynamic, are presented for passive and active suspensions. Three controllers, i.e. PID-ZN, LQR and a PID-LQR are designed in order to improve the passenger comfort. This comfort is evaluated in terms of the passenger displacement, acceleration and frequency as a response of a two types of rail imperfection excitations. Results show that passenger comfort can be improved up to 98%. The obtained results prove that the active suspension with a PID- LQR controller yields the best results by regrouping the advantage of both PID and LQR controllers.

Method and algorithm of automatic estimation of road surface type for variable damping control

In this paper authors presented an idea of road surface estimation (recognition) on a base of suspension dynamic response signals statistical analysis. For preliminary analysis cumulated distribution function (CDF) was used, and some conclusion that various roads have responses values in a different ranges of limits for the same percentage of samples or for the same limits different percentages of samples are located within the range between limit values. That was the base for developed and presented algorithm which was tested using suspension response signals recorded during road test riding over various surfaces. Proposed algorithm can be essential part of adaptive damping control algorithm for a vehicle suspension or adaptive control strategy for suspension damping control.

A fuzzy-genetic control system in the ABS for the control of semi-active vehicle suspensions

The aim of this paper is to create a new ABS (Antilock Braking System) control system of a Soft-Computing type, on the grounds of the excellent results obtained in the field of automobiles in former studies [1]. Such a system should make it possible to enhance performance in all conditions. The novelty lies in the fact that the system improves not only the physical nature of the hydraulic and electronic components used [2,3], but also the functioning of these, by means of a new control strategy based on a fuzzy-type algorithm optimised with genetic algorithms. In this way the performance of the system may be improved or alternatively the control logic may be simplified for the same degree of performance, offering satisfactory results in all possible conditions. The target performance aimed at may be summarised in two points: reduction in braking distance and improved directional control of the vehicle. The study was optimised on a monocorner model, subsequently to be extended to a complete vehicle model.

H 2 control of a one-quarter semi-active ground vehicle suspension

Magneto-rheological (MR) dampers are effective solutions in improving vehicle stability and passenger comfort. However, handling these dampers implies a strong effort in modeling and control. This research proposes an H2 controller, based on a Takagi-Sugeno (T-S) fuzzy model, for a two-degrees-of-freedom (2-DOF) one-quarter vehicle semi-active suspension with an MR damper; a system with important applications in automotive industry. Regarding performance criteria (in frequency domain) handled herein, the developed controller considerably improves the passive suspension's efficiency. Moreover, nonlinear actuator dynamics usually avoided in reported work, is included in controller's synthesis; improving the relevance of research outcomes because the controller is synthesized from a closer-to-reality suspension model. Going further, outcomes of this research are compared (based on frequency domain performance criteria and a common time domain test) with reported work to highlight the outstanding results. H2 controller is given in terms of quadratic Lyapunov stability theory and carried out by means of Linear Matrix Inequalities (LMI), and the command signal is applied via the Parallel Distributed Compensation (PDC) approach. A case of study, with real data, is developed and simulation work supports the results. The methodology applied herein can be extended to include other vehicle suspension's dynamics towards a general chassis control

Vibration control of a semi-active railway vehicle suspension with magneto-rheological dampers

This article presents vibration control performances of a semi-active railway vehicle suspension system using a magneto-rheological damper tested on the roller rig. In order to evaluate control performances, a mathematical railway vehicle model with 15 degrees of freedom is first derived to represent the lateral, yaw and roll motions of the car body, bogie frame, and wheel set, respectively. Based on the formulated model, the design parameters of magneto-rheological damper are determined to undertake a compatible comparison with dynamic performances of conventional (existing) passive railway vehicle suspension system. The designed magneto-rheological damper is manufactured and its field-dependent damping force characteristics are experimentally evaluated. Subsequently, in order to enhance the ride quality of a railway vehicle suspension equipped with magneto-rheological damper, a skyhook controller associated with an extended Kalman filter is designed in a state space representation. The railway suspension system incorporated with the car body and two bogies is then experimentally set up on the roller rig in order to evaluate the ride quality. It is demonstrated from experimental realization of the controller that the ride quality of the suspension system with magneto-rheological damper can be significantly enhanced compared with the existing passive suspension system.

Optimal vibration control of nonlinear systems with multiple time-delays: An application to vehicle suspension

ABSTRACTThis paper addresses optimal vibration control problem for nonlinear systems with state, control, and measurement delays. By using the functional transformations, the original system is reduced to an equivalent delay-free one. The approximating sequence method is applied to simplify and solve the nonlinear optimal vibration control (NOVC) problem, which is reduced to a linear two-point boundary value problem of approximating sequences. The nonlinear optimal control law is obtained from the convergence solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. The proposed control strategy is applied to design a vibration controller for an active vehicle suspension. The nonlinear vehicle suspension system with delays is modelled, as well as the road disturbance model is established. Comparing with a passive controller and a non-delay-compensation controller (NDCC), the simulations for the designed NOVC are demonstrated. The simulation results illustrate the effectiveness and the simplicity of the proposed approach.

