Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 263424, 18 pages
http://dx.doi.org/10.1155/2015/263424

Research Article

Global Chassis Control System Using Suspension, Steering, and Braking Subsystems

Carlos A. Vivas-Lopez,¹ Juan C. Tudon-Martinez,² Diana Hernandez-Alcantara,¹ and Ruben Morales-Menendez¹

¹Tecnológico de Monterrey, School of Engineering and Sciences, Avenida E. Garza Sada No. 2501, 64849 Monterrey, NL, Mexico
²Universidad de Monterrey, Avenida Ignacio Morones Prieto No. 4500, 66238 San Pedro Garza García, NL, Mexico

Received 4 August 2015; Accepted 21 October 2015

Academic Editor: Xinggang Yan

Copyright © 2015 Carlos A. Vivas-Lopez 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.

A novel Global Chassis Control (GCC) system based on a multilayer architecture with three levels: top: decision layer, middle: control layer, and bottom: system layer is presented. The main contribution of this work is the development of a data-based classification and coordination algorithm, into a single control problem. Based on a clustering technique, the decision layer classifies the current driving condition. Afterwards, heuristic rules are used to coordinate the performance of the considered vehicle subsystems (suspension, steering, and braking) using local controllers hosted in the control layer. The control allocation system uses fuzzy logic controllers. The performance of the proposed GCC system was evaluated under different standard tests. Simulation results illustrate the effectiveness of the proposed system compared to an uncontrolled vehicle and a vehicle with a noncoordinated control. The proposed system decreases by 14% the braking distance in the hard braking test with respect to the uncontrolled vehicle, the roll and yaw movements are reduced by 10% and 12%, respectively, in the Double Line Change test, and the oscillations caused by load transfer are reduced by 7% in a cornering situation.

1. Introduction

A road vehicle has a conjunction of interconnected subsystems, such as brakes, steering, suspension, engine, and tires, which is difficult to be controlled [1]. These subsystems interact among them modifying their individual behavior and consequently the overall performance of the vehicle; these interactions could cause negative effects. For example, the way the suspension system is tuned can dramatically affect the performance of the steering system; a soft suspension affects the tire grip decreasing the ability of the vehicle to steer; if the suspension is too stiff, tires will hop causing loss of control. Additionally, all vehicle subsystems have a nonlinear behavior, making their coordination a complex task.

Normally, each vehicle subsystem has an independent control system to accomplish a specific objective. For example, the brake system has the Antilock Braking System (ABS) to prevent tires from locking during hard braking avoiding skidding and loss of control [2]. Also, it has the Electronic Stability Control (ESC) which creates a turning moment using the brakes to prevent loss of control. Both control systems have conflicting principles, the ABS releases the brake pressure whereas the ESC generates an additional one. Table 1 summarizes the used acronyms in this document.

Table 1: Acronyms definition.

Acronyms
Description

ABS
Antilock Braking System

AS
Active Steering

AFS
Active Front Steering

CDC
Continuous Damping Controller

DC
Decentralized Controllers

DL
Decision Logic

DLC
Double Line Change

DoF
Degree of Freedom

DBC
Data-Based Controller

EMB
Electromechanical Braking

ESC
Electronic Stability Control

ECU
Electronic Control Unit

FH
Fish Hook

FCS
Force control system

FL
Fuzzy logic

FIS
Fuzzy Inference System

GCC
Global Chassis Control

IVDC
Integrated Vehicle Dynamics Control

-NN
-Nearest Neighbor

LPV
Linear parameter varying

MBC
Model-Based Controller

MF
Membership Function

PC
Principal Component

PCA
Principal Component Analysis

RMS
Root Mean Square

ROC
Receiver operating characteristic

SA
Semiactive

SAS
Semiactive suspension

SAP
Suspension Adjustment Plane

SCS
Steering control system

SISO
Single-Input Single-Output

SMC
Sliding Mode Control

TRC
Traction Control

UC
Uncontrolled

VCS
Vehicle Control System

VDC
Vehicle Dynamics Control

4WIB
Four-Wheel Independent Braking

4WS
Four-Wheel Steering

Studies in global trends aim towards achieving intelligent vehicles in upcoming years [3]. These vehicles are required to meet present and future state regulations related to efficiency, autonomy, ecology, safety, and comfort [4]. Particularly, the global automotive industry is paying special attention to safety systems that guarantee the integrity of occupants, pedestrians, and/or other drivers when an accident occurs. Even the newest safety features (Collision Mitigation or Line Keeping Systems) are oriented to prevent possible dangerous situations; the main topic of research refers to the systems that react against a dangerous situation [5].

These opportunities demand more of the actual Vehicle Control Systems (VCS). The standard solutions was to independently treat any new objective by adding a new VCS. This parallel architecture can lead to some drawbacks, for example, a VCS is normally designed to seek a specific goal, but when it interacts with other VCS the result could degrade the global performance, overruling the original objectives of the individual controllers due to inherent coupling effects. Since those controllers have to work simultaneously, they have their own information system and Electronic Control Unit (ECU) demanding more costs and space; that is, vehicle infrastructure and complexity increase [6].

The concept of GCC, also called Integrated Vehicle Dynamics Control (IVDC), proposes the coordinated integration of those different VCS to pursuit a common goal [7]. This integration offers (1) the ability to simultaneously control various subsystems, (2) the ability to coordinate the actions of individual subsystems regarding a general goal [8], and (3) the ability to share information from sensors and actuators (also functions) [9].

