Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

结合卡尔曼滤波器的车辆主动悬架轴距预瞄控制研究

利用轴距预瞄信息，即前后轮路面输入之关系，同时结合卡尔曼滤波器作为状态估计器，本文提出了一种算法用于车辆悬架控制律的设计，根据模拟结果，研究了算法的可行性，分析了卡尔曼滤波器对状态变量的估计精度，以及轴距预瞄控制对进一步改进车辆性能的潜力。     

An Investigation of the Origins of Vibration of an Automobile Rear Axle

An investigation was carried out to determine the origins of vibration of an automobile rear axle with the object of establishing the significance of road-surface-induced vibratory inputs. This was achieved by measuring the vibratory acceleration of the rear axle of an automobile as it traverses straight sections of typically paved roads, at uniform speeds, then comparing the results with those obtained by laboratory simulation.

The investigation revealed significant levels of vertical, longitudinal and, to a much lesser extent, lateral vibrations. The main source of vertical vibrations is shown to be induced mainly by vertical displacements imposed by the road-surface irregularities on the vehicle tyres. The longitudinal and lateral components are shown to be induced mainly by the engine and the drive-line (including tyre/wheel assemblies) as well as due to coupling between the vertical, longitudinal and lateral motions of the rear axle imposed by the geometry of the rear axle suspension.     

A Pitch-Plane Model of a Vehicle with Controlled Suspension

A vehicle model incorporating front and rear wheel suspensions and seat suspension is presented. The suspension control includes algorithms to provide both dynamic and steady state (levelling) control. Vehicle response to (a) vertical inputs due to ground disturbances at the wheels and (b) longitudinal inputs due to the inertial forces during braking and accelerating, are investigated. It is shown that the static (self-levelling) control causes a slight deterioration in dynamic performance. The active ride control produces improvements of ride comfort under dynamic conditions compared to an equivalent passively suspended vehicle. In steady state the proposed control eliminates the error heave of the body caused by tilting of the vehicle with active suspension.     

An Optimal Continuous Time Control Strategy for Active Suspensions with Preview

A continuous time control strategy for an active suspension with preview, based on optimal control theory, is presented. No approximation is needed to model the time delay between the excitation of the front and the rear wheels. The suspension is applied to a two DOF model of the rear side of the tractor of a tractor-semitrailer. The purpose of the suspension is to reduce either the required suspension working space or the maximum absolute acceleration of the sprung mass, without an increase of the dynamic tire force variation. For a step function as road input, reductions of 65% and 55%, respectively, are possible compared with a passive suspension.     

Optimal Control of a Vehicle Suspension Incorporating the Time Delay between Front and Rear Wheel Inputs

An optimal control law for a vehicle suspension is developed using a discrete linear quadratic regulator framework. The time delay between the disturbance due to the road at the front and rear wheels is incorporated into the model, and it is shown that the optimal control law requires information gathered at the front wheels. A comparison is made between the optimal control law and a suboptimal one which does not incorporate front wheel road information.     

Tractor Handling during Control Loss on Sloping Ground

Tractor behaviour on sloping ground following a control loss due to rear wheel locking is examined. A mathematical model to predict the tractor trajectory is presented and the results obtained from this model are compared with those obtained from experiments with a remotely controlled tractor.

Reasonable agreement is reached between measured and predicted results - the discrepancies arise from limited tyre data or local random variations in slope, ground roughness or tyre/ground frictional values.

Within these limitations, the model is used to examine possible driver strategies following a control loss. Applying and maintaining full lock for this particular type of accident appears to improve safety; it certainly tends to avoid the worst situation in which the tractor accelerates backwards down the slope and reaches dangerously high speeds although inevitably it increases the likelihood of a low speed overturn.     

Optimal Preview Control of Rear Suspension Using Nonlinear Neural Networks

The performance of neural networks to be used for identification and optimal control of nonlinear vehicle suspensions is analyzed. It is shown that neuro-vehicle models can be efficiently trained to identify the dynamical characteristics of actual vehicle suspensions. After trained, this neuro-vehicle is used to train both front and rear suspension neuro-controllers under a nonlinear rear preview control scheme. To do that, a neuro-observer is trained to identify the inverse dynamics of the front suspension so that front road disturbances can be identified and used to improve the response of the rear suspension. The performance of the vehicle with neuro-control and with LQ control are compared.     