Optimal Controller for Active Vehicle Suspension Disturbed by Sinusoidal Signals

The problem of optimal control of systems disturbed by sinusoidal signals for infinite control time is considered in the paper. The control laws described in [1] is base of a modified mean-square performance index with an infinite control time. The performance index was formulated in such a way that each sinusoidal component corresponds to a separate weight matrix. This allows energy constraints on the control signals to be differentiated based on frequency. An optimal solution to the optimization problem was found. In the paper the problem of the impact of time on the identification of sinusoidal disturbance on vibration isolation system frequency characteristic. The controller was synthesized for slow-active vehicle suspension [2,3]. The model of suspension, synthesis of the controller and implementation of the system was described. The results of simulations of the designed vehicle active suspension system are presented.

Guideway based damping control of vehicle suspensions

AbstractThe information on the routing of a road provided by a navigation system can be used by the driver of a vehicle with adaptive shock absorber to decide either for optimal comfort or optimal safety depending on the course of the guideway. However, the assessment criteria comfort and safety are with respect to the shock absorber in conflict with each other. In particular, maximal safety on a curvaceous road results in lower comfort. Thus, deciding on high safety means low comfort conveying a warning to the driver to reduce the speed. The methods applied in this paper originate from multibody dynamics, and they are extended by the stochastic road unevenness and the guideway curvature available to the driver from a navigation system using GPS data. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Pro-active optimal control for semi-active vehicle suspension based on sensitivity updates

This article suggests a strategy to control semi-active suspensions of vehicles in a pro-active way to adapt to future road profiles. The control strategy aims to maximise comfort while maintaining good handling properties. It employs suitably defined optimal control problems in combination with a parametric sensitivity analysis. The optimal control techniques are used to optimise the time-dependent damper coefficients in an electro-rheological damper for given nominal road profiles. The parametric sensitivity analysis is used to adapt the computed nominal optimal controls to perturbed road profiles in real time. The method is particularly useful for events with a low excitation frequency such as ramps, bumps, or potholes. For high-frequency excitations standard controllers are preferable; so we propose a switched open–closed-loop controller design. Various examples demonstrate the performance of the approach.

Control of vehicle suspension using an adaptive inerter

In this paper, we study the suspension performances with an adaptive inerter under the assumption that the inertance may be adjusted in real-time. A quarter-car model with an inerter installed in parallel with a spring and a damper is considered. First, for a given suspension system, a study of the effects of using a fixed inerter is provided. It shows the difficulty in choosing a fixed inerter to satisfy the vehicle performances at the sprung mass natural frequency without deteriorating significantly at the unsprung mass natural frequency. Then, a state-feedback H2 controller for an active suspension system is designed. The active force is approximated by an inerter with adjustable inertance. Ride quality, suspension deflection and tyre deflection performances are considered independently as the prime objective. Simulation results show that comparing with the passive suspension with fixed inerter, for ride quality and tyre deflection, the suspension with adaptive inerter can achieve improvement at the sprung mass natural frequency at the expense of a relatively small deterioration at the unsprung mass natural frequency. For suspension deflection, a better performance can be achieved at high frequencies with almost no loss of performance at other frequencies. This method is easier to implement in practice than the optimized passive suspension with a fixed inerter, which calls for complicated layout.

Semiactive Control for SDOF Vehicle Suspension on IVNs via Delayed Positive Feedback

This paper addresses delayed controller design for a single degree of freedom (SDOF) semiactive suspension on in-vehicle networks (IVNs). Employing the Nyquist curve approach, the sufficient and necessary conditions of the feedback gains and the delays are derived. The controller is designed by using delayed positive feedback of a controllable-damping and a variable spring-stiffness. Some examples are illustrated for a quarter-car suspension model. The simulation results demonstrate the effectiveness and the simplicity of the proposed controller.

A state feedback input constrained control design for a 4-semi-active damper suspension system: a quasi-LPV approach

This paper addresses a semi-active suspension control of the full vehicle equipped with 4 controlled semi-active dampers by using a full 7 degree of freedom (DOF) vertical model. First, the dissipativity conditions of the semi-active dampers are recast as saturation conditions on the control inputs. Then, the suspension controller is derived by solving a state feedback control design problem for a class of linear parameter-varying (LPV) system in the presence of actuator saturation. To this aim, a generalized sector condition for LPV system is applied to treat the nonlinearity, caused by the input saturation and to relax the stability condition. The proposed control law ensures the disturbance attenuation by reducing the L2 gain from the disturbance to the controlled output. This controller, derived in the LPV/H∞ framework, is based on the LMI solution for polytopic systems. Some realistic simulation results are presented in order to illustrate the effectiveness of the proposed approach.