This concept has been investigated in the literature. The approaches can be differentiated regarding the number of Degrees of Freedom (DoF) in which they act (vertical, longitudinal, or lateral dynamics). Some cases have been studied as functional integrations (specific objective or single DoF). In [10], an integration of the braking and Semiactive (SA) suspension system is proposed to decrease braking distance in an emergency maneuver; but, in this case, there is no coordination. An integration of active suspension and braking is proposed in [11] to prevent a rollover situation using a Linear Parameter-Varying (LPV) controller driven by a scheduling parameter related to load transfer; the controller is highly model dependent.

Most of the research of this topic lays in the case of multipurpose integration (i.e., multiple DoF). An integration of steering and braking to enhance horizontal dynamics using robust control is proposed in [12]; however, the coordination algorithm and controller synthesis are not clear. In [13] the authors proposed a controller based on inverse-model dynamics to generate the desired control commands for braking and steering subsystems; the method is highly dependent in an accurate model of the system and sensitive to modeled dynamics. In [14] an integration of steering and braking systems is proposed. The goal is to maintain an optimum tire forces using Sliding Mode Control (SMC). It uses an optimization procedure to compute the optimum force distribution among the tires. In [15] a control strategy to improve the horizontal dynamics involving the braking and steering subsystems is proposed; it uses an optimization procedure to allocate the desired yaw moment; but, the cost functions have to be modified depending on the situation. In [16] a loss prevention control system is introduced using the braking and steering subsystems; this strategy relies on physical infrastructure in the road to calculate the reference signals, which nowadays is not available in most roads.

Only few works have been published on full dynamics integration (able to act in the vertical, longitudinal, and lateral dynamics). In [17], an integration of an active suspension, a 4-Wheel Steering (4WS), and a driving/braking force control using Traction Control (TRC) and ABS is proposed, but the coordination algorithm is not clear and the use of active suspension and 4WS is expensive. In [1], a strategy using the differential braking for horizontal dynamics and the active suspension for vertical is proposed; this method has to calculate the control command of each sampling time by optimization; this demands a lot of computational resources. The authors in [18] divide the problem; they treated vertical and horizontal dynamics separately. For vertical dynamics, it determines the desired force for each damper based on the LPV framework; but, its performance is fixed by design. For horizontal dynamics, it uses a gain scheduling parameter to decide when to apply braking control or a combination of steering with braking control. It defines some driving conditions (i.e., stable or unstable) but they are limited. The work of [19] proposed a control architecture capable of identifying the actual driving situation; based on the estimated situation, the control mode of each subsystem is changed. Even when this method is capable of reacting against different situations, it does not consider the switching implications in the control system, which could lead to unexpected behaviors. In [20], a control system based on LPV is proposed; in this case all three directions are simultaneously controlled using two varying parameters, one for suspension-steering and another for braking; however, the controller operates under predefined conditions without depending on the driving situation.

Although there are interesting results, they do not include the full dynamics integration; others are strongly model-dependent or they are robust to some uncertainty which could generate conservatism issues. Furthermore, some of them are not easy to implement in on-board Vehicle Dynamics Controllers.

The main contribution of this proposal lays in a new GCC system based on a discrimination of the operation conditions of the vehicle. The strategy architecture is a supervisory decentralized control to improve flexibility and modularity [21]. The goal is to identify the current driving situation, based on vehicle measurements using clustering methods [22]; then, the control modes of each subsystem are coordinated to ensure the best global performance. The coordination includes three subsystems: SAS, AFS, and 4-Wheel Independent Braking (4WIB), a full dynamics integration. The effectiveness of the new strategy was validated in CarSim.

The paper is organized as follows. Section 2 describes the problem. Section 3 presents the GCC architecture and modules in detail. Section 4 discusses the results, based on a case study. Section 5 concludes the research and proposes future work. Tables 2 and 3 summarize all the used variables in this work.

Table 2: Modeling: variables description.

Variable
Description
Units

,
Hysteresis coefficients related to displacement and velocity
s/m, 1/m

Viscous damping coefficient
Ns/m

,
Cut-off frequency of the actuator dynamics
Hz

Force coefficient due to manipulation
N/V

Damper force
N

Semiactive damper force
N

Stiffness coefficient
N/m

Vehicle wheel base
m

,
Sprung/unsprung mass
kg

,
Actuator output
MPa, deg.

,
Actuator controller output
MPa, deg.

,
Vehicle/tire longitudinal vel
m/s

, ,
Longitudinal/lateral/vertical displacement
m

, ,
Longitudinal/lateral/vertical velocity
m/s

, ,
Longitudinal/lateral/vertical acceleration
m/s²

,
Damper deflection and velocity
m, m/s

, ,
Road/sprung mass/unsprung mass vertical position
m

Vehicle side slip angle
deg.

Steering wheel angle
deg.

Driver’s steering command
deg.

Tire slip ratio
—

Damper manipulation
V

, ,
Pitch/roll/yaw angle
deg.

, ,
Pitch/roll/yaw rate
deg./s

Desired yaw rate
deg./s

Rotational speed of the tires
rad/s

Table 3: Algorithms: variables description.

