1INTRODUCTION
One of the most studied active safety system which aims at enhancing the vehicle yaw stability is the Vehicle Dynamics Control system (VDC). Indeed loss of vehicle yaw stability may result either from inappropriate driver’s action or from unexpected yaw disturbances like side wind force, tire pressure loss or μ-split braking due to unilaterally different road such as icy or wet pavement, or obstacle avoidance under emergency, as shown in Figure 1. Safe driving requires the driver to react rapidly and properly. Unfortunately, average drivers may exhibit panic reaction and may not be able to work out adequate steering and/or braking/throttle commands. The main goal of vehicle dynamics control systems is to compensate for the driver’s inadequacy and generate a control yaw moment through either steering or braking control inputs or both. VDC systems have been established in the automotive industry as a safety/performance/comfort feature. They generally provide a control action which prevents the vehicle from understeer or oversteer in a handling maneuver (e.g. lane change, slalom, etc.), particularly on a low friction coefficient surface. VDC system directly controls yaw moment by generating differential longitudinal forces on left and right tires, which in turn effectively affect the vehicle lateral motion [1]-[4].
The proposed National Highway Traffic Safety Administration (NHTSA) rule would require all manufacturers to begin equipping passenger vehicles under 10,000 pounds with VDC starting with the 2009 model year and to have the system available as standard equipment on all vehicles by the 2012 model year or September 2011 when the model year begins. Therefore, vehicle dynamics control system will definitely receive more attention.
This work is supported by Natural Science Foundation of Liaoning Province of China 20061014 To evaluate the effectiveness of the proposed driveline modeling, the dynamics control model based on sliding mode control was generated in Matlab /Simulink environment. A full vehicle model developed in ADAMS/CAR was built so that co-simulation can be performed. In this paper will present and discuss vehicle dynamics control using sliding mode control (EMC), the simulation results show the effectiveness of the VDC system in achieving yaw stability control.
sudden stop
Fig. 1. Obstacle avoidance under emergency
2HOW VDC SYSTEM WORKS
The control architecture for the vehicle dynamics control system is hierarchical and is shown in Figure 2. The controller has the objective of ensuring yaw stability control and assumes that it can command any desired value of yaw torque. To better control vehicle dynamics under all driving conditions, the VDC system needs some additional inputs against ABS. This includes a steering angle sensor to monitor the driver’s steering inputs, a yaw sensor to detect changes in vehicle momentum that might cause the vehicle to spin out, oversteer or understeer, and a lateral acceleration (g-force) sensor to monitor changes in deceleration [5]-[8]. Using these measurements and a control law, it computes the desired value of yaw torque.
Vehicle Dynamics Control Based on Sliding Mode Control Technology
Siqi Zhang1,2, Shuwen Zhou2, Jun Sun1
1. Traffic & Mechanical Engineering School, Shenyang Jianzhu University, Shenyang 110168, China
E-mail: zhangsiqicn@https://www.doczj.com/doc/bf6283646.html,
2. College of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004
E-mail: shwzhou@https://www.doczj.com/doc/bf6283646.html,
Abstract: The paper presents a vehicle dynamics control strategy devoted to prevent vehicles from spinning and drifting out. With vehicle dynamics control system, counter braking are applied at individual wheels as needed to generate an additional yaw moment until steering control and vehicle stability were regained. A sliding mode controller was designed to produce demanded yaw moment according to the error between the measured yaw rate and desired yaw rate. Vehicle dynamics control system utilizes the demanded yaw moment to calculate the brake torque on wheels respectively. With this improved control system, the vehicle can afford nice manoeuvrability and stability.
Key Words: Vehicle Dynamic Control, Sliding Mode Control, Vehicle Yaw Rate, Co-simulation
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The controller ensures that the desired value of yaw torque is indeed obtained from the active torque distribution system.
When the driver steers the vehicle, the steering angle sensor
keeps the VDC control module informed about where the
driver is aiming the vehicle and the rate at which the
steering wheel is being turned (fast or slow). At the same time, the VDC control module looks at the inputs from its wheel speed sensors to determine if there are any differences in the rotational speeds of the right and left front and rear wheels. Turning a corner causes the inside wheel to rotate at a somewhat slower rate than the outside wheel.
