Mathematical Problems in Engineering

Volume 2015, Article ID 614989, 12 pages

http://dx.doi.org/10.1155/2015/614989

## Adaptive Gearshift Strategy Based on Generalized Load Recognition for Automatic Transmission Vehicles

^{1}State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130025, China^{2}Geely Group R&D Center, Hangzhou 311200, China^{3}China FAW Group Corporation R&D Center, Changchun 130013, China

Received 28 January 2015; Revised 17 May 2015; Accepted 31 May 2015

Academic Editor: Dan Simon

Copyright © 2015 Yulong Lei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Recognizing various driving conditions in real time and adjusting control strategy accordingly in automatic transmission vehicles are important to improve their adaptability to the external environment. This study defines a generalized load concept which can comprehensively reflect driving condition information. The principle of a gearshift strategy based on generalized load is deduced theoretically, adopting linear interpolation between the shift lines on flat and on the largest gradient road based on recognition results. For the convenience of application, normalization processing is used to transform generalized load results into a normalized form. Compared with the dynamic three-parameter shift schedule, the complex tridimensional curved surface is not needed any more, so it would reduce demands of memory space. And it has a more concise expression and better real-time performance. For the target vehicle, when driving uphill with gradient 11%, the vehicle load is about 280~320 Nm; when driving downhill, the value is around −340~−320 Nm. Road tests show that generalized vehicle load keeps near 0 in zero-load condition after calibration, and an 11% grade can be estimated with less than 1.8% error. This method is convenient and easy to implement in control software and can identify the driving condition information effectively.

#### 1. Introduction

The effects of various driving conditions, such as grade, vehicle loading, and road resistance, on the powertrain control strategy should be considered carefully. For instance, the grade resistance increases during uphill driving, so a large transmission ratio should be selected to avoid frequent shifting. A large ratio should also be used during downhill driving to take full advantage of the engine braking effect and avoid gear shift-up. Similarly, aerodynamic resistance and rolling resistance increase during vehicle loading, so a large ratio should still be used to improve vehicle dynamic performance. Therefore, automatic transmission vehicles should recognize the aforementioned driving conditions in real time and adjust the corresponding shift algorithm to improve the vehicle’s dynamic, passing, and comfort performance. Driving environment recognition is a prerequisite in achieving intelligent control.

Many driving environment recognition algorithms are available. For instance, Yuhai et al. [1] and Jin et al. [2, 3] developed certain methods to calculate the grade using an equation deduced by the principle of vehicle system dynamics. Ohnishi et al. [4] utilized an additional sensor, and Jo et al. [5] used GPS to identify the ramp and load, which will increase costs in practical application. Parameter identification is widely used to identify the driving environment [6–8], which not only depends on some vehicle parameters but also requires additional vehicle sensors. In addition, the process of real-time parameter estimation requires the electronic control unit (ECU) to have a higher computing speed. Another commonly used method is based on the fuzzy logic inference model [9–13], where the fuzzy rule can be flexibly adjusted according to the actual application situation. However, recognition results are generally the judgment and classification of the current vehicle condition instead of the precise slope or vehicle load.

Notably, Hebbale et al. [14] and Bai et al. [15] introduced a method using the difference between the vehicle actual acceleration and nominal vehicle model (i.e., when driving on a flat and suitable asphalt concrete road with no load) acceleration to reflect the current vehicle load. According to the classic longitudinal vehicle dynamics equation [16], this study defines a generalized vehicle load concept based on the torque difference, which can comprehensively reflect driving condition information, such as the grade, loading mass, aerodynamic resistance, and rolling resistance. A corresponding generalized load recognition method is introduced, and its basic principle and factors that affect recognition result in different driving conditions are described and analyzed. The principle of a gearshift strategy based on generalized load is deduced theoretically. And linear interpolation is adopted to get corresponding shift lines under different driving condition. This method is adaptive to the general driving environment. Compared with the dynamic three-parameter shift schedule, the complex three-dimensional surface is not needed any more, so it would reduce demands of memory space. And it has a more concise expression and better real-time performance. Real vehicle tests showed this method is convenient and easy to implement in control software, the busy-shift phenomenon on the slope road can be eliminated, and drivers’ dynamic requirement can be satisfied.

