Car-trailer Combinations Research Articles

Optimization of Gain Scheduled Controller for an Active Trailer Steering System Using an Evolutionary Algorithm

Car–trailer combinations can experience unstable motion modes such as trailer-sway, jackknifing and rollover that can lead to fatal accidents. These unstable motions can be mitigated with the use of an active trailer steering (ATS) system. Prior studies in ATS have leveraged the linear quadratic regulator (LQR) as an ATS controller but for many of these designs it was assumed that the vehicle and operating parameters were constant. In reality, vehicle and operating parameters may vary and have an impact on the stability of a car–trailer combination. In this paper, the weighting matrices of the LQR controller are determined using the GDE3 evolutionary optimization algorithm with the objective of addressing the design trade off between minimizing the car–trailer’s path-following performance for low vehicle speeds and minimizing the rearward amplification for high vehicle speeds. The effectiveness of the approach is demonstrated using a numerical simulation car–trailer model developed in the CarSim simulator. Our results show that the multi-objective tuned gain scheduling controller outperforms a non-tuned gain scheduling controller in terms of improving the lateral stability and the path following performance of car–trailer combinations in driver in the loop single lane-change maneuvers at a constant vehicle forward speed.

On nonlinear model predictive direct yaw moment control for trailer sway mitigation

In car–trailer combinations, the hitch angle is the relative yaw angle between towing car and trailer. The literature has shown that the inclusion of the hitch angle measurement for the feedback control of trailer oscillations can bring safety benefits, compared with conventional trailer sway mitigation algorithms based on the yaw rate of the car. Given the nonlinearity of the vehicle system in the typical conditions requiring the hitch angle control function intervention, nonlinear model-based controllers could be an effective solution. This paper presents four real-time implementable nonlinear model predictive control (NMPC) formulations, using the hitch angle measurement for the torque-vectoring (TV) control of an electric front-wheel drive car towing a trailer. The simulation results show that: (i) the active safety is enhanced by the proposed NMPC TV formulations, with respect to a benchmarking NMPC TV controller only based on the control of the towing car; (ii) the NMPC formulations that directly constrain the hitch angle error, or perform continuous hitch angle tracking, outperform those that modify the reference yaw rate or yaw rate error based on the hitch angle error; and (iii) the NMPC approaches including a dynamic model of the trailer are robust with respect to variations of trailer parameters.

A study on body sway of car-trailer combinations considering dry friction in steering subsystem

Considering the stability of vehicle system, static instability and dynamic instability are two different instability problems. Because of the dynamic coupling between car and trailer, the problem of dynamic stability of car-trailer combination (CTC) is more obvious. This instability is called body sway or flutter in engineering, its boundary is often described by dynamic critical speed ( vcrit). It has been proved by experiments that the steering system characteristics have an important impact on the dynamic stability of CTC, but the specific mechanism is not clear. In this paper, the characteristic and influence of steering subsystem are studied for the first time. Firstly, a 6-DOF nonlinear dynamic model of CTC is established by Lagrange equation. The steering subsystem characteristics, incl. stiffness, damping, rotational inertia, and dry friction, are considered in theoretical modeling. On this basis, the influences of steering characteristics, especially the dry friction, on vcrit and axle cornering stiffness of CTC are analyzed. Simulation results show that the vcrit can increase by 16% and 23.2% respectively via adjusting the steering stiffness and the sliding friction factor. Therefore, a fine selection of steering subsystem characteristics can effectively improve the dynamic stability and safety of CTC. The research results of this paper can provide reference for the design of steering system considering dynamic stability.

Influence of braking on dynamic stability of car-trailer combinations

The influence of braking on dynamic stability of a car-trailer combination (CTC) is studied in this paper. The braking is simply modeled and integrated into a single-track model (STM) with a single-axle trailer. On this basis, some fundamentals and analysis results related to system dynamic stability are given through simulation. Furthermore, it is found that the axle load transfer and braking force distribution have a great influence on system dynamic stability. In order to further analyze the influence of these two factors, both of the braking force distribution and the pitch motion are considered in the modeling. Finally, the ideal braking force distribution domain is proposed. Results can be adopted to explain the experimental phenomenon and serve as a guideline for the differential braking strategy in stability control of the CTC.

An overview of control schemes for improving the lateral stability of car-trailer combinations

This paper reviews the state-of-the-art control schemes for enhancing the lateral stability of car-trailer (CT) combinations. Various studies have been conducted on lateral stability control of single-unit vehicles, e.g., cars. However, much less attention has been paid to lateral stability control of multi-unit vehicles, e.g., CT, which usually exhibit poor manoeuvrability in curved-path negotiations and low lateral stability under high-speed evasive manoeuvres. The low lateral stability may lead to unstable motion modes, e.g., trailer-sway and jackknifing, causing severe accidents. To improve the lateral stability, various control schemes were designed considering relevant performance measures and evaluated using either numerical simulations or testing methods. Thus, the topics surveyed in this paper include: directional performance measures, evaluation methods, important parameters affecting the directional performance, and active control approaches for CT combinations. Important control schemes are emphasised and their features discussed and analysed. As a result of the overview, future research efforts are identified.

An overview of control schemes for improving the lateral stability of car-trailer combinations

This paper reviews the state-of-the-art control schemes for enhancing the lateral stability of car-trailer (CT) combinations. Various studies have been conducted on lateral stability control of single-unit vehicles, e.g., cars. However, much less attention has been paid to lateral stability control of multi-unit vehicles, e.g., CT, which usually exhibit poor manoeuvrability in curved-path negotiations and low lateral stability under high-speed evasive manoeuvres. The low lateral stability may lead to unstable motion modes, e.g., trailer-sway and jackknifing, causing severe accidents. To improve the lateral stability, various control schemes were designed considering relevant performance measures and evaluated using either numerical simulations or testing methods. Thus, the topics surveyed in this paper include: directional performance measures, evaluation methods, important parameters affecting the directional performance, and active control approaches for CT combinations. Important control schemes are emphasised and their features discussed and analysed. As a result of the overview, future research efforts are identified.