Variable
Description

Actuation vector

Gain of the allocation coordination

, ,
Suspension/braking/steering coordination gain

,
Softest/hardest damping coefficient

Driving class

Contribution index of the th variable in a driving situation

Minimal set of important variables for a driving situation

Euclidian distance

Driving situation

,
Slip angle/yaw rate error

ABS braking gain

IS
Initial set of vehicle variables

Number of nearest neighbors

First principal components

Number of measurements

MS
Minimal set of important variables for all driving situations

Corrective yaw moment

,
Original/reduced number of variables

Number of driving conditions

Driving situation critical condition

Driving situation importance

Situation changing waiting time

Variable contribution threshold

Driver braking torque

Right/left corrective braking pressure

Pressure gain

Noise variance threshold

,
Allocated/coordinated controller output

Full suspension road-holding/comfort suspension command

,
Single corner/full suspension control command

Data point

,
Passive/controlled th performance variable

Residual data point of the th measure in a driving situation

,
Desired vehicle slip angle/yaw rate

Corrective steering angle

,
Steering wheel/wheels directional angle

Critical tire slip ratio

Variance of the th variable in a driving situation

Covariance matrix

Data matrix of variables

,
Principal/residuals components matrix

,
Principal/residual scores matrix

,
Principal/residual transformed variables

Variable number

Driving situation

Number of neighborhoods

2. Problem Description

Passenger vehicles are equipped with a wide diversity of on-board VCS, and those focused on the management of the dynamical behavior of the vehicle are called Vehicle Dynamics Controllers (VDC), for example, Continuous Damping Controller (CDC) and Electronic Stability Control (ESC). Usually each VDC operates in a set of DoF defined by the vehicle reference system, Figure 1; the most important variables for each vehicle motion are as follows:

(i)Vertical dynamics refers to the movements that affect mainly the comfort of the passengers (vibration reductions); the important variables are pitch (turn around -axis, ), roll (turn around -axis, ), and vertical acceleration () in the Chassis and wheels.(ii)Lateral dynamics refers mainly to the stability and handling (safety) of the vehicle; the important variables are lateral displacement (), side slip angle (), and yaw (turn around -axis, ).(iii)Longitudinal dynamics refers to vehicle stability (safety) and its performance (power train); the important variables are longitudinal velocity (), wheel rotational velocity (), and tire slip ratio ().

Figure 1: Vehicle reference system and important dynamical variables.

A VDC can have one or more of these three control goals: stability, handling, or vibration mitigation:

(1)Stability: when a vehicle has crossed its handling limits and tires lost their grip, it is said that the vehicle has become unstable and cannot be controlled by the action of the driver only; here, the main objective is to recover the driver’s control to guarantee passengers safety.(2)Handling: it refers to how well a vehicle can achieve cornering at high speeds; this condition is related to the safety characteristic of the vehicle.(3)Vibration mitigation: it refers to the comfort that the passengers will experience during riding; this consists in the limitation of the unpleasant vibrations and movements caused by road irregularities; also, road-holding is considered, that is, vibration reduction in the unsprung mass at high vehicle velocities.

To develop a full dynamics integration in the vehicle it is necessary to control/coordinate the different subsystems simultaneously [17]. Usually the selected subsystems are (1) Active Front Steering, (2) Independent Braking, and (3) SAS. Another requirement is the use of different controllers acting in those subsystems depending on the current driving situation [23]; but, this feature leads to switching those controllers, which could cause unstability [24].

In road vehicles, the inherent coupling effects among their subsystems impact the overall performance of the vehicle. The coupled effects plus the issues that come with the interactions of different independent control systems increase the complexity of controlling the vehicle dynamics.

The above conditions can be handled with integrated control strategies, where subsystems and control actions are efficiently coordinated. Such strategies avoid contradictions in the control goals of the subsystems to obtain a better global performance from them at each situation [25]. Model-based control approaches represent a complex and unpractical solution, considering the vehicle as a highly nonlinear system. On the other hand, Data-Based Controllers could represent a reliable option in practice, assuming that the vehicle dynamics is monitored by some sensors. Figure 2 compares the two approaches under the road profile with bump test. This test is used to evaluate the road isolation characteristics of the control systems. Here 3 cases are compared: (1) Passive: a vehicle with nominal shock absorbers, (2) a Model-Based Controller (MBC): a full suspension controller designed to minimize the vertical acceleration () and the pitch () movements of the sprung mass, and (3) a Data-Based Controller (DBC): a controller that considers the classical Sky-Hook and Ground-Hook algorithms.

(a) Vertical acceleration ()

(b) Pitch angle ()

Figure 2: Comparison of MBC and DBC approaches.

From Figure 2 it can be seen that the two approaches have a very similar performance. Quantitatively the MBC improved the vertical acceleration in 14.5% and the pitch movements in 9.74% with respect to the Passive case, whereas the DBC achieved an improvement of 9.1% and 17.8%, respectively. Both approaches result in similar performances, but the DBC is simpler and faster to implement, compared to the MBC which has large dimension matrices inside the controller.

Based on the results of the literature review, VDC systems that achieve full dynamics integration are still a research topic.

