Wind Disturbance Rejection In Active Front Wheel Steering Engineering Essay

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Abstract- One function of Active Front Wheel Steering (AFS) which is wind disturbance rejection is discussed in this paper. A full vehicle model is developed to simulate the AFS system using ideal controller. The control structure involve with two types of feedback which are yaw rate and side slip angle. A PI controller is used to optimise feedback from the side slip angle while a constant gain is used to optimise feedback from yaw rate. Three cases including varying of speed, force and force location has been setup to test the robustness of the controller. Results show that the controller is robustness since it can maintain the vehicle according to original direction.

Keywords: Active steering, PI controller, side slip angle, yaw rate.

INTRODUCTION

Current development in driver assist system has create various type of system that can electronically control vehicle subsystem such as Antilock Braking System (ABS) for braking system and Electronic Power Steering (EPS) for steering system. This two driver assist systems has widely used in most of current vehicle and already been proven the effectiveness of the system to enhance the safety and comfortable of the manoeuvring vehicle. Beside the EPS, another type of potential driver assist system for steering system is Active Front Wheel Steering (AFS) system. As been defined by [1], AFS is an electronically controlled superposition of an angle to the hand steering wheel angle that is prescribed by the driver.

A lot of researchers have already pay great attention to develop the control structure for the system. But until now, very few of car manufacturer interested to make the system as a must-have system in their vehicle. Function of AFS is basically to remove or at least to minimise unwanted yaw motion occurred during the manoeuvre since this yaw motion will possibly cause to change in direction of travel of the vehicle. The major distraction for the driver is when the car starts to skid and can cause to accident. Source of problem that will cause to unwanted yaw motion are for example side wind, slippery road and emergency braking. Other than this, AFS system also can provide variable steering ratio that can change steering ratio for high speed and low speed manoeuvre and able to reduce steering effort by driver [2].

In this paper, only one function of AFS has been study which is side wind disturbance rejection. To objective of the control system is to eliminate the effect of side wind force or in other word to make the vehicle maintain the direction of travel even the side wind force act at the side of the vehicle. According to [3], the lateral motion of the vehicle is described by yaw rate and sideslip angle. Furthermore, feedback from side slip angle can recover the path deviation occurring from the yaw rate control. Vehicle model is used to test the control structure which is based on the feedback from the yaw rate and side slip angle of the vehicle.

Vehicle Model

To simulate the behaviour of PI controller on the system, one complete full vehicle model has been build using Matlab Simulink software. The model based on four wheeled vehicle dynamics that has nine degree of freedom which is one degree of freedom for each tyre and another five degree of freedoms relate to the body of the vehicle such as lateral acceleration, longitudinal acceleration, yaw moment, pitch moment and roll moment. The vehicle axis system is shown in Figure 1. Two types of vehicle model is build which is for vehicle without AFS and with AFS. The differences between those two models are the introducing of side wind force, Fw at the right side of vehicle and PI controller to do steering correction.

Figure 1: Vehicle axis system

The equation of motion gathered from [4] has been used to build the vehicle model. First is the equation for longitudinal and lateral acceleration. The equation is derived through handling model as shown in Figure 2.

Figure 2: Handling model

(1)

(2)

To find side slip angle, β, lateral and longitudinal acceleration can be integrated to get lateral and longitudinal velocity that can be used in the equation 3.

(3)

The equation for yaw motion can be derived by taking moment at the vehicle centre of gravity, G.

(4)

Roll motion, , and pitch motion, , is derived by considering only the sprung mass since unsprung mass did not effect by roll and pitch motion.

(5)

(6)

Longitudinal force, , act at each tyre can be get through tyre model and for this vehicle model, Calspan tyre model has been used. From literature review, this tyre model can provide useful force for use in full vehicle model since it containing interactions between longitudinal and lateral forces from small level through saturation. In order to calculate the lateral and longitudinal force, the tyre model needs vertical force, , tyre slip angle, , and tyre slip rates, , for each tyre which can be calculated through the equation below.

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

The accuracy of the vehicle model is validated with CarSim software through double lane change test at speed 100km/h. The side wind force acting at the right side of the vehicle is removed during the validation process. The model is consider validated when the graph for lateral acceleration, yaw angle, roll angle, pitch angle, x and y position follow the graph from CarSim software.

Control Structure

The vehicle tends to steer to the direction of side wind force when the force acts on a moving vehicle. So, the AFS controller suppose to minimise the reaction cause by the disturbance in order to prevent from the vehicle enter into critical condition where driver totally loss control on the vehicle. The controller will provide steering correction to counteract the reaction cause by the disturbance. First, feedback from the yaw rate is used to reduce the value of lateral acceleration and side slip angle. Another output from vehicle model used is side slip angle that can get the position of vehicle back to original direction. Both of the outputs are compared with the reference value which is zero. The reason reference at zero is vehicle suppose to maintain zero in yaw rate and side slip angle to neglect the effect from the disturbance.

