2007-01-0822

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SAE TECHNICALPAPER SERIES 2007-01-0822

Vehicle-Trailer Handling Dynamics and StabilityControl — an Engineering Review

Xiaodi KangQuantech Global Services

Weiwen DengGeneral Motors Corporation

Reprinted From: Vehicle Dynamics & Simulation, 2007(SP-2138)

2007 World CongressDetroit, MichiganApril 16-19, 2007

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2007-01-0822

Vehicle-Trailer Handling Dynamics and

Stability Control ─ an Engineering Review

Xiaodi Kang Quantech Global Services

Weiwen Deng General Motors Corporation

Copyright © 2007 SAE International

ABSTRACT

This paper presented an engineering review on the state of the art in the research and development of vehicle-trailer handling dynamics and stability controls. The issues and potential technical solutions were identified in various areas and the unique characteristics of vehicle-trailer as a combined system were investigated and compared to a single-unit vehicle system. Many approaches taken in modeling, analysis, simulation and testing were examined, and various control methods, actuations and control implementations were evaluated. As a result of this study, further research areas were also identified. While it is important to maintain the stability of a trailer, thus the stability of a vehicle-trailer combination, it remains one of the major challenges in designing an appropriate control law to balance effectively the requirements between stability and handling performance, which often set conflicting objectives.

INTRODUCTION

Vehicle-trailer system is generally referred to as combination vehicle or articulated vehicle. Directional dynamics and stability have been the primary concern for vehicle-trailer combinations, which are known to have some undesirable response properties when laden and traveling at high speed or on low-friction surface [1]. The handling performance of a vehicle when towing a trailer can also be deteriorated due to the adverse influence from the trailer in dynamics and kinematics. As two pivot-connected units, the trailer is more prone to instability such as lateral swing or even jackknife, while the vehicle’s issue is more related to the handling performance since driver typically perceives only vehicle’s dynamics. Compared to a single-unit vehicle, the driver of vehicle-trailer combination has an additional task of coping with trailer oscillation, possible instability and path following to the vehicle. Both often pose conflicting objectives in control design. The balance between overall system stability and towing vehicle handling performance often becomes a compromise due

to limited control channels available. In addition, a vehicle-trailer combination is of higher order than a single unit vehicle, and thus is a more complex plant, which further makes the control design more complicated [1].

The handling dynamics and stability characteristics of various vehicle-trailer combinations have been extensively investigated along with stability and safety-related issues [1-10]. The main design and operation parameters related to the behaviors of vehicle-trailer combinations have also been examined [11-23]. For example, University of Michigan Transportation Research Institute (UMTRI) conducted numerous investigations on combination vehicle dynamics through its comprehensive Phase I to Phase IV programs in the 1980s [13]. More recently Vehicle Research and Test Center of NHTSA ((VRTC) has done considerable investigations on vehicle-trailer system modeling, testing and stability control, and have developed the National Advanced Driving Simulator (NADS) [2]. These investigations have been, however, mainly focused on heavy vehicle combinations, such as tractor and semi-trailer systems, though [21] presented a review on handling characteristics of car-trailer systems. Despite extensive engineering activities found in the literature on vehicle-trailer combinations, there are still many areas which lack sufficient research and analysis, which are mostly attributed to the complexities of vehicle-trailer combinations and lack of appropriate control design criteria. To help identify these areas and to promote further engineering activities, this paper reviews and summarizes the progress made in the areas of modeling and simulation, analysis and synthesis on the handling dynamics and stability controls for vehicle-trailer combinations, and various control methods developed to achieve desired performance and a proper balance of some conflicting objectives. Unlike some reviews found in the literature with focus on heavy commercial vehicle combinations, the interest of this paper is mainly on light


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vehicle-trailer systems, such as car or light truck trailer combinations.