3. Global Chassis Control

The architecture of the GCC system is divided into three main layers, Figure 3:

(1)Decision layer: it identifies the current driving situation and its stability; it decides how to coordinate the subsystems actions and their operating mode.(2)Control layer: it receives the control goal from the decision layer and determines the proper orientation for each of the local controllers.(3)Physical layer: it comprehends the actuators and sensors from the vehicle; it receives the control output from the control layer and sends the process variables from the sensors.

Figure 3: GCC architecture, hierarchical approach.

This multilayer and hierarchical architecture has some advantages: (1) it divides the computational load into several ECUs, (2) it allows information sharing, (3) it improves system flexibility (reconfigurability), and (4) it introduces a modular scheme capability [26]. The information bus contains sensors measurements and actuators functions. Since the methods to observe or estimate the considered variables are not within the scope of this work, they are assumed to be available. Figure 4 shows a full scheme of the proposed GCC system.

Figure 4: Control scheme of the GCC system.

3.1. Decision Layer

This layer has two main tasks: (1) classify the current driving situation and (2) coordinate the control strategy for the classified situation.

3.1.1. Classification Algorithm

The first step of the algorithm is to decide, from an Initial Set () of variables, which is the Minimal Set () to classify the current driving situation. The elements of must be variables that describe the global behavior of the vehicle, as well as variables that are commonly used in VCS:

Some vehicle variables are correlated; for example, pitch is correlated to deflections of the suspension. Besides, not all variables have the same importance in all driving situations; for example, in a riding situation the vertical acceleration will gain more importance, but during cornering yaw moment could be the most important. To determine the most representative vehicle variables during a driving situation, a Principal Component Analysis (PCA) is carried out.

Measurements of the variables in the set under different driving situations are used in this step, where is the number of driving situations to be considered, , with , is the data matrix of variables, and , and measurements, with zero mean and unit variance after a scaling process. To neglect the noise effect in the scaling process, variables with small variance are not considered; , where is a defined threshold.

Based on [27], is obtained; it contains the first eigenvectors from the covariance matrix and which contains the last eigenvectors. The first eigenvectors associated with the PC have to explain at least 90% of the total variance of the original data for each driving situation. Then, the scores matrices and are obtained:

By decomposing with

the modeled data is obtained with principal and residual components, respectively.

According to [28], using the residual components, , the contribution of each variable can be obtained in each driving situation as

Once the contributions are obtained, if , then , where is the set of the variables that contributes in each driving situation and is a defined threshold. Finally, the set is formed by

with the resultant number variables equal to .

After defining the set that contains the most representative variables for all studied driving situations, a clustering technique is exploited as classifier. Because of its easy computation, fast clustering response, and good performance, the -Nearest Neighbor (-NN) algorithm was used.

The -NN approach is one of the simplest machine learning algorithms, which it is based on the minimum distance criterion. A data set of reference patterns in a multidimensional feature space is required to establish the learning of this classifier, where the Euclidian distance is the most common metric. In this case, set contains the reference patterns of the studied driving situations.

Given a new data vector of variables, the -NN algorithm assigns each new observation into a class of driving situation according to

where is the number of nearest neighbors used in the classification associated with the driving situation and is the Euclidian distance between a new observation and the nearest neighbors of reference defined by . A large value of reduces the effect of noise in the classification; cross-validation can be used to define this parameter. For the vehicle, the sensor measurements contained in the MS set are used to construct the features space. The online result given by this clustering technique is sent to the Decision Logic (DL) module to classify the situation.

3.1.2. Decision Logic Module

Based on a set of heuristic rules, the DL module is in charge to decide (1) whether a driving situation is critical or normal, (2) if the control actions should change, and (3) when to change from one situation to another based on the importance of the previous situation.

First, the structure for a driving situation, , must be defined. For this purpose, the DL module depends on the number of subsystems to use and the amount of driving situations, , to consider. The definition of a is as follows:

(i)Each driving situation is defined with a vector in in the form: .(ii) refers to normal () or critical () situation.(iii) indicates the critical level of the driving situation: is a stable situation with negligible danger while corresponds to the most dangerous condition.(iv) is the actuation vector for the subsystems that must be accomplished according to the detected driving situation; that is, . Considering an on-off control law for each subsystem, the control output is dichotomic .

Then, a set of rules that manage the transition between driving situations is defined. Figure 5 shows the graph diagram with the transition rules; the DL rules are carried as follows:

(1)A with bigger overrules a with a smaller index, and is updated.(2)At any safe driving situation, independently of the index, the current updates the actuation vector .(3)In an unsafe driving situation, the current keeps the actuation vector in safe mode until the index decreases through the time () to ensure completely the vehicle safety and avoid any false alarms.

Figure 5: Graph for the DL module.

Finally, the DL layer sends the mode of operation of the subsystems controllers in the control layer.

3.2. Control Layer

This layer comprehends the control actions (allocation, manipulation) to be taken through the physical layer. The desired control allocation is determined based on the information received from the previous layer, and then the desired control manipulations are computed.

3.2.1. Control Allocation

Based on the driving situation, the desired control action for each subsystem is defined in this sublayer. The control mode acts as a gain in the form of

where is the controller output which depends directly on the gain of the coordinated allocation ; that is, means that the GCC demands the actuation on the subsystem, and vice versa (i.e., when ). Thus, is the local controller output of the subsystem obtained from any control law, but before the full dynamics integration. The allocation controllers for each subsystems are defined as follows.

