The purpose of this dissertation is to prevent the skidding of the car in case of disturbance by using decoupling controller

1. 13016002 SEMIH UZUN
13016012 ÜZEYİR VARLİ
REPUBLIC OF TURKEY
YILDIZ TECHNICAL UNIVERSITY
FACULTY OF ELECTRICAL - ELECTRONIC
DEPARTMENT OF CONTROL AND AUTOMATION ENGINEERING
ACTIVE CAR STEERING CONTROL
Advisor: Asst. Prof. Dr. İlker ÜSTOĞLU
uzeyirvarli@gmail.com
uzun.semih@outlook.com

2. Presentation
Plan
1. Indroduction
2.The Two Steering Tasks
3.Vehicle Model
4. Simulink Model of the Nonlinear Single Track Model
5. The Linearized Single-Track Model
6. Steering Actual Model
7. Unilateral Decoupling Controller
8.Simulation Results
9.Conclusion

3. 1.Introduction
 The purpose of this dissertation is that skidding of car is prevented by using decoupling
controller.
 There are a lot of dangerous situations on the roads also driver may encountered skidding.
Dangerous situations may occur because of driver can not interfere at the time.

4. 2.The Two Steering Tasks
Two steering tasks are distinguished, one to be controlled by the driver, the other one under automatic
control.
Figure 1. The Path-following task Figure 2. The disturbance attenuation task
 The task of driver is that path following
 The driver can not compensate disturbance torque which may occur from some reasons. For
example these reasons are braking from on ice, from crosswind etc…
 An automatic control system can do this disturbance compensation faster and more precisely than a
driver.
 Thus automatic control interfere when any disturbance occurs.

5. 3.Vehicle Models
 There are several types of models that can be used, the simplest is the single track model also is called
Bicycle model.
 That is conformed around that the car only has one front and one rear wheel. In its simplest form the
Bicycle model has only two degrees of freedom, lateral velocity and yaw rate.
Figure 3.1 Single track model of car
3.1 Single Track Model

6. 3.2 Nonlinear Single Track Model
 The angle 𝛽 between the vehicle center line and the velocity vector 𝑣 at the CG is called the vehicle
sideslip angle.
 Vehicle dynamics are the lateral forces at the front and rear axles:
Lateral motion
Yaw motion
𝑚𝑣 𝛽 + 𝜓 𝑐𝑜𝑠𝛽 + 𝑚 𝑣𝑠𝑖𝑛𝛽 = FyF + FyR
𝐽 𝜓 = FyF 𝑙 𝐹 − FyR 𝑙 𝑅 + 𝑀𝑧𝐷
(3.1)
FyR = FytR 𝑐𝑜𝑠δR
(3.2)
(3.3)
FyF = FytF 𝑐𝑜𝑠δF (3.4)

7. The sideslip angles 𝛼 𝑅 and 𝛼 𝐹 at the
front and rear tires are obtained by a
kinematic model from the steering
angles 𝛿 𝐹 and 𝛿 𝑅 from the state
variables 𝛽, r and v.
The local velocity vectors in front (𝑣𝐹)
and rear (𝑣𝑅) and at the CG (𝑣⃗ ) are
oriented perpendicular to the
connecting line to the momentary pole.
The front and rear chassis sideslip
angles are 𝛽 𝐹 and 𝛽 𝑅.
Figure 3.2. Kinematics variables
𝑣 𝐹 𝑠𝑖𝑛𝛽 𝐹 = 𝑣𝑠𝑖𝑛𝛽 + 𝑙 𝐹 𝑟
𝑣 𝑅 𝑠𝑖𝑛𝛽 𝑅 = 𝑣𝑠𝑖𝑛𝛽 − 𝑙 𝑅 𝑟
𝑡𝑎𝑛𝛽 𝐹 =
𝑣𝑠𝑖𝑛𝛽 + 𝑙 𝐹 𝑟
𝑣𝑐𝑜𝑠𝛽
= 𝑡𝑎𝑛𝛽 +
𝑙 𝐹 𝑟
𝑣𝑐𝑜𝑠𝛽
𝑡𝑎𝑛𝛽 𝑅 =
𝑣𝑠𝑖𝑛𝛽 − 𝑙 𝑅 𝑟
𝑣𝑐𝑜𝑠𝛽
= 𝑡𝑎𝑛𝛽 −
𝑙 𝑅 𝑟
𝑣𝑐𝑜𝑠𝛽
𝛼 𝐹 = 𝛿 𝐹 − 𝛽 𝐹
𝛼 𝑅 = 𝛿 𝑅 − 𝛽 𝑅
(3.5)
(3.6 )