This paper mainly consists of three sections. The first section reviews the unique characteristics of vehicle-trailer combination as compared to vehicle as a single-unit system. The dynamic characteristics are examined in terms of some stability and safety related issues, system configurations, operating conditions and driver-vehicle interactions. Two different vehicle-trailer configurations are distinguished in terms of hitch coupling, critical modes, trailer variation and driver-vehicle interactions. The second section presents progress on vehicle-trailer dynamics analysis and stability control. The fundamental impact of towing a trailer on vehicle dynamics characteristics is illustrated by comparing the root loci of a vehicle only and a vehicle-trailer combination. Different control methods developed are examined in terms of their control objectives and approaches. As a result, some further research areas are identified. The third section further highlights some important observations from the review regarding vehicle-trailer handling and stability control, in view of control objectives, approaches, actuations and feasibility.

VEHICLE-TRAILER SYSTEM DYNAMICS

VEHICLE-TRAILER SYSTEM UNIQUE CHARACTERISTICS

Stability

Unlike a single-unit vehicle (such as passenger car, van, and sport utility vehicle), combination vehicle (such as light vehicle-trailer system and tractor-trailer system), has some unique characteristics in dynamics, handling, stability and maneuverability due to its different configurations. Although divergence stability, caused mainly by oversteer, is common to both single-unit and combination vehicles, oscillatory instability caused mainly by trailer oscillation happens more often to combination vehicles. The following are some unique characteristics of vehicle-trailer combination [11-23].

• Relatively smaller stability region and inferior maneuverability as compared to a single-unit vehicle, including inferior controllability and stability in both yaw and roll modes at high speed, and larger off-tracking at low speed.

• Jackknifing and trailer swing phenomenon. This instability represents the uncontrolled large relative yaw motion between vehicle and trailer, and is one of the most common causes of highway accidents. It is caused by the loss of lateral force at vehicle rear and/or trailer tire-road interfaces, mostly due to hard braking.

• Lateral oscillation of trailer or snaking. This kind of instability represents the oscillation of trailer at high speed, due to low system damping. This oscillation

is inherent and sensitive to system parameters and operating conditions such as traveling speed and road surface friction. It may be excited by various disturbances, such as side wind or driver abrupt steering. Self excitation may also occur if the system parameters are not properly designed and/or the operating conditions are close to certain critical states.

• Phase lag between vehicle and trailer motions due to the separating distance. Inevitably, there is a relatively large phase shift between driver input and trailer response, which typically requires good driving skill to cope with.

• Rearward amplification (RWA). This is defined as the ratio of the peak lateral acceleration at the rearmost trailer's center of gravity to that of the lead unit or towing vehicle during a lane-change maneuver. It is particularly important for multi-unit articulated vehicles, which usually exhibits a high level of RWA, and may potentially lead to roll-over during obstacle avoidance maneuvers.

• Unstable backward motion.

System configurations and operating conditions

Compared to a single-unit vehicle, combination vehicle has considerably more uncertainties and variable configurations due to various types of hitch equipments, trailer types and dimensions, and loading conditions. For example, different trailers may be used for different towing purposes, or the loading can be changed frequently from time to time. These variable configurations greatly influence the directional dynamics and stability characteristics of vehicle-trailer system, thus requiring more robust control design.

Driver-vehicle interaction

Unlike the driver of a single-unit vehicle, the driver of a combination vehicle has an additional task of coping with trailer oscillation and possible instability. When driving a combination vehicle, however, the driver does not have enough feedback information on the behavior of the trailer, thus his/her actions (steering, braking, and accelerating) mainly depend on the actual state of the towing vehicle. Under certain critical circumstances, the driver may not be able to provide suitable control on the vehicle combination. As a consequence, this may lead to system instability, such as jackknifing, trailer swing, snaking, or even rollover. Thus, some high degree of skill and quick reaction are required in operating a combination vehicle. However, not many drivers possess such skills.

TWO CLASSES OF VEHICLE-TRAILER SYSTEM COMBINATIONS

Although vehicle-trailer system can have innumerable variety of combinations, they may be simply categorized


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into two major configurations: light vehicle (car or light truck)-trailer combinations and heavy vehicle-trailer combinations or commercial vehicle combinations in trucking industry (such as tractor and semi-trailer or full trailer combinations).

