Piotr Krauze

Automotive MR damper modeling for semi-active vibration control

The magnetorheological (MR) damper is a semi-active device in which varying electric current flow in coils mounted in the piston leads to changes of its dynamical properties. Development of an accurate mathematical model of the MR damper plays a key role in a successful implementation of semi-active vibration attenuation. This paper concerns with the problem of building a model of the MR damper used in a vehicle suspension. This is not a trivial task as the MR damper reveals highly nonlinear, bi-viscous and hysteretic behavior. Furthermore, the model has to be suitable for synthesis of a control algorithm. This means that using the inverse model it should be possible to calculate the input current for a given damping force. The so-called black-box modeling has been proposed with the relative structural simplicity comparing with the phenomenological models. The model structure is not based on a physical description of the MR damper but on the input-output relation that makes the digital controller implementation feasible. This nonlinear model is based on a heuristic approach and is convenient for application in a semi-active suspension system. Parameters of the model were adapted for data obtained during a specially designed experiment performed for the automotive MR damper mounted in the experimental vehicle.

Neural network based LQ control of a semiactive quarter-car model

The paper presents an application of LQ control dedicated to a semiactive quarter-car model (2 degrees of freedom) which includes nonlinear model of a magnetorheological (MR) damper. Optimal control gains are derived based on known quarter car model parameters and limitations imposed on absolute vertical velocities of sprung and unsprung masses as well as on desired force generated by MR damper. Solutions of the algebraic Riccati equation obtained for LQ continous time infinite horizon problem using system output and control weights matrices are approximated using neural network. The static feedforward neural network model was identified using Levenberg-Marquardt backpropagation method in order to map nonlinear relations between system variables limitations and control gains. The algorithm was adapted to the semiactive system using a linearized inverse MR damper model. Simulation based analysis of vibration mitigation was carried out in frequency domain for different experiments conditions; the analysis justifies application of neural networks in LQ based control of semiactive suspension.

Modelling and identification of magnetorheological vehicle suspension

The paper presents methods of estimation of vehicle suspension system parameters based on kinetic measurements. The vehicle suspension is assumed to include springs, linear dampers and magnetorheological (MR) dampers which are known to be nonlinear. In many cases hysteresis loop is revealed in the static characteristics of MR dampers. Nonlinear full-car vehicle suspension model is defined and adapted for using linear and nonlinear least-squares identification method. Identifications experiments are performed assuming limited number of available kinetic sensors. Solution space with respect to the location of the vehicle bodys gravity center is presented as well as quality index values and time diagrams are reported based on estimated model parameters and simulation results.

FxLMS algorithm with preview for vibration control of a half-car model with magnetorheological dampers

The paper presents a novel approach to the vehicle vibration control using magnetorheological (MR) dampers. Simulation experiments were carried out based on a half-car suspension model including the Bouc-Wen model of the MR damper. It is also assumed that information about the road excitation is available in advance as a preview signal. The tanh-based model of the MR damper was identified according to the Bouc-Wen model response and used to obtain the inverse model that is necessary in the control scheme. The adaptive feedforward LMS (Least Mean Squares) algorithm with a filtered preview signal was modified in order to control the semi-active elements. Because the MR damper can only dissipate energy, it was proposed to decompose the velocity-force characteristics of the damper into a nonlinear passive damper curve and a symmetrical control range of a pseudo active suspension actuator. Such assumption assures that the algorithm can converge to appropriate parameters of the adaptive filter. Deviation of an error signal assumed as kinematic energy of the vehicle body heave vibrations is minimized by the algorithm. Control force generated by the MR dampers and expected by the algorithm is achieved indirectly by the inverse model of the damper. The suspension model was subjected to the road-induced stimulation in the form of series of bumps within the frequency range 0.5-15 Hz. Simulation results obtained for the FxLMS (Filtered-x LMS) and Skyhook algorithms demonstrate an advantage of the modified FxLMS due to its ability to adapt to changing conditions.

Vibration control in quarter-car model with magnetorheological dampers using FxLMS algorithm with preview

The paper presents a novel approach to the adaptive control of a semi-active vehicle suspension with magnetorheological (MR) dampers. Research was carried out for a quarter-car model with two degrees of freedom and the Bouc-Wen model of the MR damper behavior. To apply vibration control the inverse model of the damper is needed to determine the current controlling the MR damper. Thus, the Bouc-Wen model was approximated by the model based on tanh function with hysteresis included, which can be easy inverted. This approach resembles the real situation, where the model used for control does not correspond perfectly to the real device. The dissipative domain of this model can be modified by subtracting a nonlinear average velocity-force characteristics from the original one. After such modification, the real semi-active element can be treated as a fictitious active actuator which generates force limited by the nonlinear boundaries dependent on the relative piston velocity. Hereby, the FxLMS adaptive algorithm can be applied for vibration control in the semi-active suspension assuming preview about the road excitation is available as the reference signal. Simulation experiments indicated the high performance of the proposed approach and its advantage over the classical Skyhook algorithm in vibration control of the suspension. Adaptability of vibration control based on the FxLMS makes the presented algorithm scalable.

