# Stabilization of Vehicle Dynamics by Tire Digital Control—Tire Disturbance Control Algorithm for an Electric Motor Drive System

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## Abstract

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## 1. Introduction

_{y}, can be represented by Equation (1) [9]:

_{p}is cornering power, K is a tire lateral stiffness, and V is a vehicle speed. Furthermore, the time constant of the longitudinal force, τ

_{x}, can be represented by Equation (2) [9]:

_{y}= 0.001 s (C

_{p}= 1.4 kN/deg., K = 10

^{5}N/m) and τ

_{x}= 0.004 s (B = 0.05 m) at vehicle speed V = 50 km/h. These values are close to 0.0008 s, which is the time constant of the electric motor. This suggests that the tire and electric motor can be a good combination to achieve a quick response for a faster control system. Hence, we proposed a new concept of tire digital control, which can stabilize the vehicle dynamics by suppressing the disturbance on tires using the electric motor before the vehicle body becomes unstable. Figure 1 shows the type of control objects corresponding to control frequency range. The conventional control objects, such as anti-lock braking system (ABS) and dynamic stability control (DSC), are targeting the frequency ranges from 0.1 to 10 s. But those of tire digital control range from 1 to 100 ms, which can be achieved only by the controller of the electric-driven system. It is also an important feature that the electric motor can control both driving and braking forces. Our study showed that the tire disturbance control with electric motors, corresponding to higher frequency range, can be more effective on critical steering performances, such as those on a wet skid pad.

## 2. Algorithm

#### 2.1. Tire Disturbance Control

_{d}, includes the disturbance noise of the tire contact patch, N1, and the vibration of un-sprung mass, N2. The tire disturbance control can cancel out these noises by electric motor [10]. The cut-off frequency was determined so as to reduce the magnitude of transfer function of slip ratio to tire driving force, F

_{d}/λ, between 10 Hz to 1 kHz, keeping the human maneuver frequency less than 10 Hz unaffected.

#### 2.2. Tire Disturbance Control Algorithm

_{d}/F

_{z}, F

_{d}is a driving force, F

_{z}is a load, M

_{w}is the mass conversion value of tire inertia, V

_{W}is the speed conversion value of tire rotational angular velocity, F

_{m}is the motor force conversion value of torque, λ is the tire slip ratio, and s represents the Laplace operator. The time constant of the vehicle body can be given by Equation (4):

_{w}, and V increase. In addition, it should be noted that as dμ/dλ approaches zero at the maximum value of μ, the time constant rapidly increases and it becomes difficult for the vehicle body to respond to control. This suggests that it is necessary to stabilize the tire before the value of μ reaches the maximum value. As shown in Figure 3, the motor driving force, F

_{m}, can be divided into the wheel inertia force, F

_{w}, and the tire driving force, F

_{d}, for moving forward the vehicle body. The output of F

_{m}can be given directly from electric motor and the input of F

_{w}can be calculated from the wheel rotation speed, V

_{w}. The output of F

_{d}is derived from the equation of F

_{d}= F

_{m}− F

_{w}as the force generated at the tire contact patch. From the comparison of F

_{d}and the force followed by the nominal model, the abrupt slip and micro vibration at a higher frequency range was extracted by low pass filter. The component of human maneuvers was compensated by high pass filter. The filtered noise component was subtracted from the command value of F

_{m}to be applied to the motor controller. In order to find the effective frequency pass, the cut-off frequency of low pass filter was varied from 0.01 to 10 kHz, and that of high-pass filter was varied from 0.01 to 10 Hz. The former can cut off the higher frequency disturbance noise from the electrical circuits and the latter can cut off the lower frequency disturbance noise, keeping the human maneuvers unaffected. It is important that all human maneuvers, such as throttling, braking, and handling, be kept unaffected by optimizing the cut-off frequency of low pass filter.

## 3. Results

#### 3.1. Test Vehicle

#### 3.2. Test Method

## 4. Results and Discussion

#### 4.1. Effect of Applied Control Frequency

_{m}and F

_{d}at the steady state of the accelerated turning test was investigated and is shown in Figure 6. According to Equation (3), when the tire keeps the grip with road surface at adhesive state, F

_{d}is proportional to F

_{m}as shown as a straight line in Equation (5). In this state most of the motor torque can be transferred to the tire driving force:

_{d}followed a straight line. This shows that the tire can keep the stable grip with the road surface under the driver’s control.

_{d}and F

_{m}in the state just before the spinout. The results showed that F

_{d}does not follow Equation (5) and fluctuates largely independent of F

_{m}. This indicated that the tire already showed signs of spinout just before the vehicle spinout and suggested that it is possible to expand the stability margin by suppressing this fluctuation by motor control.