Heavy vehicle-trailer combinations

A heavy vehicle-trailer system typically has the following characteristics:

• Hitch/fifth wheel couplings to resist roll motion of the trailer

• High CG (Center of Gravity) trailers, thus high tendency to rollover

• Operated by professional drivers

The widely used commercial tractor-trailer system is a typical example. The trailer is generally an integral part of the vehicle combination. Thus, the combination system is considered as a whole, and the main concerns are on roll stability and RWA for multi-unit combination due to the excessive dimensions and CG heights. The characteristics of commercially articulated vehicles for highway transportation are usually assessed in terms of some established performance measures, such as handling quality of the vehicle combination, static rollover threshold, dynamics rollover stability, yaw damping ratio, friction demand of the drive-axle tires, lateral friction utilization, low and high-speed off-tracking, and braking performance. An example is given in [11]. In addition, a lot of research work has been done in the Automatic Highway System (AHS) programs for highway tracking control [3, 5].

Light vehicle-trailer systems

Light vehicle-trailer combination, such as passenger car-trailer or light truck-trailer system, is essentially different from commercial tractor-trailer systems in terms of maneuverability and stability. Except for specifications, there are many variables which affect the system, such as driver’s skill, the frequency of use, loading variations and stability characteristics. A light vehicle-trailer combination usually exhibits the following characteristics:

• The standard coupling connection between vehicle and trailer is a hitch, mostly a non-torque bearing ball connection, thus allowing the trailer to rotate easily in the yaw plane.

• Many types of trailers exist, such as caravan, travel trailer, boat trailer, sport utility and special purpose trailers.

• Usually, driver’s skill is relatively lower compared to the skill of a professional driver in operating a commercial vehicle-trailer combination.

For a driver of a light vehicle-trailer system, he/she may operate the system with or without the trailer. This sets a requirement that a consistent handling behavior is desirable between the single-unit vehicle and the combination vehicle. For this, light vehicle-trailer system characteristics should be evaluated in terms of both towing vehicle only and vehicle-trailer combination.

VEHICLE-TRAILER SYSTEM DYNAMICS AND

STABILITY CONTROL

ANALYSIS ON HANDLING AND STABILITY

The handling and stability characteristics of various combination vehicles have been extensively studied in the past decades [24-52]. These studies have brought about progress in analytical techniques, such as simulations based on equations of motion, root locus approach for stability judgment, and analysis of jackknife behavior and trailer oscillations.

Two main approaches have been commonly employed. The first one is the classical analytical approach based on simple linear or linearized models for root locus analysis and vehicle stability evaluation [24-34, 41-43, 47-52]. The most popular formulation is a three-DOF (Degree Of Freedom) linearized tricycle model, which was first proposed by Jindra [23] for analyzing a tractor-semi-trailer combination in the early 1960s. The trailer is assumed to have only one axle and the system degrees of freedom include towing vehicle lateral motion, towing vehicle yaw motion and trailer yaw motion. This model is an extension of the commonly used two-DOF linear bicycle model for single-unit vehicles and is simple enough to allow freedom in obtaining a fundamental understanding of the dynamic behavior of the combination vehicles using frequency response approaches. Small steering angle and hitch angle are usually assumed in this approach. A detailed derivation of a three-DOF linearized vehicle-trailer system model based on [23] is presented in [1]. The towing vehicle can be a tractor for heavy vehicle combinations, or a car or light truck for light vehicle-trailer combinations.

The second approach is through computer simulation based on complex nonlinear-models incorporating tire and suspension dynamics for evaluating system response characteristics in time domain [35-40, 44-46].

In both approaches, parametric studies for evaluating the influence of design parameters and operation conditions on system dynamics and stability characteristics have also been conducted [1].

Based on the well known two-DOF linear bicycle model, there are essentially two poles or one pole-pair for a single-unit vehicle or vehicle only, which are associated with vehicle lateral and yaw motions. However, based on the linearized tricycle model [1, 23], there are four poles


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or two pair-poles for a three-axle vehicle-trailer combination.