Magnetorheological Damper Dedicated Modelling of Force-Velocity Hysteresis Using All-Pass Delay Filters

The paper presents a novel approach to the problem of force-velocity characteristics modelling dedicated to MR dampers. It is stated that velocity and control dedicated dynamic signal paths need to be included in MR damper model. It is shown that hysteretic behaviour may be modelled using all-pass delay filters located in the velocity dedicated signal path. Parameters of the presented model are estimated using measurement data obtained by means of Material Testing System (MTS). Experiments are performed for damper excitation frequencies assumed within range of 0.5 Hz - 2.5 Hz and control current levels restricted within 0.05 A - 1.0 A. Parameters of delay filters are estimated and accuracy of the reference acceleration based hysteresis model and referred model based on delay filters are compared. Results demonstrate that delay filters based model maps MR damper dynamics, mainly hysteretic behaviour, with high accuracy.

Mixed Skyhook and FxLMS Control of a Half-Car Model with Magnetorheological Dampers

The problem of vibration attenuation in a semiactive vehicle suspension is considered. The proposed solution is based on usage of the information about the road roughness coming from the sensor installed on the front axle of the vehicle. It does not need any preview sensor to measure the road roughness as other preview control strategies do. Here, the well-known Skyhook algorithm is used for control of the front magnetorheological (MR) damper. This algorithm is tuned to a quarter-car model of the front part of the vehicle. The rear MR damper is controlled by the FxLMS (Filtered-x LMS) taking advantage of the information about the motion of the front vehicle axle. The goal of this algorithm is to minimize pitch of the vehicle body. The strategy is applied for a four-degree-of-freedom (4-DOF) vehicle model equipped with magnetorheological dampers which were described using the Bouc-Wen model. The suspension model was subjected to the road-induced excitation in the form of a series of bumps within the frequency range 1.0–10 Hz. Different solutions are compared based on the transmissibility function and simulation results show the usefulness of the proposed solution.

Vibration control for a half-car model with adaptation of the magnetorheological damper model

The paper presents vehicle vibration control using magnetorheological (MR) dampers. Typical algorithms to control this semi-active suspension need the inverse model of the damper. Modelling of the damper is not a trivial task because of its highly non-linear behaviour. Also, effectiveness of damping vibrations caused by the road depends significantly on the quality of the model. Therefore, an identification algorithm based on iterative estimation of immeasurable signals is proposed. Two control algorithms are tested - Skyhook and FxLMS (Filtered-x LMS). Simulation experiments for a half-car model excited by road bumps show usefulness of this approach. It was also observed that the FxLMS is not very sensitive to modelling errors as it includes an internal mechanism of adaptation. On the other hand, the Skyhook fails if the model is inaccurate, so it should be used together with the identification of the MR damper.

Experimental analysis of vibration control algorithms applied for an off-road vehicle with magnetorheological dampers:

The paper presents an experimental analysis of the selected feedback vibration control schemes dedicated to magnetorheological dampers, related to ride comfort and road holding. They were applied in a complex vibration control system installed in a commercially available off-road vehicle. Original shock-absorbers of the vehicle were replaced with magnetorheological dampers. The control system takes advantage of numerous sensors installed in the vehicle tracking its motion, i.e. accelerometers, suspension deflection sensors (linear variable differential transformer) and IMU module. Vibration control algorithms: Skyhook, PI, and Groundhook were tested experimentally using mechanical exciters adapted for diagnosis of a vehicle suspension system. Since the presented semi-active vibration control requires the magnetorheological damper inverse model to be applied, accurate operation of this model significantly influences the quality of vibration control. Therefore, additional analysis was related to application of measurements from accelerometers or suspension deflection sensors in the inverse model. Presented variants of control algorithms were compared by means of transmissibility characteristics evaluated in the frequency domain as well as using ride-comfort- and driving-safety-related quality indices. It was confirmed that the Skyhook control as well as PI improved ride comfort, whereas Groundhook control improved road holding and decreases vibration of the wheels. Furthermore, it was shown that both approaches to the relative velocity estimation, based on accelerometers and linear variable differential transformers, can be used in this application. However, the first solution gives better results in the case of the Skyhook and PI control, whereas application of LVDT sensors is better for the Groundhook algorithm.

Experimental attenuation and evaluation of whole body vibration for an off-road vehicle with magnetorheological dampers

The paper presents an analysis of vehicle vibration, ride comfort and handling which have a decisive influence on health and safety of a driver. Experiments were carried out for a commercially available experimental all-terrain vehicle in the field in hard conditions with retaining the sufficient repeatability. The vehicle is equipped with a complex vibration control system, taking advantage of four automotive magnetorheological dampers. Numerous sensors, which measure acceleration in four points of the vehicle body, near the driver’s seat, feet and hands, body orientation in space and speed of vehicle wheels, are available in the vehicle. They were used for evaluation of magnetorheological dampers’ control signals and analysis of vibration affecting the driver. Constant values of magnetorheological damper control current were used for emulation of different settings of passive suspension. The analysis performed in frequency domain showed how vibration propagates in a medium-sized all-terrain vehicle and indicated that driver’s hands are mostly affected by the road-induced vibration. It was also confirmed that the greatest improvement of ride comfort can be obtained for the soft suspension, i.e. uncontrolled magnetorheological dampers. Furthermore, the Skyhook algorithm was implemented, including the proportional control of the magnetorheological damper force and the inverse Tanh model of the magnetorheological damper. It was validated for the wideband road-induced excitation contrary to the experiments commonly presented in the literature, which are performed only for harmonic excitation. It was shown that the properly tuned Skyhook algorithm enables improving vehicle handling compared to the passive suspension and simultaneously it can maintain the similar or even better results of ride comfort.