A novel control scheme is proposed to improve the yaw stability of a tractor semitrailer vehicle in critical situations. The control scheme is a two-layer structure consisting of an upper yaw moment controller and a lower brake force distributor. The tractor and the trailer are, respectively, stabilized by two independent fuzzy logic based yaw moment controllers. The controllers for the tractor and the trailer are, respectively, designed to track the reference yaw rate of the tractor and the hitch angle between the tractor and the trailer while considering the variation of the hitch angular rate at the same time. The corrective yaw moments determined by the corresponding upper fuzzy yaw moment controllers are realized by active wheel braking. The performance of the proposed control scheme is evaluated by simulations on a nonlinear vehicle model. The results demonstrate that the proposed control scheme is robust and effective in stabilizing the severe instabilities such as jackknife and trailer oscillation in the chosen simulation scenarios. It is believed that this control scheme is robust to the variation of road adhesion conditions.
Tractor semitrailer as a very common commercial heavy vehicle plays an important role in road transportations in all over the world. However, it is prone to lose lateral stability and cause fatal accidents because of its relative lower stability capability which mainly results from its particular multibody structure and high center of gravity (CG) [
In critical driving situations, a tractor-trailer may confront different forms of yaw instability such as jackknife, trailer swing, and trailer oscillation depending on the load, configuration characteristic parameters, steer input, and other external disturbances. The schematic of these instabilities are being shown in Figure
Schematic of yaw instabilities of a typical tractor semitrailer vehicle.
In critical situations, generally, it is difficult for a driver to manipulate a tractor semitrailer vehicle when he recognizes the vehicle being about to lose cornering stability. Fortunately, similar to the passenger cars, the stability of a tractor-trailer combination can also be considerably improved by active control method [
For a typical vehicle dynamics system, there are many uncertainties and nonlinearities such as vehicle configuration parameters, payload, and road adhesion conditions, which have considerable effect on the performance of the vehicle dynamics control system. In this study, in order to improve the stability of a tractor semitrailer vehicle with parametric uncertainties in critical situations, a robust control scheme is proposed based on fuzzy logic control method to stabilize the yaw dynamics of the tractor and the trailer separately and thereby improve the roll stability. Fuzzy logic control method which is described in simple vague linguistic terms and is suitable for the control of nonlinear systems especially with parametric uncertainties has been widely used in vehicle dynamics control systems [
The rest of the paper is organized as follows. In the following section, a nonlinear tractor semitrailer vehicle model is formulated replacing the real-world vehicle to assess the performance of the proposed control scheme. The detail of the proposed control system is described in Section
In this section, nonlinear models including the motions of the body, suspension, and tyre of a tractor semitrailer vehicle are formulated to replace the real-world vehicle for simulation to evaluate the performance of the proposed control scheme.
The nonlinear schematic model for a typical tractor semitrailer vehicle is shown in Figure
The schematic model of a typical tractor semitrailer vehicle.
Vehicle body model comprises the motions of longitudinal, lateral, yaw, and body roll for both the tractor and trailer and the coupling constraints between them. The pitch motions are not involved and the roll axis is fixed. The equations of these motions can be derived based on Lagrange’s approach and the principle of virtual work. The details of formulation will no longer be presented. As a result, the motions of longitudinal, lateral, yaw, and body roll for the tractor can, respectively, be formulated by the following:
Suspension model is used to predict the lateral load transfer as cornering which affects the variation of the tyre normal force. The primary components of the suspension used in this study comprise the leaf spring and the damping. The actual suspension force which is much nonlinear with respect to the deformation of the spring is calculated as follows [
Tyre normal load as one of the key factors influencing the tyre force should be well modeled. Particularly, the longitudinal and lateral load transfer should be precisely predicted. With these in mind, the tyre normal loads are calculated as
Slip angle and longitudinal slip ratio for each wheel are, respectively, defined by
Longitudinal tyre force is as follows:
For tyre
In this work, brake torque is the output of the proposed control scheme to generate an appropriate brake force on the wheel. In order to capture the dynamic behavior of the pneumatic braking actuator, a second-order model is taken into account here; consequently, the actual output of brake torque is given as
The lateral dynamics of the tractor semitrailer vehicle are stabilized by a corrective yaw moment generated by active wheel braking. The whole control scheme is a two-layer structure with an upper yaw moment controller and a lower brake force distributor. The upper controller is designed based on fuzzy logic method to determine the corrective yaw moments, respectively, for the tractor and the trailer to stabilize the yaw dynamics. The lower brake force distributor consisting of a set of rules is designed to determinate the target braking wheel and the amount of brake torque corresponding to the corrective yaw moment from the upper controller. The block diagram of the whole control scheme is illustrated in Figure
Block diagram of the control scheme.