Figure 1 presents a comparison of the root loci of a vehicle only (based on two-DOF linear bicycle model) and a vehicle-trailer combination (based on three-DOF linearized tricycle model) to illustrate the difference in dynamics characteristics of the towing vehicle with and without a trailer [1], with the arrow showing increasing vehicle speed. To simplify the description, only the root loci with positive imaginary parts are shown in Figure 1. The towing vehicle is a medium pickup truck with a total weight of about 2500 kg, while the trailer has a total weight of about 1000 kg.

The root-locus plots reveal a distinguishing distribution pattern of the vehicle-trailer system poles at a relatively high speed. One pole-pair of the vehicle-trailer combination (pole of vehicle-trailer (1), shown in dashed line) is quite comparable to that of the vehicle without trailer (pole of vehicle only, shown in solid line) and is

thus referred to as a vehicle-mode associated pole-pair, while the other pole-pair (pole of vehicle-trailer (2), shown in dash-dot line) is much closer to the imaginary axis and characterized by considerably lower damping ratio and natural frequency, which is referred to as a trailer-mode related pole-pair. Due to the impact of the trailer-related poles, the effective damping of the vehicle-trailer system is considerably lower as compared to that of the vehicle only, resulting in excessively oscillatory response in both hitch angle and hitch angle rate, especially under low-coefficient surface and/or at high speed. In addition, due to the pole deviation caused by the trailer, the towing vehicle also exhibits quite slower response, as shown in Figure 2.

STABILITY CONTROLS

Control objectives

Unlike a single-unit vehicle, such as passenger car or light truck, where stability control has typically been evaluated in terms of vehicle handling performance and driver perception, vehicle-trailer combination has its first-order requirement in maintaining its maneuverability and stability, as illustrated in Figures 1 and 2.

In contrast to a single-unit vehicle where the desired handling characteristics have been well established in the past, the desired behavior of a vehicle-trailer system is not straightforward. Therefore, suitable performance measures and evaluation criteria are yet to be defined, although some intuitively general observations have been made available based on the light vehicle-trailer system unique characteristics [1, 53].

Control approaches

In the past decades, the development of vehicle stability-control systems has shown significant progress in both theoretical and practical fields [53-87]. The available control systems for combination vehicles, however, are mostly limited to braking performance enhancement and for heavy vehicle-trailer combinations. Many active devices have already existed with the aim to prevent or inhibit jackknifing of tractor-trailer combinations through differential braking control [82, 87]. Recently, steering and differential braking controls have also been explored for improving directional stability and track followability, again, mostly for tractor-trailer systems [54-56, 58, 59, 61, 63, 65-68, 71, 73-75, 77, 80-83, 86, 87].

The most relevant approaches for light vehicle-trailer system dynamics and stability control are summarized in the following subsections:

• Direct yaw control (DYC) [54, 56, 57, 62, 63, 66-69, 72, 74, 78, 79]

The Direct Yaw Control, or DYC, is used to generate a stabilizing yaw moment on vehicle and/or trailer by intentional distribution of braking forces between left and right wheels (differential braking or DB). The DYC is

Figure 1: Root loci of a single-unit vehicle and a vehicle-trailer

combination as functions of vehicle speed

Figure 2: Step-input time responses of a single-unit vehicle and a

vehicle-trailer combination

Time (sec)

Vehicle

sideslip

0 0.5 1 1.5

-10

-5

0Vehicle only

Vehicle-trailer

Time (sec)

Vehicle

yaw

rate

0 0.5 1 1.50

1

2

3

Time (sec)

Hitch

angle

rate

0 1 2 3-3

-2

-1

0

1

2

Time (sec)

Hitch

angle

0 1 2 3-0.8

-0.6

-0.4

-0.2

-18 -16 -14 -12 -10 -8 -6 -4 -2 00

1

2

3

4

5

6

7

Real part (rad/s)

Imaginary

part

(rad/s

)

Pole of vehicle only

Pole of vehicle-trailer (1)

Pole of vehicle-trailer (2)

Increasing speed


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activated when the vehicle state variables, such as yaw rate and side slip, exceed certain predetermined thresholds, due to various reasons, such as disturbances, low-coefficient surfaces or severe steering maneuvers.