Contribution to the modeling of a pneumatic semi-active control of vehicle suspension

This paper contributes to the modeling of a semi-active control of a quarter vehicle model using air springs. A conventional mass-spring-damper model has been used along with an air spring. Based on the theory of thermodynamics, the dynamic equation of the air spring model was established. The simulation model was implemented using MATLAB and the transfer functions with varying parameters were calculated. The simulation results show that air spring pressure, the valve diameter, the dumping coefficient and the mechanical stiffness affect the dynamic response of the system. A semi-active control methodology was then established by controlling the valve diameter using two declinations of an on-off logic switch based on the velocity of the suspended mass and the relative velocity at both ends of the air spring. The obtained results show reduced oscillation amplitudes around the natural frequency of the system.

Design and Analysis of Magnetorheological Damper Paralleling with Constant Throttling Orifices

Magnetorheological damper(MRD) is a first-rate device for semiactive control of vehicle suspension. However, the traditional MRD with complex inverse model and regulating process is difficult to be applied to the practice. In order to overcome these disadvantages, a new type of MRD paralleling with constant throttling orifices is proposed. If the current of winding is set to zero, the magnetorheological fluid(MRF) flow through both inactive inducing gap and constant throttling orifices, so the damping is minimum; if the current is set to the maximum value, the inducing gap is plugged by the activated MRF and works as a pressure limiter, so the fluid only flow though the constant throttling orifices until the MRF in the inducing gap is yielded, which means the damping is maximum. The mathematical model of the proposed damper is deduced to provide theoretic foundation for structure design and damping force analysis. The feasibility of this novel MRD is verified by magnetic circuit simulation and damping experiment. Especially, the proposed MRD is appropriate to combined with on/off control strategies because the complicate inverse model and control process may be avoided. In a word, the MRD paralleling with constant throttling orifices owns significant advantages for practical application.

Frequency-Domain Analysis and Design of Linear Feedback of Nonlinear Systems and Applications in Vehicle Suspensions

Nonlinear vibration control systems (both passive and active) always involve parameter design and performance optimization tasks. A systematic and novel frequency-domain method is established to this aim in this study based on a newly developed concept-nonlinear characteristic output spectrum (nCOS). The nCOS function can be any system output function or multiobjective performance function to be optimized. It is shown for the first time that the nCOS function can be expressed into an explicit and analytical polynomial function of any model parameters which define underlying linear dynamics of the system. A simple least square algorithm is provided for the determination of this nonlinear parametric relationship. This novel nCOS function can obviously facilitate parameter analysis and design of nonlinear vibration control systems and provide a useful tool for a simple linear control design, while simultaneously considering inherent nonlinear dynamics of a system. A case study in vehicle suspension control demonstrates these new results.

Takagi-Sugeno Fuzzy Model of a One-Half Semiactive Vehicle Suspension: Lateral Approach

This work presents a novel semiactive model of a one-half lateral vehicle suspension. The contribution of this research is the inclusion of actuator dynamics (two magnetorheological nonlinear dampers) in the modelling, which means that more realistic outcomes will be obtained, because, in real life, actuators have physical limitations. Takagi-Sugeno (T-S) fuzzy approach is applied to a four-degree-of-freedom (4-DOF) lateral one-half vehicle suspension. The system has two magnetorheological (MR) dampers, whose numerical values come from a real characterization. T-S allows handling suspension’s components and actuator’s nonlinearities (hysteresis, saturation, and viscoplasticity) by means of a set of linear subsystems interconnected via fuzzy membership functions. Due to their linearity, each subsystem can be handled with the very well-known control theory, for example, stability and performance indexes (this is an advantage of the T-S approach). To the best of authors’ knowledge, reported work does not include the aforementioned nonlinearities in the modelling. The generated model is validated via a case of study with simulation results. This research is paramount because it introduces a more accurate (the actuator dynamics, a complex nonlinear subsystem) model that could be applied to one-half vehicle suspension control purposes. Suspension systems are extremely important for passenger comfort and stability in ground vehicles.

Semi-active sliding mode control of vehicle suspension with magneto-rheological damper

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.

LQR Control for Semi-Active Quarter Vehicle Suspension with Magnetorhehological Damper and Bouc-Wen Model

This paper discuss the problem of controlling quarter-car semi-active suspension system. Presently, the suspension system involves a magnetorheological (MR) damper with a hysteretic behavior captured through the Bouc-Wen model. This device can be integrated in the electric or hybrid electric vehicle. The control objective is to regulate well the chassis vertical position despite the road irregularities. In addition to these irregularities, the difficulty of the control problem lies in the nonlinearity of the system model and the inaccessibility to measurements of the hysteresis internal state variable. The control design is performed using the LQR theory and Lyapunov control design tools; it includes an observer providing online estimates of the hysteresis internal state. The controller is formally shown to meet the desired control objectives. This theoretical result is confirmed by several simulations. The latter illustrate the performances of the LQR method and compare them with those of the passive suspension.