SEMINAR REPORT ON

Submitted by

CHINMAY PAMECHA 2009UME453

in partial fulfillment for the award of the degree

of

BACHELOR OF TECHNOLOGY

IN

MECHANICAL ENGINEERING

AT

MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY JAIPUR

(2009 – 2013)

Submitted to:

Prof. P. K. Saxena Prof. G. Agrawal

Dr. T. C. Gupta

i

SYNOPSIS

Rollover crashes cause more than 10,000 fatalities and nearly 30,000 serious

injuries per year in the U.S. alone. This is due to the fact that the vast majority of

vehicles, including commercial, police, and military, lack the roof strength to preserve

occupant survival space and protect their occupants in a rollover. Recent statistical

and epidemiological studies have shown a significant relationship between roof

crush and injury. This rollover occupant protection problem is well known to

industries with large vehicle fleets; until now, this problem has eluded solution.

Within these various industries a wide variety of rollover occupant protection systems

(ROPS), both internal and external, have been designed, purchased, manufactured,

installed, and maintained locally with little expert consultation. A wide variety of

designs have emerged with an alarming variance in "assumed" crashworthiness.

Couple this alarming trend with the risk of rendering the existing occupant protection

features (e.g., airbags) ineffective, which has resulted in vehicles with inadequate

crashworthiness. This paper describes how rollover damage to a vehicle with a weak

roof and the resulting reduction of occupant headroom can be minimized to an

inconsequential amount using an innovative externally retrofitted rollover load

distribution device. This system was based on an understanding of road crash data,

empirical evidence, and innovative state of the art testing and analysis to provide

effective external ROPS structures for the commercial, police and military fleets.

In this review paper I am presenting a robust controller design methodology

for vehicle rollover prevention utilizing active steering, active suspension, differential

braking, center of gravity estimation and uses of multiple models and controllers.

Control design is based on keeping the magnitude of the vehicle load transfer ratio

(LTR) below a certain level in the presence of driver steering inputs; also an exact

expression for LTR is developed. The proposed controllers have a proportional-

integral structure whose gain matrices are obtained using the results of Pancake,

Corless and Brockman. These controllers reduce the transient magnitude of the LTR

while maintaining the steady state steering response of the vehicle. The controllers

can be designed to be robust with respect to vehicle parameters such as speed and

centre of gravity height. The paper also provides a modification to the controllers so

that they only activate when the potential for rollover is significant. Numerical

simulations demonstrate the efficacy of the approach and the resulting controllers.

A methodology based on multiple models and switching for real–time

estimation of center of gravity (CG) position and rollover prevention in automotive

vehicles is also presented here. Based on a linear vehicle model in which the

unknown parameters appear nonlinearly, a novel sequential identification algorithm

to determine the vehicle parameters rapidly in real time is proposed. The CG height

estimate is further coupled with a switching controller to prevent un–tripped rollover

in automotive vehicles. The efficacy of the proposed switched multi model/controller

estimation and control scheme is demonstrated via numerical simulations.

An anti-rollover control algorithm based on the Time-To-Rollover (TTR) metric

is proposed in this paper. A simple model with steering and direct yaw moment

ii

control inputs was constructed to calculate the TTR in real-time. Numerical

simulations on a nonlinear vehicle model show that both control structures effectively

track the driver intended yaw rate during extreme manoeuvres while also limiting the

peak roll angle. During ordinary driving, the controlled vehicle behaves identically to

an ordinary vehicle. These preliminary results show that for double lane change

manoeuvres, it is possible to limit roll angle while still closely tracking the driver’s

intent.

Also a tilting vehicle technology is described here. Theoretical analysis is

conducted to find “Perfect Tilting Condition” that is a geometric parameter set of link

mechanism that can provide both zero lateral acceleration and zero wheel load

imbalance simultaneously. This perfect tilting condition can be realized by changing

the variable length of link mechanism so that this tilting control system is a kind of

semi active control. To change the length of link mechanism on curved section,

optimal control theory is applied to the vehicle body tilting system with a newly

developed variable link mechanism. From computer simulation and experiment using

a scale model, it is clarified that the proposed tilting system is effective to suppress

both over-centrifugal acceleration and wheel load imbalance.

iii

LIST OF FIGURES Sr. No. Figure No. Caption Page No.

1. 3.1 Positions of the distribution of loads[10]* 7

2. 4.1 Single track model with roll degree of

freedom.[5]

9

3. 4.2 Differential braking force as control input[3] 11

4. 4.3 SimMechanics vehicle model layout[3] 15

5. 4.4 Tire force components[3] 15

6. 4.5 Lateral force as a function of the slip angle for

various vertical loads[3]

15

7. 4.6 Steering wheel input history for simulated ‘Elk-

Test’[3]

17

8. 4.7 LTR comparison for bicycle, SM and linearized

SM models at v=20 m/s and s,max=60 deg[3]

18

9. 4.8 LTR comparison for bicycle, SM and linearized

SM models at v=20 m/s and s,max=80 deg[3]

19

10. 6.1 CG longitudinal position and tire stiffness

estimations[5]

24

11. 6.2 CG height and suspension parameter

estimations[5]

25

12. 6.3 Multiple model switched adaptive control

structure[5]

25

13. 6.4 Steering input and the resulting CG height

estimation[5]

28

14. 6.5 LTRd for the controlled and uncontrolled

vehicles.[5]

29

15. 6.6 Vehicle states for the controlled and

uncontrolled vehicles[5]

29

16. 6.7 Vehicle speed and the normalized control

force[5] 30

17. 7.1 Flow diagram of the PI active steering

controller[7]

35

18. 7.2 Comparison of the controlled (with fixed model)

and uncontrolled vehicles.[7]

