An optimal reconfiguration control scheme based on control allocation (CA) is proposed to stabilize the yaw dynamics of the tractor-semitrailer vehicle. The proposed control scheme is a two-level structure consisting of an upper level of sliding mode yaw moment controller (SMYC) and a lower optimal brake force distributor (BFD). The upper SMYC is designed to follow the tractor yaw rate and the combination of the hitch angle and trailer slip angle and outputs the corrective yaw moment, respectively, for the tractor and the trailer. The optimal brake force allocation and reconfigurable control problem is transformed to a problem of error minimization and control minimization combination formulated by constrained weighted least squares (CWLS) optimization and further solved with active set (AS) algorithm. Simulation results reveal that the CA technique-based optimal reconfigurable control is rather effective for the tractor-semitrailer vehicle to enhance the yaw stability performance and the reliability in case of actuator failure thanks to the multiple-axle structure enriching the alternatives of possible actuator combinations in CA optimization.
Tractor-semitrailer vehicle which is the combination of a tractor and a semitrailer through the hitch point presents particular handling and stability properties compared with the passenger cars. In critical driving situations, a tractor-trailer combination may experience different forms of lateral instability such as jackknife, trailer swing, and trailer oscillation [
In fact, for a typical ESC system, controlled states are typically lateral velocity and yaw motion, while the actuation could potentially include individual wheel driving/braking, comprising a redundantly actuated system especially for the commercial heavy vehicles which are generally with multiple axles and wheels [
The rest of the paper is organized as follows: in Section
A typical five-axle tractor-semitrailer vehicle is considered in this study with the nonlinear schematic model illustrated by Figure
Nonlinear tractor-semitrailer vehicle schematic model. (a)
Body planar motions for the tractor and the trailer are, respectively, described. In the modeling, the tandem axle is simplified to one single axle. For the tractor, the longitudinal, lateral, yaw, and roll dynamics are, respectively, given by (
The equations of longitudinal, lateral, yaw, and roll motions of the trailer can, respectively, be expressed by (
The couplings exist in the longitudinal, lateral, yaw, and roll motions between the tractor and the trailer which can, respectively, be described by (
Suspension model is built to predict the lateral load transfer when cornering which affects the tyre normal force. In heavy vehicles, leaf spring is usually used and the suspension force which is nonlinear with the deformation of the leaf spring can be calculated as [
Nonlinear Dugoff model [
For the tyre
The reconfigurable control system as a two-level structure consists of two primary parts which are the upper level SMYC and the lower level BFD. In addition, state observer used to estimate vehicle states such as slip angle, hitch angle, and hitch angular rate and the brake force limit estimator supplying the upper bound of brake forces to the CWLS optimization as the supplementary modules are also included. The overall structure of the configurable control system is presented in Figure
Overall structure of the reconfigurable control system.
Model-following technique which is often used in vehicle stability control system, that is, the actual vehicle responses follow the reference or the desired responses produced by an on board model [
4DOF single-track tractor-trailer schematic model.
The reference response of the tractor yaw rate in steady-state with the front wheel steer input
In vehicle stability control system design based on model following method, the reference slip angle may be derived from the linear single-track model or directly set zero by simplicity which is also viable and can even obtain satisfying control performance [
The yaw dynamics of the tractor and the trailer are individually stabilized by a corrective yaw moment to, respectively, follow the reference responses of the tractor yaw rate and the combination of the hitch angular rate and trailer slip angle. Sliding mode control method which is robust against parametric uncertainties is employed to complete the control objective. Define the system states
Combining the 4-DOF vehicle model (
In real implementation, some vehicle states such as the tractor/trailer slip angle and hitch angle/angular rate. unsuitable to be measured directly by sensors for the cost considerations can be obtained by an observer since numerous state estimation algorithms have been proposed in the literature [
After the upper level SMYC is designed, the following step is to develop the lower level BFD to map the corrective yaw moment
With small steer angle and hitch angle assumptions, (
In order to solve the CA problem (
Influence of the tyre normal force to the brake force limit.
For the CA problem formulated by (
Since
Single lane change maneuver is carried out in this section to evaluate the proposed reconfigurable control scheme based on CA technique by numerical simulations on the 14-DOF nonlinear vehicle model constructed in Section
Vehicle parameters.
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8444 kg |
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1.18 m |
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25000 kg |
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0.75 m |
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5820 kg |
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0.60 m |
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21640 kg |
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0.80 m |
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10347 kg · m2 |
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1.93 m |
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58270 kg · m2 |
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1.84 m |
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65734.6 kg · m2 |
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1.40 m |
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560000 kg · m2 |
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2.03 m |
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2.12 m |
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0.82 m |
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4.81 m |
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1.27 m |
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2.60 m |
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0.52 m |
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11.82 m |
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40.8 kg · m2 |
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1.84 m |
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130 kg · m2 |
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0.40 m |
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9.81 m/s2 |
Front wheel steer angle.
The normal case and the failure case are realized through setting the actuator effectiveness matrix equation (
Yaw response comparison.
Side slip response comparison.
Vehicle speed response comparison.
As given by the figures, in the normal control case with the proposed reconfigurable control scheme, the vehicle represents satisfying response performance with respect to the steer input except for a bit tractor side slip. Further, in the failure control case where the trailer brake actuators are completely fails and the tractor actuators are heavy partly fails, owing to the reconfigurable coordination of the remaining functioning actuators/efforts, the vehicle can still keep stable and can generally follow the steer input except for a bit decrement of response performance compared to the normal control case. However, in the uncontrolled case, the vehicle loses control rapidly. Due to the brake actuator damage, the brake force/torque for the failure case decreases considerably and the vehicle speed shall be relatively lightly affected compared to the normal case as illustrated by Figure
Figures
Brake force limit estimation in the normal control case.
Brake force limit estimation in the failure control case.
Brake torque effort for the normal control case.
Brake torque effort for the failure control case.
Similarly, the difference in wheel longitudinal slip ratio can also be found as shown in Figures
Longitudinal slip ratio in the normal control case.
Longitudinal slip ratio in the failure control case.
Corrective yaw moment in the normal control case.
Brake force limit estimation in the failure control case.
The above simulations and analysis reveal that reconfigurable control method based on CA technique is feasible to be used in the stability control system design of tractor-semitrailer double-body vehicle. Especially, the reconfigurable control system can still keep the vehicle stable in the situation of brake actuator being damaged greatly by reconfiguring the remaining functioning actuators/efforts and thereby the reliability and safety are improved compared with the conventional single wheel brake method.
In order to evaluate the proposed reconfigurable control scheme, a 14-DOF nonlinear model is constructed for a typical five-axle tractor-semitrailer vehicle which can generally reflect the actual vehicle dynamics especially in critical driving situations. A two-level structure reconfigurable control scheme is proposed with the upper level of SMYC and the lower level of yaw moment allocator based on CWLS optimization algorithm. As a particular feature of this control scheme, the brake force limit as one of the required conditions for the CWLS optimization generally varying with the handling maneuver is estimated in real time to improve the CA performance. The reconfigurable control issue based on CA technique is transformed to a combination of error minimization and control minimization problem formulated by CWLS optimization and solved with AS algorithm. Simulations conducted on the 14-DOF nonlinear model reveal that the CA technique based reconfigurable control is rather significant for the tractor-semitrailer vehicle since its multiple-axle structure can enrich the alternatives of possible actuator combinations in CA optimization.
This project was supported by the National Natural Science Foundation of China (no. 51005109). The authors are greatly thankful for the financial support.