(i) SAS. The SA dampers must always receive a manipulation; the decision is whether to select a manipulation oriented to comfort () or to road-holding () for each corner of the vehicle:

where . Note that, according to the driving situation, the GCC can orient the suspension to comfort or to road-holding using the weighting parameter . At each corner, the SAS controller output can be oriented to comfort () or to road-holding () inspired in the classical Sky-Hook and Ground-Hook control strategies:

where and represent the softest and hardest damping coefficient, respectively.

(ii) Braking System. The braking action is computed by the fuzzy logic (FL) controller [29]. It uses two inputs: (1) side slip angle error () and (2) yaw rate error () and one output: (1) corrective yaw moment (). The control goal is to reduce the errors to zero; for this purpose the reference signals are defined as , since the goal is to have as close to zero as possible and

where is the longitudinal velocity of the vehicle, is the wheel base, and is the drivers steering angle command.

For the two input variables, five fuzzy sets with triangular Membership Functions (MFs) were used for each variable: , whereas, for the output variable, seven fuzzy sets also with triangular MFs were used: . Table 4 describes the meanings of the used linguistic terms and Table 5 shows the rules for the proposed FL controller. This FL controller uses a Mamdani Fuzzy Inference System (FIS).

Table 4: Linguistic terms.

NB
Negative big

NMH
Negative medium high

NM
Negative medium

NMS
Negative medium small

NS
Negative small

Z
Zero

PS
Positive small

PMS
Positive medium small

PM
Positive medium

PMH
Positive medium high

PB
Positive big

Table 5: FL inference rules for the braking system.

NB
NS
Z
PS
PB

NB
PB
PB
NS
NB
NB

NS
PB
PM
NS
NM
NB

Z
PM
PS
Z
NS
NM

PS
PB
PM
PS
NM
NB

PB
PB
PS
PS
NS
NB

To allocate the desired output for the braking local controllers, is transformed in terms of ESCs as

where is a parameter that relates the corrective yaw moment () and the brake pressure to be applied by the braking system.

Additionally, the coordinated allocation affects the action of the braking FL controller, including or ignoring it, using the value of as a gain:

(iii) AFS System. For this subsystem the allocation decides to introduce or not the AFS control action, as

where is the desired steering wheel angle, is the driver’s command, and is the compensation angle calculated by the AFS system. From (13), it can be seen that the driver’s command is always considered, but the compensation angle is considered if or not if .

As for the braking system, the steering action is computed using a FL controller [30]. Three input variables were selected: (1) side slip angle (), (2) yaw rate error (), and (3) steering angle input (), and one output: (1) steering correction angle (). The FL controller is oriented to create a steering wheel angle correction that minimizes the yaw rate error; the desired yaw rate is calculated using (10).

For input two fuzzy sets with sigmoid MFs were used: . For the other two input variables, five fuzzy sets with triangular MFs were used: , whereas, for the output variable, eleven fuzzy sets, also with triangular standard MFs, were used . Table 6 shows the rules for the proposed FL controller, whose linguistic definitions are given in Table 4.

Table 6: FL inference rules for the steering system.

NB
NS
Z
PS
PB

Low
NB
NS
NS
Z
PB
PB

NS
NMS
NMS
Z
PMH
PMH

Z
NM
NM
Z
PM
PM

PS
NMH
NMH
Z
PMS
PMS

PB
NH
NH
Z
PS
PS

High
NB
NH
NH
Z
PS
PS

NS
NMH
NMH
Z
PMS
PMS

Z
NM
NM
NS
PMS
PMS

PS
NMS
NMS
NS
NS
NS

PB
NS
NS
NS
NS
NS

3.2.2. Local Controllers

This sublayer contains the local controllers for each subsystem. These controllers are Single-Input Single-Output (SISO) and only interact with their particular subsystem. These controllers receive the desired set-point from the control allocation sublayer and are in charge of executing it. Also, these controllers have to be selected regarding the subsystem to control. The subsystem controllers for this strategy are the following:

(i)SAS: because the control command coming from the allocation step is binary, the force control system is defined as follows:

 where is the manipulation delivered to the SA damper, (i.e., electric current, voltage, and duty cycle).(ii)Steering: the command, in terms of tire angles, to transform it to a single gain controller is

(iii)Braking: the local controller is an ABS; it modifies the desired command as

 where is the driver braking command, is the braking command from the allocation system, and is the gain of the ABS that releases the tire when it is locked. This control law selects the maximum between the command coming from the allocation system and the command from the driver. The gain is obtained by the function

 with

 where is the slip ratio for each wheel. The operation of this ABS controller is guided by ; if grows beyond the admissible range (), the braking system releases the tire until it recovers grip and the slip ratio decreases to the admissible range, where the braking torque is again applied to the tire.

3.3. Physical Layer

The physical layer is integrated by the sensors and actuators of the SAS, AFS system, and 4WIB system.

3.3.1. Suspension System

The suspension system is composed of a linear spring and a SA shock absorber. The key element is the set of SA shock absorber, one at each corner, which needs to be modeled as a function of a manipulation signal (). The damper force () is modeled as a function of the damper deflection (), deflection velocity (), and manipulation signal [31]:

where is the SA force due to , is a viscous damping coefficient, is a stiffness coefficient, and and are hysteresis coefficients due to velocity and displacement, respectively. The SA damping force at each damper is continuous from  N.