A Model for Determining Rider Induced Energy Losses in Bicycle Suspension Systems

The energy dissipated by the suspension systems used for off-road bicycles is a major concern due to the limited power source in cycling. Rider induced energy losses are those that arise from the muscular action of the rider. The purpose of this study was to develop and verify a dynamic model of a seated cyclist riding an off-road bicycle up a smooth road. With the absence of terrain irregularities, all suspension motion was rider induced. Knowing the stiffness and dissipative characteristics of the suspension elements, the power dissipated by the suspensions was calculated.

Simulation results were compared to suspension deflections that were experimentally measured for a cyclist riding a commercially available dual suspension bicycle up a 6% grade at 6.5m/s. For this particular case, no fork motion was observed in the experiments which was consistent with the simulation results. For the rear suspension, the mean and amplitude of the largest harmonic were experimentally determined to be 6.6 and ±2.7 mm respectively. Simulation results were within 0.7mm of the mean and within 0.3mm of the amplitude. The only major discrepancy between the experiments and the simulations was the presence of a phase lag in the simulation results which was attributed to inter-subject variability. The power dissipated by the rear suspension was calculated to be 6.9 Watts or 1.3% of the total power input by the rider. Given the grade and forward velocity, this translated into an equivalent mass of 1.8 kg. Thus, the bicycle appeared to be roughly 12% heavier than it actually was.     

Messungen von Fahrbahn-Unebenheiten paralleler Fahrspuren und Anwendung der Ergebnisse

Measurement of two track road inputs and theoretical application of the results

The calculation of vehicle response to road-surface irregularity inputs requires the spectral densities of the left and right longitudinal track and their statistical dependence

This paper presents some resluts of parallel profile measurements, three typical german roads have been chosen

Random vibration of two vehicle types are digital-simulated. The dynamic tire load shows that independent suspension systems are more advantageous than beam axles, because by wheel tramp this type increases the dynamic tire load.     

Dynamic Measurements in the Research and Development of Rail Vehicles

This paper reviews the measurements which are necessary to all aspects of vehicle dynamics as applied to rail vehicles. Although an attempt has been made to introduce some reference to measurements made in Europe and America, the detailed discussion has been limited to those techniques employed by British Rail. This has the advantage that the discussion can be first hand and therefore more specific.

For convenience the measurements have been collected together under four broad headings.

1. Measurements of rail system data.

2. Measurements of vehicle parameters.

3. Measurements to validate theory and predictions.

4. Measurements of vehicle performance.     

Optimal Linear Preview Control of Active Vehicle Suspension

The problem of linear preview control of vehicle suspension is considered as a continuous time stochastic optimal control problem. In the proposed approach minimal a priori information about the road irregularities is assumed and measurement errors are taken into account. It is shown that estimation and control issues can be decoupled. The problem formulation and the analytical solution are given in a general form and hence they apply to other problems in which the system disturbances are unknown a priori, even in a stochastic sense, but some preview information is possible.

The solution is applied to a two-degree-of-freedom (2-DOF) vehicle model. The effects of preview information on ride comfort, road holding, working space of the suspension and power requirements are examined in time and frequency domains. The results show that the greatest potential is for improving road holding properties. This effect could not have been observed in previous studies based on a 1-DOF vehicle model. It is also demonstrated that the presence of preview drastically reduces power requirements, thus relieving the performance versus actuator power dilemma.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

Semi-Active Suspension with Preview Using a Frequency-Shaped Performance Index

The objective of this study is to develop a control law for a semi-active suspension for the purpose of ride quality improvement. The semi-active control law is determined by reproducing the control force of an optimally controlled active suspension while suppressing its damping coefficient variation. The performance index of the optimal control for the active suspension is modified to include frequency-shaping by use of Parseval's theorem, which allows us to de-emphasize the effects of particular variables over specific frequency bands.