37

19. 7.3 Comparison of the controlled (with fixed model)

and uncontrolled vehicle states and

trajectories.[7]

37

*The figure in [ ] denoted references given at the end of the report.

iv

20. 7.4 Comparison of the robustly controlled and the

uncontrolled vehicles (v = 70km/h peak =

150◦, and h = 0.45m).[7]

38

21. 7.5 Comparison of the trajectories and states of

robustly controlled and the uncontrolled

vehicles (v = 70km/h peak = 150◦, and h =

0.45m).[7]

38

22. 8.1 Top row: Vehicle‟s CG drops during rollover

and then rises again;

Bottom row: Hoop maintains vehicle‟s CG at

constant height, thus reducing roof load [1]

40

23. 8.2 Photograph of the major components of the

JRS[1]

41

24. 8.3 HALO™ Prototype 2; No noticeable

deformation to the roof structure[1]

41

25. 9.1 Government vehicle rollover victim David[1] 43

26. 9.2 Government vehicle rollover victim Luis[1] 44

27. 9.3 Military vehicle fleet - U.S. Marine transport

van case study[1]

45

28. 10.1 Rollover Air Bags[14] 47

29. 13.1 Comparison of the trajectories and states of

robustly controlled and the uncontrolled

vehicles (v0 = 140km/h, dpeak = 120◦, and h =

0.375m).[2]

50

30. 13.2 Comparison of continuous and switched robust

controllers at a non critical maneuver (v =

140km/h, dpeak = 50◦, and h = 0.375m) [7]

51

v

LIST OF TABLES

Sr. No. Table No. Title Page No.

1. 4.1 Model parameters and their

definitions[5]

9

2. 4.2 Model parameters [3] 16

3. 4.3 Conditions for wheel lift, |LTRd| = 1

and vehicle rollover [3]

19

4. 7.1 Fixed model parameters [7] 36

5. 8.1 Test results for the HALO™

Prototype 2 [1]

42

vi

CONTENTS: Synopsis……………………………………………………………………………………….i List of Figures………………………………………………………………………………..iii List of Tables…………………………………………………………………………………v 1. Introduction……………………………………………………………………………….1

1.1 Around the world…………………………………………………………………1 1.2 Types of rollovers…………………………………………...............................1 1.3 Control measures………………………………………………………………..2

2. Contributing Causes…………………………………………………………………….4 2.1 The Physical factors……………………………………………………………4 2.2 The Driving factors……………………………………………………………..5 2.3 The human factors……………………………………………………………..5

3. Drivers’ Training…………………………………………………………………………6 3.1 Vehicle Center of Gravity………………………………………………………6

3.2 Load Security…………………………………………………………………….6 3.3 Radius of Curves and Slope of Roadways…………………………………...6

3.4 Vehicle Speed ………………………………………………………………….7

3.5 Trailer towing…………………………………………………………………….7

3.6 Vehicle condition and preparation……………………………………………8

4. Vehicle Modelling and LTRd………………………………………………………………………………………..9

4.1 Vehicle model and control design……………………………………………..9

4.2 The load transfer ratio (LTRd)………………………………………………...11

4.3 Actuators, sensors and parameters…………………………………………13

4.4 A high fidelity non-linear simulation model………………………………..14

4.5 Simulation of SM model………………………………………………………17

5. Vehicle Parameter Identification………………………………………………………20

5.1 Identification of lateral dynamic parameter…………………………………20

5.2 Identification of roll dynamic parameter……………………………………..21

5.3 Numerical Analysis……………………………………………………………22

6. Switching Rollover Controller (Center of Gravity Estimation)………………………24 6.1 Rollover controller based on single model…………………………………26 6.2 Switched rollover prevention…………………………………………………26 6.3 Numerical analysis…………………………………………………………….27 7. Active Steering…………………………………………………………………………..31 7.1 State feedback controller for robust disturbance attenuation…………….31 7.2 Rollover control design………………………………………………………..34 7.2.1 Actual steering PI controller with known parameters……………34 8. ROPS (Rollover Occupants Protection System)…………………………………….39 8.1 The Concept……………………………………………………………………39 8.2 The Apparatus…………………………………………………………………39 8.2.1 The JLS………………………………………………………………39 8.2.2 HALOTM Prototype 2. Development and testing…………………41 9. Case Studies…………………………………………………………………………….43 9.1 U.S. Border Patrol vehicles…………………………………………………..43 9.2 U.S. Marine transport van…………………………………………………….44 10. Global Scenario………………………………………………………………………..46

vii

10.1 ESC (Electronic Stability Control)…………………………………………..46 10.2 Rollover air bags……………………………………………………….........47 11. Indian Scenario……………………………………………………………………….48 12. Future Aspects…………………………………………………………………………48 13. Conclusion……………………………………………………………………………..50 References…………………………………………………………………………………..a Bibliography…………………………………………………………………………………b Annexure…………………………………………………………………………………….c

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1. INTRODUCTION

1.1) Around the world:

It is well known that vehicles with a high center of gravity such as light trucks

(vans, pickups, and SUVs) are more prone to rollover accidents than other types of

passenger vehicles. According to recent statistical data, this class of vehicles were

involved in nearly 70% of all the rollover accidents in the USA during 2004, with

SUVs alone were responsible for about half of this total. The fact that the

composition of the current automotive fleet in the U.S. consists of nearly 36% light

trucks, along with the recent increase in their popularity worldwide, makes rollover an

important safety problem.

