Keywords

1 Introduction

The relationship between torque differentials characteristics on the left and right wheels by Direct Yaw Control (DYC) and vehicle dynamics has been well-established [1,2,3,4,5]. Less research has been conducted on the correlation between four-wheel independent yaw moment control and vehicle dynamic characteristics, as well as factors such as the maneuverability and the passenger lateral ride comfort. This paper presents an independent evaluation of a model based, yaw modifying, DYC system on an experimental vehicle with In-Wheel Motors (IWMs). The coordinate system is defined in Fig. 1.

Fig. 1.
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Coordinate system.

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2 Target Steering Response Using Torque Vectoring Control

2.1 Control Strategy

Torque vectoring systems have been included in production vehicles for more than 20 years. Originally this was achieved by electronic differential or brake control and is limited to relatively slow control algorithms which modify understeer/oversteer characteristics in near-limit situations. IWMs developments have enabled significantly higher bandwidth control algorithms which can subtly modify the yaw dynamics of the vehicle to change the feeling of ‘agility’ in sub-limit situations [6]. The experimental vehicle provided has a model based, agility modifying DYC control system called Torque Vectoring Control (TVC), enhancing the vehicle’s response to rapid steering inputs, known to influence driver ease of maneuver [7].

The control strategy developed is illustrated in Fig. 2. The development is carried out in three steps:

  1. 1)

    Identify the yaw transfer function of the vehicle from steering wheel to yaw angular velocity.

  2. 2)

    Identify the yaw transfer function for the vehicle from road wheel torque differential to yaw angular velocity.

  3. 3)

    Develop a control algorithm such that the overall transfer function from steering wheel angle (through traditional steering and through wheel torque differential) to yaw angular velocity matches some ideal characteristic.

The controller development is carried out in the frequency domain as this is a more natural environment for vehicle agility. Note that final tuning is carried out in the vehicle to ensure that non-linearities and model errors do not cause poor performance.

Fig. 2.
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A control block diagram of an experimental vehicle equipped with IWMs on all four wheels. The base vehicle is controlled to reduce the assumed yaw inertia. Note that the Yaw angular velocity has been represented to Yaw rate (YR) in this figure.

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2.2 Experimental Vehicle

The experimental vehicle is equipped with the IWMs capable of independent control of all four wheels. It can switch between with and without TVC. In addition, the driving force distribution can be adjusted from FWD to RWD, continuously.

2.3 Steering Response Results

The results of the frequency response of lateral acceleration and yaw angular velocity to the sinusoidal steering inputs using the experimental vehicle are shown in Fig. 3. The frequency response of lateral acceleration and yaw angular velocity to the sinusoidal steering inputs clearly shows the improved steering response characteristics achieved by TVC. The implementation of TVC increased the gain of lateral acceleration and reduced the phase lag in yaw velocity. These observations indicate an overall improvement in the vehicle response to a rapid steering inputs.

Fig. 3.
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Frequency Response Characteristics to Steering Inputs. Sinusoidal steering inputs at 40 kph constant speed, steering angle ±30° with moderate frequency incrementation ranging from 0.5 to 2.0 Hz.

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3 Evaluation Methods

3.1 Open Loop Test

To clarify the effects of TVC under certain conditions, the angular velocities of the vehicle pitch, yaw and roll motion, and the lateral acceleration on the front and rear axles are measured when the driver input is an open loop step of approximately 30° at a car speed of 40 kph. These measurements are taken under conditions both with and without TVC activation. Furthermore, similar tests are executed with varying drive configurations, specifically FWD and RWD, to elucidate the influence of distinct axes of TVC implementation on the dynamic behavior of the vehicle.

3.2 Closed Loop Test

To validate the effectiveness of TVC in steering response characteristics, a closed-loop test was conducted. Ten participants executed an emergency avoidance scenario shown in Fig. 4, wherein they travel at 35 kph and encounter an obstacle in their lane, and they move to the opposite lane and immediately return to their original lane to avoid oncoming vehicle with and without TVC. Subjective evaluations were conducted based on their individual experiences as both drivers and passengers. Participants were selected randomly, including both beginner and experienced drivers.

Fig. 4.
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The trajectory of the experimental vehicle executing the emergency avoidance scenario. The spacing between pylons is determined based on the vehicle's overall length and width, as well as the real world driving of a skilled driver.

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4 Evaluation Results

4.1 Open Loop Test

Experimental results of a 30° step steering maneuver at 40 kph are shown in Fig. 5. Both the yaw angular velocity and lateral acceleration of the front and rear wheel axles exhibit quicker responses and increased peak values with TVC activation compared to when TVC is deactivated. The presence of TVC results in quicker responses and larger peak values in both yaw angular velocity and lateral acceleration on the front and rear axles compared to when TVC is deactivate.

Additionally, experiments are conducted with TVC activation in both FWD and RWD configurations. According to driver feedback, the sensation while driving differs between FWD and RWD configurations with TVC activation. In the case of FWD, subjective feelings of being pulled a front toward steered direction are noticed by driver. On the other hand, in the case of RWD, a feeling of being pushed a rear toward opposite direction of steering. The comparative results of FWD and RWD are shown in Fig. 6. However, the lateral acceleration data for both the front and rear axles do not exhibit significant differences as perceived by the drivers.

Fig. 5.
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Comparison results with and without TVC.

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Fig. 6.
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Comparison between FWD and RWD configurations with TVC activation.

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4.2 Closed Loop Test

The subjective evaluation results are presented in Fig. 7. All assessment criteria show the improvement with TVC. Particularly notable are the ease of avoidance perceived by drivers and the smoothness of lateral motion experienced by rear-seat passengers.

As representative data, Fig. 8 shows the measured data of steering angle and yaw angular velocity during the emergency avoidance scenario executed by driver G. TVC contributes to the reduction in time delay from driver input to vehicle response. Furthermore, it can be read from the Lissajous waveform that the hysteresis of the response has decreased. These indicate that the response has been improved.

Fig. 7.
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Subjective Evaluation Results. Averaged subjective ratings of all participants on 7-point scale.

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Fig. 8.
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Time-domain Waveform and Lissajous Waveform during Emergency Avoidance Scenario

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5 Conclusion

Tests were conducted to validate the effectiveness of steering response enhancement using TVC with four-wheel independent controlled IWMs. The subjective evaluation results indicated the improvements in an ease of operation and in a perceived safety margin during emergency avoidance scenarios with the implementation of TVC. The improvement in subjective evaluation was proved by the physical data, indicating a reduction in phase lag and an increase in gain in vehicle yaw angular velocity and lateral acceleration with TVC under rapid steering inputs.

The vehicle dynamics under rapid steering input was improved by TVC with four-wheel independent controlled IWMs.

The subjective evaluation of maneuverability by drivers did not yield differences in data when altering the front-to-rear control distribution of TVC. These investigations will be the subject of further studies.