Through the numerical simulations, it was found that the semi-active suspension may reduce the vertical acceleration of the driver's seat and the sprung mass motions significantly. The road-holding and tire deflections were not affected much.     

Optimal Preview Control of Rear Suspension Using Nonlinear Neural Networks

SUMMARY

The performance of neural networks to be used for identification and optimal control of nonlinear vehicle suspensions is analyzed. It is shown that neuro-vehicle models can be efficiently trained to identify the dynamical characteristics of actual vehicle suspensions. After trained, this neuro-vehicle is used to train both front and rear suspension neuro-controllers under a nonlinear rear preview control scheme. To do that, a neuro-observer is trained to identify the inverse dynamics of the front suspension so that front road disturbances can be identified and used to improve the response of the rear suspension. The performance of the vehicle with neuro-control and with LQ control are compared.     

6自由度半车悬架解耦及其分层振动控制的研究

通过对6自由度半车悬架簧载质量的受力分析,推导出其前后1/4悬架间的定量耦合关系,并以其为基础构建分层振动控制算法.中央控制层以悬架质心处的垂向加速度和俯仰角加速度为控制目标,前后两个1/4悬架构成的两个底层分别采用H_∞和LQR控制策略,并接受中央控制层的协调指令.利用MATLAB的仿真表明,与传统控制相比,分层控制由于前后两个1/4悬架的控制量可以并行解算,计算时间大幅缩短,因而可针对路面激励实施详尽的控制,达到了改善车辆行驶平顺性的目的.     

Railway Vehicle Active Suspensions

This paper reviews the state-of-the-art of active suspensions for use on railway vehicles. The primary focus of the paper is on ride quality control, both vertical and lateral, and on lateral stability control.

The section on theoretical considerations summarizes the results of a one-degree of freedom optimization and then investigates analytically the use of active suspensions for lateral ride and stability augmentation. It is shown that separate control structures using different measurements and actuator actions are very effective in controlling both ride quality and stability.

A section on a survey ofcurrent activities reviews published research on active railway suspension work around the world.

Finally a concluding section indicates future trends in active suspension applications.     

Nähere Untersuchungen zur stationären Kurvenfahrt von Einspurfahrzeugen

Detailed Investigations of the Steady State Turning of Single Track Vehicles

In the paper the steady state turning of single track vehicles on a horizontal, even road is investigated, supposing the air to be at rest. The vehicle model used has six degrees of freedom: rolling, yawing, pitching and bouncing of the vehicle, rotation of the front wheel system (steering) relatively to the main frame and distortion of the rear wheel system due to limited stiffness of its linkage, and also takes into account wind drag and gyroscopic effects generated by wheels and other vehicle components. A special importance is given to the geometry of the vehicle

The results show a comparison of two types of motorcycles with different geometries and tires. To characterize the vehicle behaviour the roll, side slip and steering angle as functions of the normal acceleration are used. A more detailed study in respect to the steering torque is added.     

Preview Control Algorithms for the Active Suspension of an Off-Road Vehicle

The potential performance improvement using preview control for active vehicle suspension was first recognized in the late nineteen sixties. All work done since that time has been based on optimal control theory using simple vehicle models.

In this article, the performance of quarter vehicle preview controllers when applied to a real off-road vehicle is simulated using both two degree of freedom quarter and ten degree of freedom full vehicle models. The results, which are compared with non-preview active and conventional passive suspensions, confirm that preview control reduces vertical acceleration of the body centre of gravity, which results in improved ride quality. Further, reductions in pitch and roll motion result from smaller vertical displacements of the vehicle quarters. Coupling between quarters, through the vehicle body, appears to have a smoothing effect on the control.

As an alternative to optimal control theory based controllers, a simple ad hoc preview controller based on isolating the vehicle body from dynamic loads transmitted through the suspension is proposed. Simulation results show that such a controller outperforms the optimal control theory based controllers over small discrete disturbances but responds poorly to disturbances encountered from other than steady state.