3.3.2. Steering System

A steer-by-wire Active Steering (AS) system is used to provide an additional steering angle for corrective purposes; the actuator model is given by [32]

where Hz is the cut-off frequency of the actuator dynamics, is the steering controller output, and is the actuator output; the bounded limits of actuation are [].

3.3.3. Braking System

The corrective front and rear braking torques are provided by brake-by-wire Electromechanical Braking (EMB) actuators; the model of these EMB actuators is given by [32]

where Hz is the cut-off frequency of the actuator dynamics, is the braking controller output, and is the actuator output. The bounded limits of actuation for each braking actuator are  MPa.

4. GCC System Evaluation

The results of this proposal are presented based on a case study.

4.1. Case Study

CarSim was used to generate an accurate vehicle model whose VDC were hosted in Matlab/Simulink. A -class sedan was the selected vehicle. Seven driving situations were considered (). Figure 6 illustrates some of the implemented tests to represent the driving situations; these tests are as follows:

(a)Road profile with bump test: this test is intended to evaluate the road isolation characteristics of the control strategy; it consists in a rough road with a sharp bump of 35 mm height and 400 mm length.(b)Brake distance test: it consists in a hard braking action by the driver to measure the distance that takes the vehicle when it goes from 100 km/h to a full stop.(c)Double Line Change (DLC) maneuver: it consists in a change of driving line to simulate an obstacle avoidance maneuver or an overtaking action at high speed (120 km/h); a rapid steering maneuver is taken by the driver to change from the original line, and then another rapid steering action to turn back to the original line.(d)Fish Hook (FH) maneuver: this maneuver consists in a wide, but constant steering action; first a movement of 270° of the steering wheel is taken to one side at a constant turning rate; then a turn of 540° to the opposite side is executed transferring the vehicle load from one side to another; then the steering angle is held to create a cornering situation which maintains the load transfer at a dangerous limit.(e)Split -surface braking test: the intention of this test is to evaluate how well a vehicle can keep its line during a braking action while riding with different friction coefficients in each side of the vehicle; this test is intended to cause loss of vehicle control from the driver.

Figure 6: Implemented tests in CarSim.

4.2. Decision Layer

For space limitations, the results of the DL are presented just for the rapid steering driving situation.

4.2.1. Classification Algorithm

The set has a cardinality of elements (variables). Table 7 describes the considered variable set. These variables were selected because they describe completely the behavior of the vehicle.

Table 7: IS set.

ID
Variable
Description

1–4

Damper deflection

5–8

Damper deflection rate

9

Pitch

10

Pitch rate

11

Roll

12

Roll rate

13

Yaw

14

Yaw rate

15

Longitudinal acceleration

16

Lateral acceleration

17

Vertical acceleration

18

Vehicle slip angle

19

Vehicle slip angle rate

20

Steering wheel angle

21

Steering wheel angle rate

Figure 7 shows the correlation level among the elements in the set, for the DLC test. Each square represents the level of correlation between two variables; for example, in the grid the principal diagonal shows a correlation of 1 (dark red) because it is the correlation of the variable with itself. A correlation of −1 (dark blue) indicates that the variable has an inverse correlation with the variable in question; for example, variable #1 () has a correlation of 1 with variable #2 () and a correlation of −1 with variable #3 (). The above example can be interpreted as follows: during a roll situation, caused by the steering maneuver, the dampers of the same side (left) have the same compression whereas the dampers of the other side have the same movement, but in the opposite direction. It is notable that there is an inherent correlation among some variables, some of them can be neglected.

Figure 7: Correlation matrix of the set for a rapid steering driving situation.

To find the set for this situation, the PCA algorithm was performed, Figure 8. These results point out that only 4 PC could explain more than 90% of the total variance of the test. Figure 8 demonstrates that when the cumulative variance marker (green line) surpasses the 90% mark (horizontal red dotted line), the number of components is 4.

Figure 8: PCA result for the rapid steering situation.

It is important to relate the result with the set, such that the contribution of each variable to explain the total data variance can be studied in the residual space. Figure 9 shows the contribution of all variables for the DLC test. Those variables that overshoot the threshold (red dotted line) are considered the most representative variables in this driving situation; they integrate the set.

Figure 9: Contribution plot of the variables in the set.

Table 8 presents the PCA results for the seven driving situations. It can be concluded that the minimum set of variables for identifying any driving situation in . Once set is defined, the clustering step runs.

Table 8: PCA results.

ID
Test
of PC
of explained variance
Variables in MS set

1
Ride
7
92.7
8, 12, 14, 17, 21

2
Road irregularity
4
90.2
9, 10, 17

3
Acceleration/braking
4
97.8
5, 6, 7, 8, 10

4
Hard braking
5
97.5
5, 6, 7, 8, 10

5
Cornering
7
93.1
10, 13, 18, 20

6
Rapid steering
4
93.7
10, 13, 15, 21

7
Loss of control
7
92.6
13, 14, 18, 19

A -NN classifier with was trained to classify 4 major driving situations (riding, cornering, rapid steering, and loss of control), where the first four tests in Table 8 are tagged as riding situation. Figure 10 shows the clusters distribution in 2D (pitch angle versus roll rate); note that clusters are differentiated by color. More than one cluster determine one of the four driving conditions: a cornering situation uses two clusters (red and cyan cluster).