It is observed that when the oscillation of a trailer can be kept small, the influence of the trailer on a vehicle is also reduced and the handling of the whole vehicle-trailer combination is effectively improved.

The main advantage of DYC is that it can be easily implemented on combination vehicles equipped with Anti-lock Braking System (ABS). There is no need for additional actuators since nearly all existing hardware of an ABS system is sufficient for operation with minor software modifications only. The drawback is that influencing the lateral dynamics by a differential braking force distribution also affects the longitudinal dynamics, thus reducing vehicle’s momentum. In addition, since the braking activation is not related to the driver’s intention, it is considered to be obtrusive to the driver.

• Vehicle rear wheel steering (RWS) [1, 53, 64-67, 70, 71, 73, 76]

The purpose of RWS is to stabilize the vehicle-trailer combination by influencing trailer motion through hitch coupling in order to stabilize the trailer. As a result, a more stable trailer tends to reduce its impact on vehicle, its lateral acceleration amplification tends to decrease, and the rollover risk for the overall system tends to reduce as well. Different steering control approaches from the literature are summarized below.

� Open-loop RWS controller

Open loop RWS control is formulated such that the rear wheel steer angle is proportional to vehicle front wheel steer angle as a function of vehicle speed. This proportional gain may be obtained based on either zero vehicle sideslip angle in a steady-state turn, or desired minimum trailer lateral acceleration.

The open-loop RWS controller can not only enhance system lateral dynamics and stability at high speed, but also improve vehicle-trailer system maneuverability at low speed by reducing turning radius.

� Optimum RWS controller

The optimum RWS control uses state feedback of vehicle-trailer system, such as vehicle sideslip and yaw rate, hitch angle and hitch angle rate, to stabilize the system and to achieve vehicle-like handling performance by minimizing the difference of vehicle yaw rate and sideslip between cases with and without towing a trailer.

The optimal control can be formulated with the performance index defined below.

.

dtrrwvvwwJ dddss

T

])()()([ 23

22

2

01

2 −+−+−+= ∫ θθφ(1)

where v, r, and θ denote vehicle lateral velocity, vehicle

yaw rate and hitch angle respectively, and φ denotes hitch angle rate. vd and rd are the desired responses of vehicle lateral speed and yaw rate, which can be derived from the desired vehicle performance for vehicle alone to preserve vehicle-like handling performance or driver's

perception. θdss is the desired hitch angle as defined from steady-state analysis [1]. wi (i=1, 2 and 3) is the weighting factor.

The objective of the optimal control in Eq. (1) is to force the vehicle-trailer system to track the desired handling performance of the towing vehicle in order to preserve driver’s perception when driving the vehicle alone. In addition, the control is to stabilize the trailer by minimizing hitch angle rate and driving hitch angle to the desired one. In the control design, it is assumed that all states are available either through measurement or by estimation.

While RWS control is effective in reducing trailer impact on vehicle handling performance, some compromises still exist. However, with both front and rear wheel steering control, a much better vehicle-trailer characteristics can be obtained in balancing both vehicle handling and trailer stability requirements.

� Virtual model following RWS control

Similar to the optimum RWS control, virtual model following RWS control is to have an actual vehicle-trailer system track a virtual but desired vehicle–trailer model. This is derived by minimizing the error between two systems in terms of all four state variables, namely vehicle yaw rate and side slip, hitch angle and high angle rate.

Simulations using a complex vehicle model for heavy-vehicle combination show remarkable improvement potentials for combination vehicles in various areas, such as braking on split adhesion surfaces, in which the trailer lateral oscillation can be drastically reduced.