Each year in the United States (U.S.), approximately one in every three traffic-

related deaths is the result of a rollover crash. Australia has similar annual statistics;

about one in every four occupant fatalities occurred in vehicles that rolled. In Europe,

around 15% of vehicle occupant fatalities involve some element of a rollover[1]. The

high incidence of rollover crashes have become a concern to global mining and

petroleum companies, U.S. border patrol police and U.S. military personnel because

of occupational health and safety requirements. The vehicle is considered a

workplace environment. Hence, duty of care to provide a safe work environment

extends to employees, police and military personnel travelling in either a company or

government vehicle, including protection in a rollover crash. This is particularly true if

the driver was travelling at the posted speed limit, all occupants were seat belted,

and the crash was not due to driver or occupant error or negligence.

1.2) Types of rollovers:

There are two distinct types of vehicle rollover: tripped and un-tripped[2]. A

tripped rollover commonly occurs when a vehicle slides sideways and digs its tires

into soft soil or strikes an object such as a curb or guardrail. Driver induced un-

tripped rollover however, can occur during typical driving situations and it poses a

real threat for top-heavy vehicles. Examples are excessive speed during cornering,

obstacle avoidance and severe lane change manoeuvres, where rollover may occur

as a direct result of the lateral wheel forces induced during these manoeuvres.

Rollover has been the subject of intensive research in recent years, especially by the

major automobile manufacturers, and the majority this work is geared towards the

development of rollover prediction schemes and robust occupant protection systems.

While robust active rollover control systems achieve the goal of preventing this type

of accidents, such a control approach may be too conservative, and it can potentially

compromise the performance of the vehicle under noncritical driving situations. It is

however, possible to prevent rollover accidents in an effective and efficient manner

by continuously monitoring the car dynamics and applying the proper and sufficient

control action to recover handling of the vehicle in emergency situations.

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1.3) Control measures:

The height of CG along with the lateral acceleration are the most important

parameters affecting the rollover propensity of an automotive vehicle; while the

former is available as part of standard sensor packs, the CG height can not be

measured directly. With this background in mind, we first propose our CG estimation

method based on multiple models, and then use the technique in designing a

switching rollover controller. As part of the feedback implementation we utilize

multiple simplified linear models, which are parameterized to cover uncertainty in the

vehicle parameters. Switching between these models yields a rapid estimation of

unknown and time-varying vehicle parameters through the selected models, which is

then used to switch among a set of suitable controllers in order to improve the

performance of active rollover mitigation systems[4].

Our motivation for considering a switching controller implementation is

twofold. Firstly, switching controllers are the alternative option to the robust ones and

they can potentially provide higher performance. Robust controllers have fixed gains

that are chosen considering the worst-case that the plant undergoes; for the rollover

problem, the worst operating condition translates to operating the vehicle with the

highest possible CG position[3]. While choosing the controller gains for the worst-

case guarantees the performance (i.e., safety) under the designed extreme

operating condition, the feedback performance of the robustly controlled systems

under less severe or even normal operating conditions are suboptimal. Our second

motivation is related to the time constant of rollover accidents, which is on the order

of seconds. While conventional adaptive controllers are known to have slow

convergence rates and large transient control errors when the initial parameter errors

are large (a factor that renders these control approaches unsuited for use in rollover

mitigation applications), utilization of MMST type algorithms may overcome these

problems and provide high performance adaptive controllers. Therefore, when

improving the controller performance and speed for the rollover problem is

considered, MMST framework come an ideal choice as it can provide rapid

identification of the unknown parameters as part of the closed loop implementation.

This way we can rapidly switch to a controller that is more suitable for the vehicle

operating conditions, thus improving the overall safety of the vehicle without

sacrificing its performance.

In this paper a robust rollover prevention controller design methodology based

on differential braking is also presented. The proposed control design is an

application of recent results on the design of control systems which guarantee that

the peak values of the performance outputs of a plant do not exceed certain

thresholds when subject to bounded disturbance inputs. The main selected

performance output for the rollover problem is the Load Transfer Ratio LTRd. This

measure of performance is related to tire lift-off and it can be considered as an early

indicator of impending vehicle rollover[5]. The paper also includes the braking force

as a performance output to take into account limitations on the maximum braking

force. The aim of our control strategy is to maximize the magnitude of the allowable

disturbance inputs which do not drive the performance outputs outside their

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prespecified limits; in this case the disturbance input is the driver steering input. We

also want to guarantee robustness with respect to the parameter uncertainty that

arises from changing vehicle speed. We indicate how our design can be extended to

account for other sources of uncertainty such as unknown vehicle center of gravity

and tire stiffness parameters.

In terms of serious injuries, the National Highway Traffic Safety Administration (NHTSA) estimates around 24,000 serious injuries occur in approximately 273,000 rollover crashes. Recent work by Mandell et al investigated the Crash Injury Research Engineering Network (CIREN) database and the National Automotive Sampling System (NASS) CDS database for belted, adult (older than 15 years), outboard occupants in rollover crashes from 1999 to 2009. They used a logistic regression to establish a relationship between roof crush magnitude and severe-to-fatal (AIS≥3) injury. They found that the risk of mortality, traumatic brain injury, spine, and spinal cord injury increased with increasing roof crush. For spine injury, increased risk was observed when roof crush exceeded 3 inches (8 cm).

The relationship between roof deformation and serious injury in rollovers was

also investigated by Rechnitzer and Lane in 1994. Their study of Australian crashes

concluded that roof crush was a significant factor in serious-to-fatal injury occurrence

in rollovers. It is worth noting that rollover crashes are the leading cause (17%) of

spinal cord injury in Australia.

A retrofitted structural system that distributes roof loads and can minimize roof

crush during a rollover crash will best protect occupants. In order to distribute the

roof loads the geometry of the roof structure must be changed. This paper extends

the work of Grzebieta et al (2009). The hypothesis was that loads applied to the roof

structure and hence roof crush and injury risk can be reduced by reinforcing the roof

structure of a weak roof vehicle. The authors showed this using the “proof of

concept” device (HALOTM prototype 1)[1], a hoop mounted to an external frame to

hold the vehicle up as it rolls from one side of the roof to the other, thus changing the

geometry[1]. Results from the production vehicle and HALOTM Prototype 1 are

presented in Grzebieta et al (2009). This paper provides further proof of this concept.