8. Figure: 3.4 Block diagram of car steering

9. 4 Simulink Model of the Nonlinear Single Track
Model
The non-linear single track model shown in Figure 4.1 consists of the
following subsystems:
 Tire Model
 Tire Chasis Projection
 Vehicle Dynamics
 Kinematics-Geometry

10. Figure 4.1 Simulink Model of the Non-Linear Single Track Model

11. 4.1 Tire- Chassis Projection


Figure 4.1.1 Tire-Chassis Projection Block
 Ff: Front lateral force in the tire coordinate axis
Fr: Rear lateral force in the tire coordinate
axis
delta_f: front tire steering angle
delta_r: rear tire steering angle
And the output ports of the block are:
Fx: the sum of forces in the x-axis.
Fy: the sum of forces in the y-axis
Mz: the sum of moments around the z axis.

12. 4.2 Vehicle Dynamics Block
Figure 4.2.1Simulink implementation of the vehicle dynamics
This block takes Fx, Fy and Mz as input arguments and
calculates
 V=vehicle(m/s)
 psi_dot: (߰) yaw rate (rad/s)
 beta (𝛽) : vehicle side slip angle at its output.
𝑚𝑣 𝛽 + 𝑟
𝑚 𝑣
𝐽 𝑟
=
−𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛽 0
𝑐𝑜𝑠𝛽 𝑠𝑖𝑛𝛽 0
0 0 1
Fx
Fy
𝑀𝑧 + 𝑀𝑧𝐷

13. 4.3 Kinematics / Geometry Block
 Simulink model of
 𝛽 𝑅 and 𝛽 𝐹
Figure 4.3. Kinematics eqations of the vehicle
𝑡𝑎𝑛𝛽 𝐹 =
𝑣𝑠𝑖𝑛𝛽 + 𝑙 𝐹 𝑟
𝑣𝑐𝑜𝑠𝛽
𝑡𝑎𝑛𝛽 𝑅 =
𝑣𝑠𝑖𝑛𝛽 − 𝑙 𝑅 𝑟
𝑣𝑐𝑜𝑠𝛽

14. 5 The Linearized Single-Track Model
For small values of β the nonlinear expressions explained in the previous section can be reduced by using:
𝑐𝑜𝑠𝛽∼1 𝑎𝑛𝑑 𝑠𝑖𝑛𝛽 ∼𝛽
and for small steering angles the tires can be modelled by using linear equations.

15. 5.1 Linear Tire Model
 For small angles the tire forces can be
expressed by using the following linear
equations:
 𝐹𝑦𝐹 = 𝐹𝑦𝐹 𝛼 𝑓 = 𝜇𝑐𝑓 𝛼 𝑓
 𝐹𝑦𝑅 = 𝐹𝑦𝑅(𝛼 𝑟) = 𝜇𝑐 𝑟 𝛼 𝑟
 Which was modeled in Simulink as shown in
Figure 5.1.
Figure 5.1 Simulink Linear Tire Model
(5.1)
(5.2)

16. 5.2 Tire Chasis Model
Disturbance torque will occur because of
lateral force. .
 𝐹𝑦 = 𝐹𝑦𝐹 + 𝐹𝑦𝑅
 Mz=𝐹𝑦𝐹 𝑙 𝑓 + 𝐹𝑦𝑅 𝑙 𝑟
Figure 5.2 Linearized Tire/Chassis Projection Block
(5.4)
(5.3))