Figure 10: Clustering distribution for 2 dimensions.

To evaluate the classifier performance, a test, with a series of different driving situations, was designed. The test begins with the vehicle being driven in a rough road ; afterwards it has a rapid steering maneuver ; once the DLC maneuver passes and the vehicle is stabilized again, the test finishes with a cornering action (, FH maneuver). Figure 11 shows the target as well as the classification result for this test. This test was selected because the two conditions ( and ) are really similar in essence: both include steering action, but the difference lays in the velocity of the steering movement. From Figure 11, it is clear that rapid steering action is well detected by the classifier, but cornering has some drawbacks. During the rapid steering situation, some variables related to the vertical and lateral dynamics are highly sensitive, but during cornering the steady behavior of some movements is misjudged as riding conditions.

Figure 11: Validation test for the -NN classifier.

Figure 12 presents the ROC of the classifier results for the test in Figure 11. The riding situation is well classified, with a false alarm rate of 20%. For the other two situations, the false alarm is zero but the detection error is 10% because of the rapid steering situation, while the cornering condition has the worst identification performance (error of 50%).

Figure 12: ROC for the -NN classifier.

From the previous analysis it can be concluded that the situations that involve roll and yaw movements can be well classified, but other driving situations (road irregularity, acceleration/braking, and hard braking) which are mostly pitch related can not be classified since all other driving situations also involve pitch movement.

To assist the -NN classifier, a Suspension Adjustment Plane (SAP) was designed. SAP studies the vertical load transfer caused by vehicle movements, to adjust the SAS system. Its objective is to select the suspension settings depending on which area of the plane the vehicle is in. For example, if the vehicle is in a frontal pitch situation (braking) the system sets the two front dampers in road-holding mode, since most of the load is transferred to those tires. The same happens with a roll movement where the tires of the same side receive most of the load. The center area (between the red dotted lines) of the SAP is concerned with a normal riding situation. This area was defined by considering different riding conditions (road roughness and velocities). Figure 13 shows the SAP with different driving situations and also the proper suspension combinations are marked for each region. With this plane it is possible to classify which riding situation occurs (riding per se, a road irregularity, an acceleration/braking situation, or a hard braking).

Figure 13: Suspension Adjustment Plane (SAP).

In Figure 13, the dotted lines delimit the threshold for pitch and roll movements caused by road roughness; outside those limits it is considered that the experienced movements are caused by other driving situations. The central vertical zone includes primarily pitch situations, like braking, whereas the horizontal central zone refers to primarily roll movements like cornering.

4.2.2. Decision Logic

Table 9 presents the proposed values for vector at each driving situation.

Table 9: vectors for different driving conditions.

Driving situation

Ride
1
0
0, 0, 0, 0
0
0

Road irregularity
2
0
SAP
0
0

Acceleration/braking
3
0
SAP
0
0

Hard braking
4
0
SAP
0
0

Cornering
5
0
SAP
1
0

Rapid steering
6
1
SAP
1
1

Loss of control
7
1
1, 1, 1, 1
1
1

4.3. Control Layer

The performance of the proposed GCC system is evaluated and compared with two additional control cases. The first case corresponds to an uncontrolled (UC) system; that is, it is a vehicle which lacks any control system and is equipped with standard actuators and a passive suspension system. The second case corresponds to a vehicle with a set of dynamics controllers without a coordination strategy in Decentralized Controllers (DC); that is, a set of controllers are acting simultaneously seeking their own control goals.

To evaluate quantitatively the performance at each driving test, the Root Mean Square (RMS) value of the signals is used. To have a point of comparison the RMS values of the controlled cases (DC and GCC) are normalized with that obtained by the UC case using

4.3.1. Road Profile with Bump Test

For this test, two variables are important: (1) vertical acceleration of the sprung mass (), Figure 14(a), and (2) pitch angle (), Figure 14(b). For the vertical acceleration, Figure 14(a), the GCC system achieves 9.6% of improvement in vibration mitigation when compared with the reference case (UC); on the other hand the DC case achieves 3.11%. During this test the bump it intended to excite the pitch motion of the vehicle, which is also related to the comfort of the passengers, Figure 14(b); the GCC system manages to reduce the pitch motion of the vehicle by 11.7% whereas the DC case achieves 10.8%, both results when compared with the UC case. The main improvement of the control strategy can be seen after the bump (1 second mark); during that transient response the vehicle reaches a stable behavior faster than the reference case.

(a) Vertical acceleration ()

(b) Pitch angle ()

Figure 14: Road profile with bump test.

4.3.2. Braking Distance Test

Two variables are the most important for this test: (1) brake distance, Figure 15(a), and (2) pitch angle , Figure 15(b). Regarding brake distance, the reference case (UC) takes 69 m to fully stop, whereas the controlled cases have improvements of 8.7% for the DC and 14.5% for the GCC, meaning a stop distance of 10 m less than that of the UC case. For the pitch angle, the improvement of the DC against the UC was 6.2%; whereas GCC has an improvement of 10.3%. Also, in Figure 15(b) it can be seen that the GCC has less overshoot and shorter stabilization time. Those oscillations cause loss of grip of the tires and produce uncomfortable movements for the passengers. Even when the improvement indices for both controlled cases are marginal for the pitch angle, the uncomfortable behaviors are successfully attenuated.