#### 2. Definition of Generalized Vehicle Load

##### 2.1. Definition

The general driving environment is a combination of different environmental factors in the vehicle driving-resistance balance equation [16], including ramp, load, weather, and road conditions. Therefore, the essence of general driving environment recognition is recognizing automobile driving resistance. Vehicle load generally refers to the mass of cargos or passengers, and this study extends this concept on the basis of the vehicle dynamics equation. We define a special zero-load driving condition and generalized vehicle load.

*Zero-load driving condition* refers to driving of a no-load vehicle on a flat, straight, and suitable asphalt concrete road in normal weather without braking.

*Generalized vehicle load* (or vehicle load) is defined as the force difference between the vehicle driving force in current driving conditions and resistances in zero-load condition when driving with the same speed and acceleration. This factor can be expressed in the following equation on the basis of the classic longitudinal vehicle dynamics equation:where is the vehicle load in unit Nm, is the current vehicle driving force, is the rolling resistance in zero-load condition, is the aerodynamic resistance in zero-load condition, and is the accelerating resistance in zero-load condition.

Given the flat road, the grade resistance does not appear in (1). Generalized vehicle load reflects the sum of the outside driving resistance. The larger the generalized vehicle load, the more the vehicle power demand. Therefore, the generalized vehicle load also reflects the external environment demand of vehicle power.

##### 2.2. Conversion of Vehicle Load Formula

Equation (1) is obtained by the direct transposition of the vehicle dynamics equation, which is in an easily understood form. However, the equation is further transformed to facilitate the following driving condition recognition operation.

Taking automated manual transmission (AMT) vehicles as an example, we can express the vehicle dynamics equation in a zero-load condition as follows:

The term on the left is the current vehicle driving force, , where is the actual engine output torque, is the current gearbox ratio, is the final drive gear ratio, is the transmission mechanical efficiency, and is the wheel rolling radius.

The first term on the right refers to the rolling resistance on a flat road, where is the mass of a no-load vehicle, is the acceleration of gravity, and is the rolling resistance coefficient on standard road.

The second term is the aerodynamic resistance , where is the aerodynamic resistance coefficient, is the frontal area, and is the vehicle speed in unit km/h.

The third item refers to accelerating resistance, , where is the vehicle speed in unit m/s and is the correction coefficient of the rotating mass with no load calculated by the following equation:where is the wheel moment of inertia and is the flywheel moment of inertia.

Next, the terms of are moved to the right side of (2). The term on the left is the current gearbox output torque, , whereas the term on the right is the sum of all types of resistance torques in zero-load condition. Based on (1), the vehicle load can be re-redefined as follows:

Equation (4) shows that the vehicle load is a torque-based expression in Nm. It represents the torque difference between the gearbox output torque in the current driving condition and resistance torques in a zero-load condition when driving with the same vehicle speed and acceleration.

The reason for converting (1) is that the parameters and can be affected by the driving condition. Through conversion, and are included in the resistance torques, and the driving torque is calculated directly by the engine torque and ratio. The parameters of other resistance torques can be obtained through calibration in a zero-load driving condition.

##### 2.3. Principle of Driving Condition Recognition Based on Vehicle Load

If we suppose that one or more parameters are changed in (4) (i.e., one or more constraint conditions in the zero-load condition are changed), then varies accordingly and reflects these alternations. If we can obtain the vehicle load accurately in real time, then the driving condition information can be recognized. Its recognition result can then be used in the vehicle control strategy.