The results also show that using information from both units (towing vehicle and trailer) helps vehicle to retain stability better than driver control. It is suggested that information about the hitch angle and hitch angle rate has to be integrated in the control algorithm to determine the vehicle rear wheel steering angle.

• Trailer steering control [80, 81, 84, 86]

This approach applies to trailers with steerable wheels. Trailer steering control is usually formulated to stabilize the trailer and reduce its negative influence on vehicle, to


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reduce trailer lateral acceleration and to mitigate rollover risk for vehicle-trailer system.

� Trailer steering control based on root-locus analysis

The objectives are typically to improve the directional stability and handling, and to reduce trailer off-tracking. The control law in determining trailer steering angle is formulated as a function of hitch angle and hitch angle rate, or as a function of vehicle front wheel steering angle, based on root-locus analysis or based on zero vehicle body side slip in a steady- state turn.

It is observed that hitch angle input alone does not have a good effect on stabilization. However, the steering control system with hitch angle rate input can not only stabilize vehicle-trailer combination, but also improve vehicle behavior such that it becomes closer to that of a vehicle alone. Simulations and small scale model experiments have been conducted, which confirmed the analytical results.

� Trailer steering control design based on vector following controller

By looking at the smoothness of locomotion, it is desirable for trailer to be pulled straightforward in the direction of its centerline. Therefore, the control objective is to have the trailer centerline in line with the velocity vector at the hitch point. Trailer steering angle is defined as a function of vehicle front wheel steering angle and speed.

It is shown that this kind of controller can greatly improve the trailer response in both overshooting and damping properties, and considerably reduce the off-tracking of vehicle-trailer combination, which has been verified using scale model experiments.

• Other control approaches [75, 82, 83]

Two-loop full-state feedback control is another approach using two control loops, a major loop and a minor loop. The major loop with full-state feedback based on a reference model is to improve system stability and disturbance rejection, particularly for yaw rate response enhancement, while the minor loop is to improve low speed maneuverability and followability. Full-state feedback, however, requires extensive instrumentation or properly designed observers.

Other control approaches include vehicle suspension control with controllable spring stiffness and/or bushing compliance to affect the understeer behavior of vehicle-trailer system. The control purpose is to achieve consistent vehicle handling response characteristics under different rear loading conditions during trailer towing. In addition, several damping and motion restraining mechanisms or passive devices have also been introduced to stabilize the trailer, such as rotational damper or torsional spring, or both, to control the motion

of the trailer. Although these approaches are much more cost effective, they do not directly control the trailer, thus are less effective in achieving desired handling and stability performance.

REMAINING ISSUES

There are still some areas lacking sufficient information from the literature, which include mechanical coupling between vehicle and trailer and its impact on controller design, reference model design for tracking desirable and achievable handling and stability characteristics, and various control implementation issues, in particular, those related to state measurement or estimation for state feedback control, control design and product feasibility related to instrumentation of controller and sensor(s) on vehicle or trailer, or both.

In addition, most of the available work on vehicle-trailer control mainly focuses on design and analysis aspects using computer simulations. There is a serious lack of real vehicle test data and experimental verification reported in the literature. This makes it difficult to assess the true value of the reported results or to compare the results achieved by different researches.

Furthermore, the feasibility of the various stability controls, such as state estimations and control implementation issues, needs to be further explored.

VEHICLE-TRAILER SYSTEM CONTROL STRATEGIES

CONTROL OBJECTIVES

For a light vehicle-trailer combination, the characteristics of vehicle alone are considered to be the benchmark of the vehicle-trailer system for a consistent yet desirable vehicle-like handling performance. Therefore, it is desirable that the vehicle have an optimal dynamics behavior for both with and without trailer cases, that is, good handling performance and trailer towing stability. Thus the control objective can be defined to stabilize the system without significantly changing the characteristics of vehicle-alone to maintain consistent and predictable vehicle handling quality to drivers. In addition, similar to single-unit vehicles, other general control objectives should also be considered to enhance directional stability and controllability for vehicle-trailer combination, and to maintain desired steering response characteristics against changes in system parameters and operating conditions.