The evolution of the HALOTM prototype 1 into the current HALOTM rollover load

distribution device is described, including the design, construction, and JRS testing

of 3 prototypes. A dolly rollover test of a HALOTM prototype is also presented here.

The innovative HALOTM rollover load distribution device was designed for and is well

suited for the Commercial, Police, and Military Vehicle fleets.

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2. CONTRIBUTING CAUSES

Vehicles can roll over in several ways. These include excessive cornering

speed, tripping, collision with another vehicle or object, or traversing a critical slope.

Rollovers caused by excessive cornering speed occur when cornering forces

destabilize the vehicle. As a vehicle rounds a corner, three forces act on it: tire

forces, inertial effects, and gravity. The cornering forces from the tire push the

vehicle towards the center of the curve. This force acts at ground level. The force of

inertia acts horizontally through the vehicle's center of mass in the direction opposite

to the one it is turning. These two forces make the vehicle roll towards the outside of

the curve. The force of the vehicle's weight acts downward through the center of

mass in the opposite direction. When the tire and inertial forces are enough to

overcome the force of gravity, the vehicle starts to turn over. Most passenger

vehicles will slide or spin before this happens, but this is a common type of rollover

for taller vehicles, including light trucks (SUVs, vans and pickup trucks), buses, and

heavy trucks[9].

A vehicle may perform a complete rollover, rolling onto its side, roof, far side

and finally ending up on its wheels again, or even going on to roll further.

Tripping rollovers occur when a vehicle is sliding sideways, and the tires strike

a curb, dig into soft ground, suddenly regain traction, or a similar event occurs that

results in a sudden lateral force. The physics are similar to cornering rollovers.

A collision with another vehicle or object can cause a rollover. These occur

when the collision causes the vehicle to become unstable, such as when a narrow

object causes one side of the vehicle to accelerate upwards, but not the other,

causing the vehicle to rotate along its long axis. A side impact can accelerate a

vehicle sideways. The tires resist the change, and the coupled forces rotate the

vehicle. In 1983, crash tests showed that light trucks were prone to rolling over after

colliding with certain early designs of guide rail.

A rollover can also occur as a vehicle crosses a ditch or slope. Slopes steeper

than 33 percent (one vertical unit rise or fall per three horizontal units) are called

'critical slopes' and often contribute to rollovers.

A vehicle may roll over for other reasons, such as when hitting a large

obstacle with one of its wheels or when manoeuvring over uneven terrain.

These factors can be listed as follows[8]:

2.1) The Physical factors:

The arc of the curve and the bank of the roadway.

Steepness of the crown of the road.

Liquid sloshing: worst case liquid sloshing occurs when tankers are filled

to 40-70% capacity, and the tanker is not equipped with baffles.

Speed at which you enter the curve or ramp.

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You need friction to turn: pavement friction generated by truckes is less

than that generated by a passenger car, but the effective friction demand

for trucks is higher.

High crosswinds.

2.2) The Driving factors:

Tight radius turns.

Short deceleration lanes preceding tight radius exits.

Curbs on the outside of curves.

Downgrades leading into ramps.

Unrealistic speed limits for ramps off of high speed highways.

Curves with a negative bank (usually for drainage purposes).

Tripping.

Traversing a critical slope.

Collision with another vehicle.

2.3) The Human factors:

Driver fatigue.

Driver inexperience in transporting loads with a high center of gravity.

Drifting off the road, then quickly counter-steering.

Failure to anticipate sharp ramp or curve.

Entering a turn or ramp too fast.

Driver distraction.

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3. DRIVERS’ TRAINING

Start by training your drivers in the six important factors that can affect vehicle

stability. These six factors are[10]:

3 Vehicle Center of Gravity.

4 Load Security.

5 Radius of Curves and Slope of Roadways.

6 Vehicle Speed

6.2 Adjusted to environmental/road conditions.

7 Trailer Towing.

8 Vehicle Condition and Preparation.

* Should wear Safety Belts.

Vehicle control factors:

3.1) Vehicle center of gravity:

The height of a vehicle's center of gravity and the length of the

wheelbase determine the vehicle's stability.

3.2) Load security:

Improperly secured loads can change a vehicle's center of gravity and

its stability. Bulk tank trucks are inherently less secure because fluids can

surge when trucks brake or go around curves, thereby altering the center of

gravity. Also, a vehicle loaded with containers will have a higher center of

gravity. Additionally, it is important that payloads are secured as closely as

possible to the lateral centerline of the truck or trailer bed. If the payload is

not centered properly, the vehicle stability will not be equivalent when turning

to both the right and left. (see fig 3.1).

3.3) Radius of curves and slope of roadways:

These are important because they generate a centrifugal force that

acts sideways on the vehicle, thereby decreasing vehicle stability.

Figure 3.1 (a)

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3.4) Vehicle speed:

As the vehicle's speed increases, the centrifugal force, or sideways

force increases. Faster speeds also result in decreased driver response

times. Speed is the factor over which the driver can exercise the most

control. When maneuvering through curves or sudden traffic situations, a

vehicle with a high center of gravity can easily turn over.

Speed is even more important when the movement of liquid cargo is "in

phase" with the vehicle's maneuver. If the liquid is on one side during the first

curve, then shifts to the other side during the next curve, the liquid is

positioned to shift back to the first side with four times the side force it had

during the initial curve.

Sudden vehicle maneuvers are especially risky because the combination of

speed and load shift makes the vehicle unstable.