17. 5.3Linearized Vehicle Dynamics
Figure 5.3 Simulink Implemetation of the Linearized Vehicle Dynamics Block
𝛽 =
𝐹𝑦
𝑚𝑣
− 𝑟
𝑟 =
𝑀𝑧
𝐽
(5.5)
(5.6)

18. 5.4 Kinematics Model
The Kinematics block is:
𝛽𝑓 = 𝑟
𝑙 𝑓
𝑣
+ 𝛽
and
𝛽𝑟 = 𝛽 − 𝑟
𝑙 𝑟
𝑣
Simulink implementation of the linearized
kinematics/geometry equations is shown
sin(β) ~ β, cos (β)~1 and tan(β)~ β resulting in below. Figure 5.4 Simulink Implementation of the
Linearized Kinematics Block
(5.8)
(5.9)

19. 6 Steering Actual Model
 An electric motor under
position control is assumed
here to be a steer-by-wire
actuator, which is used to
set the total front wheel
steering angle.
Figure 6.1 Actuator Model
(6.1)

20. Figure 6.2 Graphs 𝛿 𝑓𝑟𝑒𝑓 𝑎𝑛𝑑 𝛿 𝑓

21. 7 Unilateral Decoupling Controller
The first idea is to choose a position at a distance 𝑙 𝑑𝑝 in front of the CG such that the lateral acceleration
𝑎 𝑦𝑑𝑝 at this point does not depend on 𝐹𝑦𝑅
𝑙 𝑑𝑝=
𝐽
𝑚𝑙 𝑟
(7.1)
The lateral acceleration at he decouple point is
𝑎 𝑦𝑑𝑝 =
𝐹 𝑦𝐹l
𝑚𝑙 𝑟
+
𝑀𝑧𝐷
𝑚𝑙 𝑟
(7.2)
So if 𝐹𝑦𝐹 is not depent on r, then 𝑎 𝑦𝑑𝑝 is indepent of r.
The plant input is the front wheel steering angle δ𝑓. In the active steering system, it is composed of a
conventional steering angle δ𝑓, commanded by the driver and an additive steering angle δ𝑐, generated by
the feedback controller, such that
δ𝑓=δ𝑐+δs

22. For unilateral decoupling δ𝑐 must compensate the influence of r on
δ 𝑐 = −𝑟 +
cos 𝐵𝑓
𝑉
l 𝑓 − l 𝑑𝑝 𝑟 cos 𝐵𝑓 + l 𝑓 𝑟2 − 𝑎 𝑥 𝑠𝑖𝑛𝐵𝑓 + r 𝑟𝑒𝑓
It is linearized 𝑠𝑖𝑛𝐵𝑓 = 0 𝑎𝑛𝑑 𝑐𝑜𝑠𝐵𝑓 = 1
Taking laplace transform,
δ 𝑐 𝑠 =
r 𝑟𝑒𝑓−𝑟
𝑠
+
l 𝑓−l 𝑑𝑝
𝑣
𝑟(𝑠)
Figure 7.1 Feedback controlled aditive steering angle δ 𝑐
(7.3)
(7.4)

23. Figure 7.2 Simulink model of unilateral decoupling

24. 8)SIMULATION RESULTS
Below figures show that controlled car attenuates the disturbance and goes straight. However, in
conventional car, until the driver shows reaction car skid, then driver controls the car. Also yaw rate and
lateral acceleration goes zero in controlled car, but it is not in conventional car.

25. Figure 8.1 𝜇=0.5 𝑣=25𝑚/𝑠

26. Figure 8.2 𝜇=1 𝑣=50𝑚/𝑠

27. 9 CONCLUSION
 In conventional car value of lateral acceleration and value of yaw rate are not
equal to desired values. There are vital differents between these values. Also in
conventional car, driver reaction to attenuate disturbance can cause accident.
 However, in controlled car, automatic control interfere directly without driver
command and fixes the vehicle then controlling the car is not diffucult to driver.
 In conclusion, we have developed the concept of unilateral decoupling of car
steering dynamics. Its effect is that the driver has to care much less about
disturbance attenuation. The important quick reaction to disturbance torques is
done by the automatic feedback system. The yaw dynamics no longer interfere
with the path-following task of the driver.

28. THANK YOU!