If a vehicle begins to oversteer in a turn and the rear end starts to come around (which would cause the car to spin
out), the speed difference between the left and right front wheels increases. If the vehicle understeers (loses front
traction and goes wider in a turn), the speed difference
between the left and right front wheels decreases.
If the stability control software in the VDC control module detects a difference in the normal rotational speeds between the left and right wheels when turning, it immediately reduces engine power and applies counter braking at individual wheels as needed until steering control and
vehicle stability are regained.
Fig 2. System configuration of vehicle dynamics control
1-pressure regulator; 2-master cylinder; 3-wheel speed sensor; 4-yaw sensor;5- lateral accelerometer; 6-ECU; 7-steering angle sensor;8-brake cylinder
3 VEHICLE DYNAMICS ANALYSIS
A vehicle may be regarded as a control system upon which various inputs are imposed. During a turning maneuver, the steer angle induced by the driver can be considered as an input to the system, and the motion variables of the vehicle, such as yaw rate, lateral acceleration, and curvature, may be regarded as outputs.
The desired yaw rate and desired side-slip angle for the vehicle can be obtained from steering angle, vehicle speed and vehicle parameters as follows [1]
δψ
)
(2)
()(2
r f ar af af f ar r x r f x
des l l C C C l C l mV l l V +?+
+= (1) δ
β)
(2)()()(222r f ar af af f ar r x r f r f ar x
f r des l l C C C l C l mV l l l l C mV l l ?+++?= (2) where af C and ar C are the cornerin
g stiffness for eac
h front and rear tire respectively, the lengths f l and r l refer to the longitudinal distance from the c.g. to the front wheels, longitudinal distance from the c.g. to the rear wheels, m is total mass of vehicle, x V is longitudinal velocity of the vehicle and δ is steering wheel angle.
The vehicle would follow in response to a steering input from the driver if the road were dry and had a high tire-road friction coefficient. In this case the high friction coefficient
is able to provide the lateral force required by the vehicle to
negotiate the curved road. If the coefficient of friction were small or if the vehicle speed were too high, then the vehicle would be unable to follow the nominal motion required by the driver, and understeer or oversteer will occur. The function of the yaw control system is to restore the yaw rate of the vehicle as much as possible to the nominal motion expected by the driver (desired yaw rate) [5]-[6].
The objective of vehicle dynamics control is to keep the yaw rate as close to desired yaw rate as possible by applying differential braking.
4 SLIDING MODE CONTROL
Sliding mode control is a type of variable structure control where the dynamics of a nonlinear system are altered via
application of a high-frequency switching control. In this paper, sliding mode control was used to drive and then
constrain the vehicle yaw rate to lie within a neighbourhood
of the desired yaw rate. There are two main advantages of
this approach. Firstly, the dynamic behavior of the system may be tailored by the particular choice of switching
functions. Secondly, the closed-loop response becomes totally insensitive to a particular class of uncertainty. In
addition, the ability to specify performance directly makes
sliding mode control attractive from the design perspective. This design approach consists of two components. The first, involves the design of a switching function so that the
sliding motion satisfies design specifications. The second is conserved with the selection of a control law, which will
make the switching function attractive to the system state. 24362009Chinese Control and Decision Conference (CCDC 2009)
In this paper, the proportional switch law was utilized to design the controller u [9].
)sgn()||(s e
e u βα+= e
ce s += (3) where s is the switch function, e is the error between
measured yaw rate mes ψ and desired yaw rate des ψ , α and β are constant greater than zero.
Fig 3. The scheme of sliding mode control
Figure 3 shows the scheme of sliding mode control. The
reference model calculates the desired yaw rate des ψ
using formula (1) with given vehicle speed x V and steering
wheel angle δ. The sliding mode controller computes the demanded yaw torque using the error between desired yaw rate and measured yaw rate. The VDC system works out the braking force on wheels respectively.
5 VEHICLE DYNAMICS SIMULATION We employ the linear bicycle model to generate the
reference vehicle behavior, such as yaw rate of neutral
steer. The difference of yaw rate between the reference
model and the multi-body model is considered as control
signal to the vehicle multi-body model. In order to verify the vehicle dynamics control strategy, we performed a dynamic analysis using ADAMS/CAR and Simulink. The co-simulation system is shown in Figure 4. There are four input signals to adams sub (vehicle, multi-body model), left front brake, left rear brake, right front brake and right rear brake. To prevent any wheel lock under braking, the slip ratio of four wheels is calculated using vehicle speed and
wheels speed. If any wheel slip ratio reach the threshold value preset, the VDC system will active corresponding trigger to release the braking force. The SMC Controller is shown in Figure 5. The gains, i.e. the α and β in formula
(3) need to be adjusted many times until a satisfied result.