THREE POSSIBLE APPROACHES

• Adapt a control system for a vehicle in such a way that it improves system dynamic performance with trailer stabilization. No control system is equipped on the trailer. It seems favorable to have all control devices and sensors mounted on the towing vehicle only. However, in order to enhance stability of combined system while preserving the vehicle-like handling performance, it is necessary to have some


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information available from the trailer, such as trailer yaw rate or hitch angle rate. Otherwise, some trade-off becomes unavoidable.

• Provide a separate trailer control system with its own sensor(s) such that the trailer can be stabilized by the controller and the negative influence from trailer to vehicle be minimized. With this approach, the trailer with the controller can be attached to any vehicle without modification or instrumentation of the vehicle. However, the additional hardware will make the trailer more expensive, and it is difficult to set the vehicle power to the actuator on the trailer. In addition, without synchronization between vehicle and trailer control systems, an optimum performance may not be achievable.

• Mount control devices on both vehicle and trailer. This control configuration can achieve the best overall performance in stabilizing trailer and maintaining vehicle-like handling performance. Some tuning between the two units with respect to vehicle-trailer parameters and other configuration variations is necessary to take full advantage of this control configuration.

CONTROL ACTUATIONS

Similar to a single-unit vehicle system, two major control actuation systems can be developed to influence the dynamic behavior of a vehicle-trailer system, namely augmented steering and differential braking. Steering control can effectively influence the lateral dynamics nearly without restrictions on the longitudinal dynamics. However, this requires a costly actuator. For differential braking control, nearly all existing hardware of an ABS system is sufficient for operation with minor software modifications. While this control can effectively affect the lateral dynamics, it may impact the longitudinal dynamics and driver perception, such as slowing down the vehicle-trailer combination or adding intrusion to drivers.

Other less effective but more cost-effective approaches may consist of using some kind of controlled or smart components and passive systems, such as adjustable suspension spring and bushing compliance to affect the understeer behavior of the vehicle-trailer system in order to maintain consistent vehicle handling performance, rotational damper or torsional spring or both to stabilize the trailer.

CONCLUSIONS

Compared with a single unit vehicle system, a vehicle-trailer combination exhibits certain unique characteristics, such as smaller stability region and inferior maneuverability, jackknifing and trailer swing, trailer oscillation and reward motion amplification; widely varying system configurations and operating conditions as well as complicated driver-vehicle interactions.Two distinguishing vehicle-trailer configurations, namely

heavy tractor-trailer combination and light vehicle (car or light-truck)-trailer combination are different in terms of hitch coupling mechanism and critical modes, trailer variation as well as driver-vehicle interactions, and thus pose considerably different dynamics and control requirements.

Review of progress on vehicle-trailer dynamics analysis and stability control shows that the approach using linear modeling and analysis is common and effective in the analysis of system characteristics and control design for vehicle-trailer combination. Unlike the control design for a single-unit vehicle, maintaining stability of trailer and overall vehicle-trailer combination is found to be one of the foremost important tasks. For a light vehicle-trailer combination, it is further desirable that the vehicle have an optimal dynamics behavior for both with and without trailer cases. Thus the control objective can be defined to stabilize the system without significantly changing the characteristics of vehicle alone to maintain consistent and predictable vehicle handling quality to drivers. However, it remains one of the major challenges in designing appropriate control laws to effectively balance the requirements between stability and handling, which often set conflicting objectives. It is also found that some areas are still lack of sufficient information from the literature, such as mechanical coupling between vehicle and trailer and its impact on controller design, reference model design for tracking desirable and achievable handling and stability characteristics, and various control implementation issues. Similar to a single-unit vehicle system, two major control actuation systems may be employed to influence the dynamic behavior of a vehicle-trailer system: augmented steering and differential braking, each having its advantages and drawbacks. The most cost-effective approaches may consist of using some kind of controlled or smart components and passive subsystems to affect the dynamics behavior of the towing vehicle or to stabilize the trailer so as to maintain consistent vehicle handling performance with or without towing a trailer.


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