Nonlinear Dynamics Analysis of the Body Sway of Car-trailer Combinations

Nonlinear Dynamics Analysis of the Body Sway of Car-trailer Combinations

An optimal robust controller for active trailer differential braking systems of car-trailer combinations

This paper presents an optimal robust controller for active trailer differential braking (ATDB) systems of car-trailer (CT) combinations. To design ATDB systems, controllers based on the linear quadratic regulator (LQR) technique have been explored. In these LQR controller designs, vehicle forward speed, trailer payload, etc., were assumed as constants. In reality, a CT combination is frequently confronted with variations of operating conditions and vehicle parameters, which may impose significant impacts on the lateral stability of these vehicles. This motivates the investigation into robust controller designs. An ATDB controller is designed using the µ synthesis technique. A new method using a genetic algorithm (GA) for tuning the weighting function parameters for the robust controller is presented. In the parameters tuning process, the lateral stability is emphasised and the path-following capability is considered. Simulation results confirm the validity of the ATDB controller.

Analysis of Dynamic Stability of Car-trailer Combinations with Nonlinear Damper Properties

The dampers (shock absorbers) installed in the suspensions of the towing car have some nonlinear property in road tests, like a practical piecewise-linear property. Its influence on the dynamic stability of car-trailer combinations are investigated in this paper. This nonlinearity is modeled by a Magic Formula damper model and then integrated into an extended single-track model with a tandem-axle trailer. Both the system local stability and global stability are analyzed with different theoretical methods. The results of system phase portrait show a limit cycle and the corresponding longitudinal velocity is identified as the system dynamic critical speed vcrit, which is ca. 147.2 km/h.

An optimal robust controller for active trailer differential braking systems of car-trailer combinations

An optimal robust controller for active trailer differential braking systems of car-trailer combinations

Nonlinearity-induced time-varying harmonic dynamic axle load and its impact on dynamic stability of car–trailer combinations

ABSTRACTA nonlinearity-induced time-varying harmonic dynamic axle load is found in the road test of a car–trailer combination. To understand its influence on system dynamic stability, a corresponding linear single-track model (STM) is proposed. System dynamic stability is described and sensitivity analysis for the system parameters is achieved. The contribution of the harmonic force is quantified by a derived effective axle load. Because the harmonic effect might be time varying in practice, a time–frequency analysis-based parameter identification method is introduced. Experimental study shows that a time-varying harmonic effect really exists. A yaw-rate-based simulation method is designed to simulate this behaviour. The sensitivity analysis of the influence of the harmonic amplitude or phase on dynamic stability is performed with a simulation study. With appropriate modification of the harmonic amplitude and phase shift applied in selected time windows, the time-varying system characteristics in the road test can be simulated very well.

A Study of caravan unsteady aerodynamics

The high speed stability and handling characteristics of car-trailer combinations are affected by both road and aerodynamic forces. While the tyre-to-road interaction is well understood the action of gusts, passing large vehicles and even small steering inputs will disturb the symmetry of flow and generate aerodynamic forces and moments which are suffcient to affect the handling of the system. Although accidents caused by high speed instability are relatively uncommon a better understanding of these aerodynamic effects will improve safety. In this paper a series of wind tunnel investigations using scale models are presented. Steady state investigations were used to measure the aerodynamic properties of the car-caravan pair while a novel technique was developed to measure the aerodynamic damping derivatives in yaw and side force for a caravan model. These damping derivatives were shown to be destabilizing in most cases of sideslip and stabilizing in yaw although it was demonstrated that high damping derivatives were attained at certain frequencies of excitation.

Closed-Loop Directional Stability of Car-Trailer Combinations in Straight-Line Motion

SUMMARY This work focuses on the interaction between a driver and a car-trailer combination. A model characterizing human operator behavior in regulation task is employed to study directional stability of the overall system. The vehicle-trailer model retains nonlinear cornering force and other kinematic nonlinearities. Linear stability of the straight line motion is analyzed by the application of Routh-Hurwitz criteria and stability boundaries in parameter space are constructed by setting appropriate Hurwitz determinant to zero. It is shown that two types of transition in stability are possible in the driver/car-trailer system. They correspond to one pair or two pairs of complex conjugate eigenvalues crossing the imaginary axis simultaneously. The implications in terms of resulting motions for the nonlinear system are also discussed. It is shown that stabilization of the combination can be achieved by adding a passive controller at the articulation point. Articulation damper turns out to be a more useful ...

STABILIZATION OF ARTICULATED VEHICLES BY SEMI-ACTIVE CONTROL METHOD

SUMMARY This paper describes the stabilization of articulated vehicles at high speeds by a steering system set up on the trailer. First, the equations of motion of the articulated vehicles with a steering system on the trailer were obtained. Furthermore, the steering angle of the trailer in the presence of disturbances was studied by solving these equations through the application of modern control theory. From such analysis, the magnitude of the optimal feedback coefficients of each state variable was obtained. It was found that the stability of articulated vehicles at high speeds was significantly improved by the active control method for the trailer steering system. However, the active control system needs a power supply, and it is difficult to apply it to articulated vehicles at present, especially for passenger car-trailer combinations. Thus, a new trailer steering system with viscous coupling arms to be set between the tractor and trailer was proposed. Furthermore, the semi-active control method whi...