(a) Brake distance

(b) Pitch angle ()

Figure 15: Brake distance test.

4.3.3. DLC Test

Figure 16 shows the vehicle trajectory for each case. It can be observed that the GCC has the smallest -coordinate deviation, and also its finish is straight, whereas for the UC the -coordinate deviation is bigger and at the end its path is diverging. The DC has a performance similar to the UC, but at the end the -coordinate deviation is bigger (more negative) than the other cases.

Figure 16: Vehicle trajectory for a DLC test.

After assessing the vehicle trajectory, it is important to analyze the behavior of the related variables to the vehicle stability, such as roll angle (), Figure 17(a), and yaw angle (), Figure 17(b). Figure 17(a) illustrates that the GCC system has less roll movement than the other cases, that is, 10% less than UC; also the roll movement has less duration having a rapid stabilization. For the DC the roll movement is abruptly caused by the lack of coordination of the steering and braking; this causes those oscillations and a deterioration of 8.9% compared to the UC case. In Figure 17(b) also the GCC system has less yaw motion, 12.5% less than the UC, while the DC has a deterioration of 4% compared to the UC case.

(a) Roll angle ()

(b) Yaw angle ()

Figure 17: DLC test.

4.3.4. FH Test

In this test, the evaluation starts with the assessment of the vehicle trajectory. Figure 18 shows the trajectory for the three cases. As it can be seen, the GCC system has a smaller turn radius than the other two cases, especially when compared with UC; this indicates more handling capabilities in GCC. Also, the proposed GCC has a shorter trajectory, which indicates less skidding than other cases.

Figure 18: Vehicle trajectory for FH test.

The significant variables are (1) roll angle (), Figure 19(a), and (2) lateral acceleration (), Figure 19(b). Since the induced cornering situation by the steering movement is really similar regardless of the control system, the important features to study are the transient responses of the variables at the time when the cornering starts and ends. From Figure 19(a) it is evident that in GCC the induced oscillations by the change of load transfer are better absorbed by the suspension system, that is, 7% less oscillations than in the UC case and 3% less than in DC. Regarding lateral acceleration, Figure 19(b), GCC has less oscillations when the change of load takes place, even when the improvement is marginal: 2% with respect to UC. There is no significant improvement with respect to DC.

(a) Roll angle ()

(b) Lateral acceleration ()

Figure 19: FH test.

4.3.5. Split -Surface Test

This test is designed to evaluate the ability of a vehicle to remain in control against a critical situation. It is important to verify how well the vehicle remains in its original path after the braking action starts. Figure 20 shows the trajectory of the three Vehicle Control Systems. The controlled vehicle with GCC remains in straight line during the whole test, whereas UC moves away from the original trajectory. On the other hand, the vehicle with DC also manages to remain close to the straight path.

Figure 20: Vehicle trajectory for Split -surface braking test.

The important variables for this test are (1) steering wheel angle (), Figure 21(a), (2) lateral acceleration (), Figure 21(b), and (3) yaw rate (), Figure 21(c). Figure 21(a) shows that the driver does not affect significantly the steering wheel angle, that is, the GCC and DC approaches can stabilize the vehicle. On the other hand, the UC vehicle begins to lose control and the driver has to make a huge adjustment to try to keep the stability of the vehicle. It can be noticed that the steering allocation system takes action increasing the steering maneuver for DC; this extra movements cause the vehicle to diverge slightly from the original path. The steering action for GCC is 87.9% less than UC vehicle, while DC has 80.6% less movement. Because the lateral acceleration is induced by the steering action, similar results are obtained, Figure 21(b). GCC has 88.7% less lateral acceleration than UC and 10.1% less acceleration than DC.

(a) Steering wheel angle ()

(b) Lateral acceleration ()

(c) Yaw rate ()

Figure 21: Split -surface braking test.

Finally, to evaluate the rotational movements of the vehicle in the road, the yaw rate is analyzed. Figure 21(c) shows that in UC the driver loses completely the vehicle control causing too much yaw motion. GCC has 98% less yaw rate than UC and 96% less than DC.

5. Conclusions

A novel Global Chassis Control system was proposed. It combines fuzzy logic inference systems, data-based logic and heuristic techniques as classifiers, allocation systems, and model-free controllers; also, it takes the advantages of a priori knowledge of a vehicle driving to develop an efficient control strategy. Also, it has the advantage of being modular and computationally light; based on Principal Components Analysis data reduction was applied. Most of the computing is done offline; the onboard systems only execute the classification of the driving situations and calculate the allocation and control procedures.

The evaluation of the strategy was performed with several well-known tests using CarSim. Simulation results showed that the performance of the Global Chassis Control system outperforms the uncontrolled vehicle case and the Decentralized Controllers scheme that do not have coordination features. Qualitative and quantitative results of the evaluation demonstrate the importance of a coordination level when different controllers coexist and interact in an integrated system as a vehicle. Such coordination level consists in a classification algorithm, based on the -Nearest Neighbor clustering technique, supported by a Suspension Adjustment Plane to identify different driving situations.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The authors thank Tecnológico de Monterrey and CONACyT for their partial support through the Automotive Consortium research chair and PCP 03/10 and 06/13 bilateral (México-France) projects.

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