Vehicle velocity and roll angle are important information for active safety control systems of four-wheel independent drive electric vehicle. In order to obtain robustness estimation of vehicle velocity and roll angle, a novel method is proposed based on vehicle dynamics and the measurement information provided by the sensors equipped in modern cars. The method is robust with respect to different road and friction conditions. Firstly, the dynamic characteristics of four-wheel independent drive electric vehicle are analyzed, and a four-degree-of-freedom nonlinear dynamic model of vehicle and a tire longitudinal dynamic equation are established. The relationship between the longitudinal and lateral friction forces is derived based on Dugoff tire model. The unknown input reconstruction technique of sliding mode observer is used to achieve longitudinal tire friction force estimation. A simple observer is designed for the estimation of the roll angle of the vehicle. And then using the relationship, the estimated longitudinal friction forces and roll angle, a sliding mode observer for vehicle velocity estimation is provided, which does not need to know the tire-road friction coefficient and road angles. Finally, the proposed method is evaluated experimentally under a variety of maneuvers and road conditions.
Vehicle active safety control systems such as yaw stability control system and roll stability control system can significantly reduce the number of road accidents [
In [
In this paper, using the measurements from the existing sensors equipped in the four-wheel independent drive electric vehicle, including the wheel angular velocities, longitudinal and lateral accelerations, yaw rate, roll rate, wheel steering angles, and wheel torques, a method for vehicle velocity and roll angle estimation with road and friction adaptation is proposed based on the nonlinear vehicle dynamics and Dugoff tire model. The proposed method is evaluated experimentally under a variety of maneuvers and road conditions.
As shown in Figures
Vehicle maneuvering model.
Force induced by road grade angle and vehicle roll model.
Force induced by road grade angle
Vehicle roll model
Due to the presence of measurement errors such as biases and noise from the sensors, some feedback should be used to make the estimated results converge, and then the vehicle dynamics is introduced into the vehicle model (
The nonlinearity of vehicle tires will become a critical factor during emergency maneuvers in which the linear tire model is not sufficiently accurate anymore. To account for the nonlinearities of the tire friction force, Dugoff tire model [
For four-wheel independent drive electric vehicle, the torque balance of the wheel
In the wheel longitudinal dynamic equation (
Obviously, the unknown input
The sliding mode observer, through sliding surface design and equivalent control concept, has been proven to be an effective approach for handling the systems with disturbances and modeling uncertainties. Based on the unknown input estimation technique of the sliding mode observer, this paper proposed the following observer for longitudinal friction force estimation:
If we define the estimation error
Once the state of the observer (
Actually, the longitudinal and lateral friction forces can be calculated directly using the Dugoff tire model. But the calculation of the longitudinal and lateral friction forces needs to know the tire-road friction coefficient, which usually cannot be measured based on the sensors equipped in modern cars. The tire-road friction coefficient not only depends on the road conditions (such as asphalt, ice and snow, etc.), but also is affected by tire materials, ambient temperature, and other factors. The relationship between them is very difficult to be described by mathematical model. So the estimation of the tire-road friction coefficient is not an easy task [
According to the Dugoff tire model (
According to the vehicle roll model shown in Figure
Since the lateral acceleration and roll rate usually are measurable in modern cars, the observer for roll angle estimation in this paper is proposed as follows:
According to the vehicle kinematic model (
In modern cars, the longitudinal acceleration, lateral acceleration, and yaw rate usually are measurable. Taking into account the model mismatch of the nonlinear vehicle dynamics and the presence of measurement errors such as biases and noise from the existing sensors equipped in vehicle, the difference between the calculation value of longitudinal and lateral accelerations based on nonlinear vehicle dynamic model and the measurement value provided by the sensor as a feedback term is introduced to improve the estimation accuracy of the vehicle velocity. And the estimation method of vehicle velocity based on the sliding mode observer is proposed in this paper as follows:
The structure of the roll angle and vehicle velocity observers proposed in this paper for four-wheel independent drive electric vehicle is illustrated in Figure
The structure of the proposed roll angle and vehicle velocity observers.
To avoid excessive chattering, the
In the following, the selection of the feedback gains and sliding mode gains to guarantee the stability of the observer (
Define the estimation errors
Define the Lyapunov function
From the above discussion, it is clear that if the road is flat, the road grade angle and bank angle are zero, and
As shown in Figure
The structure of the simulation system.
To represent the most likely cause of error in true data acquisition, zero-mean-value random measure noises with Gaussian distribution are introduced into the vehicle acceleration, yaw rate, and roll rate measurements during the course of simulation. The performance of the observers is evaluated under a sudden steering maneuver on a high friction surface (
In the sudden steering maneuver, the longitudinal vehicle velocity strongly varies. As shown in Figure
The steering wheel angle and wheel torque in the sudden steering maneuver.
The road grade angle and bank angle in the sudden steering maneuver.
The measured and estimated vehicle roll angle and yaw rate in the sudden steering maneuver.
The measured and estimated vehicle velocities in the sudden steering maneuver.
The second test is a slalom maneuver on a low friction surface. The steering wheel angle and wheel torque measurements are shown in Figure
The steering wheel angle and wheel torque in the slalom maneuver.
The road grade angle and bank angle in the slalom maneuver.
The measured and estimated vehicle roll angle and yaw rate in the slalom maneuver.
The measured and estimated vehicle velocities in the slalom maneuver.
As shown in Figures
In this paper, a roll angle observer and a vehicle velocity observer have been proposed for four-wheel independent drive electric vehicle without needing to measure or estimate the road angles and surface conditions, using the available measurements in modern cars including the wheel angular velocities, longitudinal and lateral accelerations, yaw rate, roll rate, wheel steering angles, and wheel torques. The proposed observers have been validated on a high-precision vehicle dynamics simulation system based on veDYNA, and the simulation results show that good performance of the proposed observers has been achieved. Using the estimated vehicle velocities, the vehicle body sideslip angle can be calculated directly, which is also useful for the automotive chassis control systems.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (no. 61104060) and the China Postdoctoral Science Foundation (no. 2014M551244).