3.5) Trailer towing:

Vehicles towing trailers are much more prone to roll over, especially in

curves and during sudden steering maneuvers, as a result of the exaggerated

motion of the trailer.

Figure 3.1 (b)

Figure 3.1 (c)

Figure 3.1 – Positions of the distribution of loads [10]

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3.6) Vehicle condition and preparation:

It is critical the vehicle is in good operating condition before starting

your mission, with particular attention paid to the tires’ condition and air

pressure.

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4. VEHICLE MODELLING AND LTRd

In this section we introduce the model that we use for controller design. We

define the rollover detection criterion LTRd and present the assumptions on the sensors and actuators used in the design. We also present the higher fidelity nonlinear multi-body simulation model to which the controllers will be applied. For related notation, refer to Table 4.1.

Table 4.1: Model parameters and their

definitions [5]

Parameter

m Description

vehicle mass Unit

[kg] v vehicle speed [m/s]

Jxx

Jzz roll moment of inertia at CG

yaw moment of inertia at CG [kg · m2]

[kg · m2] a longitudinal CG position w.r.t. front axle [m] b longitudinal CG position w.r.t. rear axle [m] T vehicle track width [m] h distance of CG from roll axis [m] c

k

Cα , f

suspension damping coefficient

suspension spring stiffness

linear tire stiffness for front tire

[N · m · s/rad ]

[N · m/rad]

[N/rad] Cα ,r linear tire stiffness for rear tire [N/rad]

δ steering angle [deg] δs steering wheel angle [deg] λs steering ratio

4.1) Vehicle Model for Control Design[5]:

We use a linearized vehicle model for control design. Specifically, we consider the well known single-track bicycle model with a roll degree of freedom as illustrated in Figure 4.1. In this model the steering angle δ, the roll angle φ and the vehicle sideslip angle β are all assumed to be small. We further assume that all the vehicle mass is sprung, which implies insignificant un-sprung mass. The lateral forces on the front and rear tires, denoted by Fy, f and Fy,r, respectively, are represented as linear functions of the tire slip angles α f and αr , that is, Fy, f = Cα, fαf and Fy,r = Cα,rαr , where Cα, f and Cα,r are the front and rear tire stiffness parameters, respectively.

Figure 4.1: Single track model with roll degree of freedom. [3]

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Jx xx 2

In order to simplify the model description, we further define the following auxiliary

variables

(1)

where the lengths a and b are defined in Figure 4.1. For simplicity, it is assumed that,

relative to the unsprung mass, the sprung mass rolls about a horizontal roll axis

which is along the centerline of the unsprung mass and at ground level. Using the

parallel axis theorem of mechanics, Jxeq , the moment of inertia of the vehicle about

the assumed roll axis, is given by

Jxeq = Jxx+mh2, (2)

where h is the distance between the vehicle center of gravity (CG) and the assumed

roll axis and J xx is the moment of inertia of the vehicle about the roll axis through

the CG. Introducing the state x = [ β ψ̇ φ̇ φ

T ], where ψ˙ is the yaw rate of the

unsprung mass, the motion of this model can be described by

x = Ax+Bss+Buu (3)

where,

(4)

where the steering wheel angle δs is the steering input applied to the steering wheel

(in degrees) and λ s is the steering ratio between the steering wheel input and the

steering angle δ of the front wheels.

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In the model u represents the total effective differential braking force acting on

the wheels about the vertical axis. This force is parallel to the road, and it is positive

if the effective braking is on the right wheels and negative if the effective braking is

on the left wheels. Differential braking force as the control input is depicted in Fig.

4.2. In order to model the change in the vehicle longitudinal speed as a result of

braking, we assume that the longitudinal wheel forces generated by the engine

counteract the rolling resistance and the aerodynamic drag at all times. Under this

assumption, the vehicle speed is approximately governed by

(5)

Figure 4.2: Differential braking force as control input [3]

4.2) The Load Transfer Ratio, LTRd:

Traditionally, as discussed in the related work section, some estimate of the

vehicle load transfer ratio has been used as a basis for the design of rollover

prevention systems. The load transfer ratio (Odenthal et al., 1999; Kamnik et al.,

2003) can be simply defined as the load (i.e., vertical force) difference between the

right and left wheels of the vehicle, normalized by the total load (i.e., the weight of

the car)[4]. In other words,

(6)

Clearly, this quantity varies between −1 and 1, and for a perfectly symmetric

vehicle that is driving in a straight line, it is zero. The extrema are reached in the

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case of a wheel lift-off on one side of the vehicle, in which case the load transfer ratio

is 1 or −1 depending on the side that lifts off. If roll dynamics are ignored, it is easily

shown (Odenthal et al., 1999) that the corresponding load transfer ratio (which we

denote by LTRs) is approximated by

(7)

where ay is the lateral acceleration of the CG and T is the vehicle track width. Note

that rollover estimation based upon (7) is not sufficient to detect the transient phase

of rollover (due to the fact that it is derived ignoring roll dynamics). In (Solmaz et al.,

2006) we obtain an exact expression for the vehicle load transfer ratio which does

not ignore roll dynamics; we denote this by LTRd. To aid exposition we repeat the

derivation here. Recall that we assumed the un-sprung mass weight to be

insignificant and the main body of the vehicle rolls about an axis along the center line

of the track at the ground level. We can write a torque balance for the un-sprung

mass about the assumed roll axis in terms of the suspension torques and the vertical

wheel forces as follows:

(8)

Now substituting the definition of load transfer from (6) and rearranging yields the

following expression for LTRd:

(9)

In terms of the state, LTRd can be represented by the following relationship:

(10)

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4.3) Actuators, sensors and parameters:

We are interested in control design based on differential braking. Active

braking actuators are already available in many modern production cars that are

equipped with systems such as ABS (Anti-lock Braking System) and EBS (Electronic

Brake System) or similar systems, which are capable of selectively braking each of

the wheels. The fact that control designs using these actuators can be

commissioned without much financial overhead makes them the preferred actuator

candidates in the literature.