#### 4.2. Stabilization of Steering on the Wet Skid Pad

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Global Electric Vehicle (EV) Outlook 2018. Available online: https://www.iea.org/gevo2018/ (accessed on 15 April 2019).
- Anderson, Z.M.; Glovanardi, M.; Tucker, C.; Ekehian, J.A. Active Safety Suspension System. US2017/0137023, 18 May 2017. [Google Scholar]
- Wang, Y.; Fujimoto, H.; Hara, S. Driving Force Distribution and Control for EV with Four In-Wheel Motors: A Case Study of Acceleration on Split-Friction Surfaces. IEEE Trans. Ind. Electron.
**2016**, 64, 3380–3388. [Google Scholar] [CrossRef] - Nam, K.; Oh, S.; Fujimoto, H.; Hori, Y. Estimation of Sideslip and Roll Angles of Electric Vehicles Using Lateral Tire Force Sensors Through RLS and Kalman Filter Approaches. IEEE Trans. Ind. Electron.
**2012**, 60, 988–1000. [Google Scholar] [CrossRef] - Hu, J.; Wang, Y.; Fujimoto, H.; Hori, Y. Robust Yaw Stability Control for In-wheel Motor Electric Vehicles. IEEE/ASME Trans. Mechatron.
**2017**, 22, 1360–1370. [Google Scholar] [CrossRef] - Sato, M.; Yamamoto, G.; Gunji, D.; Imura, T.; Fujimoto, H. Development of Wireless In-Wheel Motor Using Magnetic Resonance Coupling. IEEE Trans. Power Electron.
**2016**, 31, 5270–5278. [Google Scholar] [CrossRef] - Nagaya, G.; Wakao, Y.; Abe, A. Development of an in-wheel drive with advanced dynamic-damper mechanism. JSAE Rev.
**2003**, 24, 477–481. [Google Scholar] [CrossRef] - Hori, Y.; Toyoda, Y.; Tsuruoka, Y. Traction Control of Electric Vehicle: Basic Experimental Results using the Test EV UOT Electric March. IEEE Trans. Ind. Appl.
**1998**, 34, 1131–1138. [Google Scholar] [CrossRef] - Clark, S.K. Mechanics of Pneumatic Tires; Chapter 9, Analysis of tire properties; National Highway Traffic Safety Administration: Washington, DC, USA, 1981; pp. 721–757.
- Wakao, Y.; Akutagawa, K. Method And Device For Controlling Vehicle. EP1502805A1, 2 February 2005. [Google Scholar]
- Hori, Y.; Sakai, S.; Sado, H.; Uchida, T. Motion Control of Electric Vehicle Utilizing Fast Torque Response of Electric Motor. IFAC Proc. Vol.
**1999**, 32, 8166–8171. [Google Scholar] [CrossRef] - Nasukawa, K.; Miyashita, Y.; Shiokawa, M. Jidousha No Soukouseinou To Shikenhou. In Efficiency Tests for Running, 3rd ed.; Sankaido: Tokyo, Japan, 1993; p. 217. [Google Scholar]

**Figure 3.**Design of tire disturbance controller for mechanical tire noise cancellation (LPF: low pass filter, HPF: high pass filter).

**Figure 5.**The aerial photo of the skid pad superimposed by the GPS trajectory of the vehicle’s center of gravity.

**Figure 6.**Relationship between the friction force, F

_{d_RR}, and the motor torque, F

_{m_RR}, at steady state in the accelerated turning test.

**Figure 7.**Relationship between friction force, F

_{d_RR}, and motor torque, F

_{m_RR}, just before the spinout in the accelerated turning test.

**Figure 8.**The magnitude of the effect on each control frequency range and the corresponding score of steering feeling.

**Figure 9.**Steering maneuvering on the wet skid pad compared between vehicles with and without the tire digital control. More details can be found in Supplementary Materials (Video S1: without control and Video S2: with control).

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**MDPI and ACS Style**

Akutagawa, K.; Wakao, Y.
Stabilization of Vehicle Dynamics by Tire Digital Control—Tire Disturbance Control Algorithm for an Electric Motor Drive System. *World Electr. Veh. J.* **2019**, *10*, 25.
https://doi.org/10.3390/wevj10020025

**AMA Style**

Akutagawa K, Wakao Y.
Stabilization of Vehicle Dynamics by Tire Digital Control—Tire Disturbance Control Algorithm for an Electric Motor Drive System. *World Electric Vehicle Journal*. 2019; 10(2):25.
https://doi.org/10.3390/wevj10020025

**Chicago/Turabian Style**

Akutagawa, Keizo, and Yasumichi Wakao.
2019. "Stabilization of Vehicle Dynamics by Tire Digital Control—Tire Disturbance Control Algorithm for an Electric Motor Drive System" *World Electric Vehicle Journal* 10, no. 2: 25.
https://doi.org/10.3390/wevj10020025