The reference responses are the steady-state yaw rate of the tractor and the hitch angle between the tractor and trailer. The steady-state reference responses are derived from a linear tractor-trailer combination model shown in Figure
Simplified linear schematic model of a typical tractor-trailer combination.
Similarly, the reference response of the hitch angle in steady state which can also be obtained from the linear model described in Figure
The upper yaw moment controller is designed based on fuzzy logic control method to determine the corrective yaw moments according to the reference and the actual responses to keep the lateral stability of a tractor semitrailer combination. The upper yaw moment controller, as shown in Figure
Schematic of the upper yaw moment controller based on fuzzy logic.
The design of the fuzzy controller here based on MATLAB fuzzy toolbox includes the processes of fuzzification, fuzzy decision, defuzzification, and output scaling. As the first step of a fuzzy controller design, fuzzification makes the inputs dimensionally compatible with the condition of the knowledge-based rules using linguistic variables. Five different levels are defined for each input and each output membership functions with the linguistic terms “NB,” “NS,” “ZE,” “PS,” and “PB,” respectively, representing “Negative Big,” “Negative Small,” “Zero,” “Positive Small,” and “Positive Big.” Fuzzy decision processes a set of rules based on the prepared rule base given in Tables
Tractor yaw moment controller rule base.
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NB | PB |
NS | PS |
ZE | ZE |
PS | NS |
PB | NB |
Trailer yaw moment controller rule base.
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PB | PB | NB | PS | NB | PB | PB | ZE | NB |
PS | PB | NB | PS | NS | PS | PS | ZE | NS |
ZE | PB | NS | PS | ZE | ZE | NB | NB | PB |
PB | PS | NB | ZE | NB | PB | NS | NB | PB |
PS | PS | NB | ZE | PS | PS | ZE | NB | PS |
ZE | PS | NS | NB | PB | NS | NB | NS | PB |
PB | ZE | NB | NB | PS | ZE | NS | NS | PB |
PS | ZE | NS | NB | ZE | PS | ZE | NS | PS |
NB | PB | PS | NS | PB | NB | NB | ZE | PB |
NS | PB | ZE | NS | PS | NS | NS | ZE | PS |
ZE | PB | NS | NS | ZE | ZE | ZE | ZE | ZE |
Membership function for the input and output variables of the tractor.
Membership function for the input and output variables of the trailer.
Fuzzy input-output curve for the tractor.
Fuzzy input-output curve for the trailer.
The lower part of the proposed control scheme is the distribution of brake force to realize the corrective yaw moment from the upper fuzzy yaw moment controller. It is known that the lateral dynamics of a vehicle can be stabilized by individual wheel braking according to the concept of ESC for passenger cars so that oversteer (OS) and understeer (US) can be corrected, respectively, by braking the outside front wheel and the inside rear wheel [
Decision on the target brake wheel for the tractor.
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Comparison | Target brake |
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“—” denotes no brake action.
Decision on the target brake wheel for the trailer.
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Comparison | Target brake |
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“—” denotes no brake action.