We also assume full state feedback information for the design of the

controllers and that all the model parameters are known. This is an unrealistic

assumption; however, our control design is easily extended to account for

uncertainty in these parameters. As a side note, although we assumed all the vehicle

model parameters to be known, it is possible to estimate some of these that are fixed

(but unknown) using the sensor information available for the control design

suggested here; this however is outside the scope of this work.

Actuators: Rollover prevention techniques may rely on several actuation

mechanisms including active steering, active suspension, active roll stabilizer bars

and differential braking. Among these techniques, differential braking systems can

be found in almost every class of passenger vehicles through ABS (Anti-lock Braking

System) and thus it has been used extensively for rollover prevention. It is the most

effective way to manipulate the tire forces, and it is the only one that can reduce the

vehicle longitudinal speed among the afore-mentioned actuator types. Although the

switching rollover controller to be described in this paper can easily be extended to

other types of actuators, differential braking will be adopted in the sequel.

Parameters: We assume that vehicle mass m is known, which can be estimated as

part of the braking system. Furthermore Cv,Ch, lv, k, c and h are all assumed be

unknown parameters of the vehicle and are estimated through the multiple model

identification algorithm. We further assume that these parameters vary within certain

closed intervals Cv ∈ Cv, Ch ∈ Ch, lv ∈ Lv, c ∈ C, k ∈ K and h ∈ H, and these

intervals can be found via accurate numerical simulations as well as field tests.

Sensors: A sensor (also called detector) is a converter that measures a physical

quantity and converts it into a signal which can be read by an observer or by an

(today mostly electronic) instrument. Devices which provide an input function to a

measurement device or control circuit are called sensors because they "sense" a

physical change in some characteristic such as temperature or displacement. Any

physical change is converted into an electrical signal corresponding to the

measurement.

P a g e | 14

4.4) A high-fidelity nonlinear simulation model:

Although we base control design on the linear bicycle model, controller

evaluation is carried out on a higher fidelity nonlinear simulation model of a vehicle

which we call the SimMechanics Vehicle Simulation Model (SM). This model is

created using the multi-body simulation package SimMechanics which is integrated

into Mathworks’s Matlab/Simulink. This is convenient for using various analysis tools

in Matlab[3].

In general, a Simechanics model consists of bodies connected together by

various joints and subject to various forces. Our SM model consists of six un-sprung

bodies (four wheels and two axles) of negligible mass and one sprung body as

shown in Figure 4.3. Between the sprung mass and each of the axles, there is a joint

which permits a roll degree of- freedom (DOF); the location of these two joints

defines the body roll axis. At each of these roll joints there is a torsional spring and

damper between the sprung mass and the corresponding axle; this models the

vehicle suspension. Connected to each axle are left and right wheels, with the front

wheels having a yaw DOF relative to the front axle to allow for a steering angle,

whereas the rear wheels are rigidly fixed to the rear axles. Each wheel has a contact

point where longitudinal, lateral and vertical tire forces are applied. These contact

points can leave the ground allowing the vehicle to roll over. This is a nonlinear

model in which any or all wheels can leave the ground and can be used to simulate

rollover.

The tire force model used here is based on the Magic Formula model

developed by Pacekja. This model captures the nonlinear characteristics of the tire

forces at large sideslip angles and the effect of the vertical tire force Fz on the lateral

tire force Fy; see Figure 4.4 for an definition of the tire force components. With zero

longitudinal force Fx, the vertical force depends on the vehicle loading and motion.

the lateral force is a function of the vertical force, the tire slip angle α, tire lateral

stiffness and the friction coefficient between the tire and ground, as described by the

Magic Formula model. Figure 4.5 shows the lateral force as a function of slip angle

for various vertical forces (with fixed tire stiffness and friction co-efficient),

demonstrating the non-linearity of the Magic Formula function. Note that the peak

lateral force and the saturation slip angle are functions of the vertical force.

The introduction of a longitudinal force Fx acting on the tire due to braking and

acceleration makes it necessary to consider the limitations of the combination of

lateral and longitudinal forces acting on the tire at the same time. The physical

limitation on the forces applied to the tire are determined by the ground/tire

longitudinal and lateral friction coefficients μx and μy, resulting in a friction ellipse of

longitudinal and lateral forces. In the case where the longitudinal and lateral friction

coefficients are equal (μ x = μy = μ), the friction limit results in a friction circle which

bounds the available lateral and longitudinal forces:

(11)

P a g e | 15

Figure 4.3: SimMechanics vehicle model layout [3]

Figure 4.4: Tire force components [3]

Figure 4.5: Lateral force as a function of the slip angle for various vertical loads [3]

P a g e | 16

Table 4.2: Model parameters [3]

Our model takes this constraint into account. The effects of camber on the tire result

in an equivalent slip angle (αeq) instead of the true tire slip angle (α), reducing the

lateral forces that can be generated by the tire. These corrections need to be taken

into consideration as the tire camber varies as with the wheel roll angle during

rollover events. The linear tire lateral stiffnesses used in the bicycle model are

equivalent to the ‘effective axle cornering stiffness’ of the SM model defined by

Pacejka. The effective axle stiffnesses are defined as the ratio of the lateral force to

virtual slip angle for each axle i in a steady state turn, where i is either the front or

rear axle.

(12)

To ensure that the linear tire characteristics are captured, the effective axle

stiffnesses have to be calculated from the SM model in a steady state turn at low

speeds to ensure that linear characteristics are captured.