Fig 4. Vehicle dynamics control co-simulation with ADAMS/Car and Simulink
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The full vehicle was assembled in ADAMS/CAR, as shown in Figure 6. The Vehicle multi-body model consists of power train, suspension, braking, chassis and steering. The input signals to the vehicle include steering angle and four wheels brake torque. The output signals are four wheels speed, vehicle longitudinal speed, yaw rate steering rack travel. Comparing to the conventional linear bicycle model, the multi-body model in this paper can consider the effect of suspension, steering or chassis on yaw rate. The Vehicle model parameters are shown in Table 1.
Fig 5. Sliding mode controller
Fig 6. Vehicle multi-body model
Table1. Vehicle model parameters
m 1715 kg z J 2700 kgm 2 f l 1.07 m r l 1.47 m af C
95117 Nm/rad
ar C
97 556 Nm/rad
The full vehicle model includes both lateral and
longitudinal dynamics as well as the non-linear ties in the system and a suspension model. The test is performed in which the vehicle is traveling at 140 km/h. Closed-loop manoeuvres (lane change, the steering wheel angle is shown in Figure 7) are executed using the driver. Simulations of violent high-speed double-lane-change manoeuvres enabled the driver’s return rate and lateral displacement feedback gains to be benchmarked for these conditions. Vehicle steering and double lane change
manoeuvres are considered using a full vehicle model. To investigate the transient handling characteristics of the proposed geometry control, double lane change manoeuvres are performed. To follow the desired trajectory, the driver must appropriately change the steering angle every time.
6 SIMULATION RESULTS
A simulation study is conducted to show the effectiveness of the proposed controller before experiments are carried out on a real vehicle. Simulation is done using a full vehicle model and simulation software based on ADAMS/CAR and Simulink. To clarify the effects of the proposed controller, vehicle dynamics both with and without the controller are shown.
S t e e r i n g w h e e l a n g l e (d e g )
closed-loop manoeuvre at 10 s. A target steering diagram (see Figure 7) can be introduced to take into account the task performance. Figures 8, Figure 9 and Figure 10 show the simulation results for double change lane manoeuvre at a velocity of 140, with a nominal friction coefficient of 0.85, a value deemed to be generally representative of smooth concrete.
Y a w r a t e (d e g /s )
Time (s)
Fig 8. Comparison between yaw rate with and without VDC
Figure 8 gives the time response of yaw rate for a controlled and uncontrolled vehicle model at a velocity of 140 km/h. Since the proposed strategy has the smallest values for double lane change manoeuvre, Figures 9 shows the best performance for side-slip angle regulation. In Figure 10, the comparison between trajectory with and without VDC is shown.
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V e h i c l e s l i p a n g l e (d e g )
Time (s)
Fig 9. Comparison between slip angle with and without VDC
Y c o o r d i n a t e (m )
Fig 10. Comparison between trajectory with and without VDC
These figures show that the response of the controlled system is better than that of the uncontrolled system. Both
yaw rate and sideslip angle almost exactly track the
reference values. The target of vehicle dynamics control system is to eliminate or reduce the difference. And Figure
8 shows that without VDC the vehicle tends to unstable as
the steer angle increase. So under emergency, the driver is definite to lost control on the vehicle without VDC. The
control system is configured to bring the vehicle yaw rate
into correspondence with a desired yaw rate value.
7 CONCLUSIONS
In this work a Vehicle Dynamics Control system for tracking desired vehicle behavior is developed. The results show that the proposed system clearly improves the vehicle stability for active safety.
In this paper a controller based sliding mode control is proposed to improve vehicle handling and stability. This controller generates the brake torque to control the yaw rate and the sideslip angle. In this case, the vehicle motion without the controller is unstable. However, the controller makes stable the vehicle motion. The amount of lateral motion is reduced and the driver is able to maintain the steering wheel in a nearly neutral position. Simulations results show that the controlled vehicle has a better performance compared with the uncontrolled vehicle because the system can be traced to the desired response to a satisfactory degree.
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