Generally, the brake torque regulator serves to determine the brake torque applied on the target wheel which can be derived directly from corrective yaw moment that is
Realization of corrective yaw moment from the upper controller. (a) Whole realization scheme. (b) Brake torque regulator.
In this section, simulations are conducted to evaluate the proposed control scheme. Considering the two typical planar lateral instabilities jackknife and trailer oscillation and the rollover instability, three critical maneuvers that are external disturbance caused by jackknife, trailer oscillation, and a single lane change maneuver manipulated by the driver are taken into account to assess the proposed control scheme. The physical parameters characterizing the tractor semitrailer vehicle model in simulation are presented in Appendix
Firstly, the simulation for control of jackknife instability is presented. In this case, it is assumed that the vehicle runs straightly without any driver’s steer input at an initial longitudinal velocity of 25 m/s and suddenly suffers from an external lateral disturbance giving rise to an initial yaw rate of 0.1 rad/s on the trailer. In order to facilitate yielding a jackknife instability in simulation, the distance from the trailer centre of gravity (CG) to the hitch point is set as
State response and comparison for the jackknife case.
Global trajectory and comparison for the jackknife case. Arrows in the figure represent the vehicle running direction.
Active brake torque for the jackknife control case.
Longitudinal wheel slip ratio for the jackknife control case.
As shown in Figure
From the response of active brake torque in Figure
The second case of simulation presented in the following aims to evaluate the control performance when stabilizing a trailer oscillation instability. In this scenario, the vehicle is also assumed running straightly at an initial longitudinal velocity of 25 m/s without any manipulation from the driver. On suffering a sudden external disturbance, an initial yaw rate of 0.1 rad/s is added to the trailer and then causes the vehicle to go into trailer oscillation. In simulation, the distance from the trailer CG to the hitch point is set as
State response and comparison for the trailer oscillation case on a dry road.
State response and comparison for the trailer oscillation case on a slippery road.
As shown in Figures
The third simulation case is focused on a single lane change maneuver which is often used to assess the handling and stability performance of a vehicle at high speed. According to the actual steering input for a single lane change maneuver field test, a one-cycle sinusoidal signal given in Figure
Front wheel steer angle for the single lane change maneuver.
Figures
State and comparison for the single lane change maneuver on a dry road.
Longitudinal velocity for the single lane change maneuver on a dry road.
Global trajectory and comparison for the single lane change maneuver on a dry road. Arrows in the figure represent the vehicle running direction.
State and comparison for the single lane change maneuver on a slippery road.
Longitudinal velocity for the single lane change maneuver on a slippery road.
Global trajectory and comparison for the single lane change maneuver on a slippery road. Arrows in the figure represent the vehicle running direction.
In this study, a stability control scheme based on fuzzy logic method is proposed to improve the yaw stability and thereby the roll stability of a tractor semitrailer vehicle in critical situations. The designed control scheme which is a two-layer structure comprises an upper fuzzy yaw moment controller and a lower brake force distributor. The upper fuzzy yaw moment controller further consists of two subcontrollers, respectively, for the tractor and the trailer serving to stabilize the lateral stability of the tractor and the trailer separately by tracking the reference yaw rate of the tractor and the hitch angle between the tractor and the trailer.
Several numerical simulations are conducted based on a nonlinear tractor semitrailer vehicle model to evaluate the controller. Two straight running with external disturbance maneuvers and a lane change maneuver are adopted and considering road adhesion conditions total five simulation scenarios are conducted to assess the control scheme comprehensively from stabilizing the LOC of jackknife and trailer oscillation to the robust of the controller. The results demonstrate that an active control is very important to keep the lateral stability of a tractor semitrailer and the proposed fuzzy logic control scheme is effective to prevent a tractor semitrailer from falling into jackknife and trailer oscillation in a wide range of road adhesion condition.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This project was supported by the National Natural Science Foundation of China (NSFC, 51465023). The authors are greatly appreciated for the financial support.