Since the SM model is sprung at both front and rear axles, the overall

suspension roll stiffness and damping is split between front and rear by the roll

stiffness ratio KF and the roll damping ratios CF. This distribution highly affects the

handling behaviour of the vehicle from under-steer to over-steer. In order to achieve

maximum cornering ability by reducing under-steer without inducing over-steer (and

thus maximizing rollover propensity), the stiffness and damping ratios are set to 60%

front bias.

Furthermore the limitations of the friction circle on the tire forces necessitates

the use of a brake bias between front and rear braking forces to minimize the case of

wheel lockup without utilizing the maximum braking force available. Although

longitudinal load transfer during braking would vary the sizes of the friction circles,

we consider the case of a static brake bias tuned to achieve maximum braking force

initially for a range of constant lateral accelerations, and this is set to 55% front bias.

P a g e | 17

4.5) Simulation of the SM model

For comparison purposes, the sprung mass of the SM model is set equal to

that of the bicycle model, while the un-sprung masses set are very small; they are

non-zero to prevent numerical singularities in the simulation. Furthermore, the

bicycle model assumes that the roll center is on the ground plane, thus the roll center

height of the SM model is set to be on the ground. The primary set of simulation

parameter values used are as defined in Table 4.2, with parameters representative

of a typical commercial van[11].

The vehicle is subjected to an ‘elk-test’ maneuver with steering wheel input

profile as illustrated in Figure 4.6. The simulated ‘elk-test’ response of the linear

bicycle model is compared with the response of both the nonlinear SM model and a

linearization of the SM model generated via MATLAB’s model linearization command

‘linearize.m’. At a speed of 20 m/s (72 kph) with a peak steering wheel angle of δ

s,max = 60 deg, Figure 4.7 demonstrates that the linearized dynamics of the SM

model agree that of the bicycle model. However this also demonstrates the limitation

of the linear bicycle model as a tool for prediction of rollover as it does not consider

the saturation of lateral tire forces. As the maximum steering input is increased to δ

s,max = 80 deg (Figure 4.8) the differences between the linear bicycle model and the

nonlinear SM model becomes even more apparent. The nonlinear SM model exhibits

a significantly lower peak LTR compared to the linear models when large steering

inputs are applied or when the initial velocity of the vehicle is large.

Figure 4.6: Steering wheel input history for simulated ‘Elk-Test’ [3]

P a g e | 18

Figure 4.7: LTR comparison for bicycle, SM and linearized SM models at v=20 m/s and s,max=60 deg[3]

Further simulations with the SM model show that with large steering inputs

and speeds the vehicle does roll over, which confirms the necessity for control

systems to prevent such phenomenon. The SM model can be used to determine the

conditions of steering input and speed which result in untripped rollover for a vehicle

with parameters given in Table 4.2. One of the distinctions that the SM model is able

to provide over the linear bicycle model is that wheel liftoff and rollover are not

equivalent. In Table 4.3 the vehicle is tested at initial longitudinal velocities of 20, 30

and 40m/s. The steering input to lift a single wheel off the ground is denoted by δ s,li

f t , whereas the input to drive the magnitude of LTRd to one is given by δs,maxLTR.

The third column of results shows δs,roll , or the steering input needed to induce

untripped rollover.

P a g e | 19

Figure 4.8: LTR comparison for bicycle, SM and linearized SM models at v=20 m/s and s,max=80 deg[3]

Table 4.3: Conditions for wheel lift, |LTRd| = 1 and vehicle rollover[3]

P a g e | 20

5. VEHICLE PARAMETER IDENTIFICATION

The problem in hand is to determine the vehicle parameters that have been

described in the previous section. While linear regression techniques, including least

squares identification can be tried, such methods require persistently exciting input

signals, which might impose unrealistic and dangerous maneuvers. Moreover, note

that the linear model introduced in Section II is nonlinear in the unknown vehicle

parameters further complicating the formulation of the estimation problem using the

traditional approaches. Thus, there is a need for alternative techniques for vehicle

parameter identification, which imposes no restriction on the driver input, has fast

convergence rates and requires minimum additional output information

(sensors)[12].

With the above motivation in mind, we now introduce our multiple model

based identification algorithm to determine the unknown vehicle parameters rapidly

in real–time. To this end, a first step approach would be to setup the multiple

identification models using (4) with u = 0. However in this case, the resulting

parameter space will be too complex to handle. Instead we adapt a modular

estimation strategy of decoupling the vehicle dynamics into subsystems by assuming

a weak relationship from the roll dynamics onto the lateral.

5.1) Identification of lateral dynamics parameters:

The identification of the longitudinal CG location lv and the lateral tire stiffness

parameters Cv,Ch makes use of the yaw–rate equation in (4), i.e.,

(13)

Define the filtered signals

(14)

Where λ1 < 0. By following the standard arguments in identification, (13) can be

rewritten as:

(15)

Where represents the parameter vector, from which the vehicle

parameters can be determined as follows:

P a g e | 21

(16)

The multiple model based identification algorithm to determine the longitudinal

CG location lv and the tire stiffness parameters Cv,Ch assumes that each unknown

parameter belongs to a closed interval such that Cv ∈ Cv, Ch ∈ Ch, and lv ∈ Lv.