Figure 3: AFS control structure

First, feedback from the yaw rate and side slip angle has to be tuned through gain scheduling process to get the best result. The objective of the control structure is to get the minimum value of Y-position. Since there is no input from the driver, steering input will be zero. So, y-position of the vehicle should be zero even after the vehicle is effect by side wind force. In order to maintain the direction of vehicle, PI controller has been introduced into the side slip angle feedback while for yaw rate; an optimum gain constant is added. Both of this feedback will be sum up together as a steering correction that will be added to the steering input from driver.

Simulation parameter:

Side wind force, Fw = 750N & 2000 N for 0.2s

Simulation time, t = 25s

Driver input, δ = 0 radian

Mass of vehicle = 1700kg

Vehicle speed, v = 60km/h and 100km/h

Result and Discussion

Simulation has been done by giving two magnitude of side wind force at the right side of the vehicle in front of body centre of gravity. Four types of output has been taken to show the performance of AFS controller which are lateral acceleration, yaw rate, y-position and side slip angle. Those graphs show the difference between the vehicle with AFS and without AFS. Three cases has been setup to test the robustness of the proposed controller.

Case 1: Varying position of side wind force

For this case, force is given at two position which are at front and behind of body centre of gravity. The parameter for force and speed is constant to 2000 N and 100 km/h respectively. Result shows in the figure below.

Figure 3: Response for v=100km/h and F=2000N at front of body centre of gravity

The result shows that the controller able to reduce the lateral acceleration when the side wind force acting on the vehicle. With AFS, the lateral acceleration is reduced to 0.04479 m/s2 from 0.1199 that has been plotted for vehicle without AFS. The percentage of the decrement is 62.6%. The behaviour of vehicle when the force acted can easily observe through the y-position curve. Without AFS, the 2000N side wind force can make the vehicle yaw from the original direction by 0.02m at time equal to 4.3 second which means 1 second after the side force is stopped. With AFS, the changing in direction of travel has been reduced to 0.01 at 4.3 second. Furthermore, the AFS control structure able to get the vehicle back to original direction where in 4 second after the disturbance, the y-position of the vehicle is 0.004m which means only 4mm difference from the original direction.

Figure 4: Response for v=100km/h and F=2000N at behind of body centre of gravity

Figure 4 shows the response of vehicle when the disturbance occurs behind of the body centre of gravity. The behaviour is slightly difference because the disturbance has make the rear of the vehicle yawing compare to the situation where force act at front of body centre of gravity, the front of the vehicle yawing. This situation has make the side slip angle is higher to the vehicle without AFS because the controller need extra magnitude of side slip angle to encounter the effect of rear yawing motion. Even the side slip angle is greater; the important result is the direction of the vehicle can be maintained near to zero. After 4 second of the disturbance, the y position is 0.01m.

Case 2: Varying speed of vehicle

For this case, the speed of vehicle is set at 60km/h and 100km/h to test the performance of controller at low and high speed. The force is fixed to 2000N and the position of force at the front of body centre of gravity.

Figure 5: Response for F=2000N at front of body centre of gravity and v=60km/h

For this case, Figure 3 and Figure 5 can be compared to observe the performance of the controller. Summary of the differences for this case is shown in the Table 1.

Table 1: Effect of variable speed

Performance Criteria

Speed (km/h)

60

100

Maximum lateral acceleration (m/s2)

with AFS

without AFS

0.0362

0.1199

0.0448

0.1199

Percentage decrement of lateral acceleration with AFS

69.8 %

62.6 %

Y-position at end of disturbance , t=4.2 (mm)

with AFS

without AFS

4.876

15.280

7.442

15.480

Percentage decrement of y position with AFS

68.1 %

51.9 %

From the table, for varying speed case, the controller performed correctly and show better performance at least more than 50% to vehicle without AFS.

Case 3: Varying magnitude of force

Two different magnitudes of force has been test on the controller which are 750 N and 2000 N to test the performance of the proposed controller in small and big amount of force. The simulation has been run at constant speed which is 100km/h and the position of force at the front of body centre of gravity.

Figure 6: Response for v=100km/h and F=750N at front of body centre of gravity

For this case, Figure 6 and Figure 3 show two different magnitude of disturbance. Both of the figures can be compared to show the performance of the controller and the summary of the significant result is shown in the Table 2.

Table 2: Effect of variable force

Performance Criteria

Force (N)

750

2000

Maximum lateral acceleration (m/s2)

with AFS

without AFS

0.0168

0.0362

0.0448

0.1199

Percentage decrement of lateral acceleration with AFS

53.6 %

62.6 %

Y-position at end of disturbance t=4.2 (mm)

with AFS

without AFS

2.752

5.775

7.408

15.370

Percentage decrement of y position with AFS

52.3 %

51.8 %

Conclusion

The simulation has been done to test the performance of the proposed controller based on those three cases. Case 1 for varying position of side wind force, case 2 for varying speed of vehicle and the case 3 for varying magnitude of side wind force. From the three cases, the controller shows a robustness against multiple condition since it can maintain the direction of vehicle according to driver input compare to vehicle without AFS.

Future Work

For further research, the proposed controller can be model with an actuator model before implemented on actual vehicle. From the actuator model, ratio of angle from electric motor and steering shaft can be determined through simulation using Matlab Simulink software. The simulation will provide correct steering correction that can be implemented on actual vehicle. Then, another test similarly to what have been presented in this paper can be done to test the whole system of AFS.

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