The principle of vehicle load-based driving condition recognition method is just the calculation process of . Thus, the part of can be seen as a vehicle reference model used to calculate the driving torque under a zero-load condition. is obtained from the actual vehicle model used to calculate the current driving torque. The process of computing the generalized load requires the current gearbox output torque and resistance torques in a zero-load condition with the same vehicle speed and acceleration. The following chapter analyzes the effects of different driving conditions on recognition results and then provides detailed recognition steps.

#### 3. Influence Factor Analysis of Generalized Vehicle Load Recognition

Given that the generalized vehicle load concept is defined in a zero-load condition, its recognition result in a zero-load condition should be investigated first before each influence factor in different driving conditions can be analyzed.

##### 3.1. Vehicle Load Recognition in a Zero-Load Condition

Although a zero-load condition qualifies some driving behavior and loading, weather, and road conditions in vehicle system dynamics, each resistance torque in (4) remains under the influence of parameters such as the vehicle speed and correction coefficient of rotating mass. In particular, the driver behavior patterns of gear shift, acceleration, and deceleration can cause resistance changes accordingly. However, vehicle driving force should always be equal to the sum of all resistances based on the vehicle driving-resistance balance equation [16]. Therefore, the recognition result of (4) in a zero-load condition should theoretically always be maintained at 0 regardless of how a driver steps on the gas pedal (i.e., at any vehicle speed and acceleration). This condition is also the origin of the term zero-load condition.

##### 3.2. Grade Factor

###### 3.2.1. Uphill Condition

When changing from a flat and straight road in a zero-load condition into an uphill condition, the vehicle dynamics equation contains the grade resistance. The rolling resistance is also affected. At this point, the following equation is used:where is the angle of grade.

Grade resistance exists during uphill driving. Given the balanced relationship between the vehicle driving force and external resistances, a driver is required to fully step on the gas pedal to counterbalance the grade resistance and reach the same vehicle speed and acceleration in a zero-load condition. Thus, the gearbox output torque is larger than that in a zero-load condition. By substituting (5) into (4), we obtain the load expression, , when driving uphill. Thus,

Equation (6) shows that the load recognition result contains two components of the rolling resistance torque and grade resistance torque. However, the rolling resistance has minimal effect on the load recognition result because the angle of grade is generally small.

###### 3.2.2. Downhill Condition

During downhill driving, the grade resistance is in the same direction as the driving force and plays the role of an accelerating vehicle. At this point, the gearbox output torque is less than that under a zero-load condition with the same vehicle speed and acceleration. Therefore,

The driver releases the throttle or simultaneously brakes to decelerate. The gearbox output torque then decreases. When not braking, we obtain the vehicle load expression of downhill, , by substituting (7) into (4). Thus,

Given , the vehicle load while driving downhill is negative when not braking. Consider

Given that the braking force originates from the brake system, the vehicle load recognition result is larger than (8) when braking and is incorrect. This study does not consider the braking condition.

Thus, the load recognition result is positive when driving uphill and negative when driving downhill, and its absolute value increases with the angle of grade.

##### 3.3. Loading Mass Factor

In the case of increasing loading in a zero-load condition, the rolling and accelerating resistances affected by the loading mass in (4) increase synchronously. Given the force balance rule, the gearbox should output a higher torque to reach the same vehicle speed and acceleration in a zero-load condition. Thus, the load recognition result calculated from (4) increases correspondingly. Setting as the new vehicle mass with loading, we can express as follows:where is the correction coefficient of the rotating mass after the loading mass is increased.

Equation (3) shows that the correction coefficient of the rotating mass is also under the influence of the loading mass. Thus, (10) considers .

Equation (10) shows that the vehicle load recognition result contains the two components of rolling resistance torque and acceleration resistance torque. The rolling resistance torque is almost constant, whereas the accelerating resistance torque is affected not only by the current loading mass but also by the vehicle longitude acceleration. Figure 1 shows the simulation result of the vehicle load recognition result of a minitype AMT vehicle when the loading mass increases from no load to full load at different acceleration values. The results indicate that the higher the acceleration value, the larger the load recognition result.