These intervals are divided into certain number of grid points that can be

represented as Cv = {Cv1 ,Cv2 ,Cv3 , . . . ,Cvp}, Ch = {Ch1 ,Ch2 ,Ch3 , . . . ,Chq},

and Lv = {lv1 , lv2 , lv3 , . . . , lvr} with dimensions p, q and r, respectively. These grid

points form the p×q×r fixed identification models. Additionally, we employ one free

running adaptive model, and one re–initialized adaptive model. The identification

error, ei, corresponding to the ith model is defined as,

(17)

where θi denotes the parameter of the i–th model. The vehicle parameters are

estimated as the parameters of the i*–th model,

(18)

Where Ji(t) is the cost corresponding to the ith identification error,

(19)

In (19), _c and _c are non–negative design parameters controlling the relative

weights given to transient and steady state measures respectively, whereas _c is the

non–negative forgetting factor.

5.2) Identification of roll dynamics parameters:

Given the vehicle lateral dynamics parameters, l*v, C*v , and C*h, we now

proceed to determine the suspension parameters k, c and the CG height h by

utilizing the roll dynamics equation in (4) which is given below,

(20)

Where the auxiliary input signal is given by,

P a g e | 22

(21)

We further define the filtered signal as

(22)

where λ2 < 0. Hence, the roll–rate equation (20) can be parameterized as,

(23)

Where represents the parameter vector. The vehicle parameters

suspension parameters and the CG height are related to as follows:

(24)

Analogous to the lateral vehicle parameter estimation, each unknown

parameter belongs to a closed interval such that h ∈ H, k ∈ K, and c ∈ C. These

intervals are divided into sufficient number of grid points and are represented as H =

{h1, h2, h3, . . . , hp}, K = {k1, k2, k3, . . . , kq}, and C = {c1, c2, c3, . . . , cr} with

dimensions p, q and r respectively. Hence we employ these p×q×r fixed models

together with one free running adaptive and one re–initialized adaptive model in the

multiple model extension. Once again, the identification error, ¯ei, corresponding to

the ith model is defined as,

(25)

where i denotes the parameter of the i–th model. Subsequently, one can

compute the associated cost value (19) corresponding to each identification error

(25). Finally, the model that is obtained from (18) yields the roll–plane parameters,

including the CG height and suspension parameters.

5.3) Numeric Analysis:

In this section, we combine the identification schemes described above as a

two step algorithm, whose first step estimates the lateral vehicle parameters Cv, Ch

and lv at each instant, and passes these values to the second step in which we

determine the suspension parameters c, k and the center of gravity height h.

Now we investigate whether the multiple model scheme using the proposed

two step algorithm has any advantages over the same two step algorithm that

employs conventional type adaptation. To this end, suppose we choose the vehicle

parameter grid points for the fixed candidate models for the lateral dynamics as lv ∈

P a g e | 23

{1.01, 1.11, . . . , 1.61}, Cv ∈ {57600, 60100, 62600}, and Ch ∈ {87600, 90100,

92600}. Similarly, we choose grid points for the fixed candidate roll plane models as

h ∈ {0.5, 0.52, . . . , 0.84}, k ∈ {35500, 36100, 36700}, and c ∈ {4760, 5010, 5260}.

We note that the simulated reference vehicle parameters of h∗ = 0.51, k∗ = 36000,

c∗ = 5000, l∗ v = 1.2, C∗ v = 60000, C∗ h = 90000 are not in the fixed candidate

model parameter set. As shown in Figs. 3–4, the free running adaptive model that is

initialized to the lower bounds of the intervals does worse than the proposed

adaptive multiple model identification algorithm. In particular, we observe that the

free running adaptive model can have a significant transient estimation error.

P a g e | 24

6. SWITCHING ROLLOVER CONTROLLER

(CENTER OF GRAVITY ESTIMATION)

We now combine the multiple model identification scheme discussed in the

previous section with a paired set of controllers in order to improve the performance

of active rollover mitigation systems. The controller design described in the sequel is

based on differential braking actuators only; however, the results can be extended to

other actuator types such as the active steering and active/semi-active suspension

with ease.

We emphasize that for the rollover prevention problem a single robust control

mechanism may be designed for the worst case scenario, i.e., for the highest

possible CG height. While such a strategy makes sense, in that, safety comes first in

rollover prevention, it also takes away from performance considerably as the

controller will always be on. In order to possibly reduce the degradation in system

performance while still preventing rollover, we therefore propose the multi

model/controller implementation shown in Figure 5. Before we synthesize a paired

set of controllers corresponding to each CG height configuration, we discuss the

design of a single rollover controller.

Figure 6.1: CG longitudinal position and tire stiffness estimations. [5]

P a g e | 25

Figure 6.2: CG height and suspension parameter estimations [5]

Figure 6.3: Multiple model switched adaptive control structure [5]

P a g e | 26

6.1) Rollover controller based on a single model:

Due its simplicity and its adequate performance in rollover prevention, we

adopt a proportional feedback controller of the form,

(26)

where ay = vx(β + Ψ˙ ) is the measured lateral acceleration, and the feedback gain K0

is chosen to maximize some system performance criterion. Suppose that the CG

height h0 is known. In this paper, we use the single track model with roll degree of

freedom in (4) to choose the feedback gain, K0, such that the peak value of LTRd is

below some pre–specified level. In other words, we want to keep

(27)

for the largest possible steering inputs, which is equivalent to keeping all four wheels

in contact with the road and thus preventing rollover. This design is done such that

(27) is satisfied for a given maximum speed vmax and a given maximum steering

input _max . This in turn will guarantee that |LTRd| ≤ 1 for all |_| < |_max| and v <

vmax corresponding to the CG height h0. In this respect, u = K0ay is a robust

controller for all CG height h ≤ h0 as well.

Comment: Note that a disadvantage of the controller designed as above is

that it is always active. In other words, it will always attempt to limit the LTRd, even in

non-critical situations, thus potentially interfering with, and annoying the vehicle

driver. It therefore makes sense to activate the controller in situations only when the

potential for rollover is significant. One can limit this by putting a threshold output for

the activation of the controllers. Since the system output considered here is the

lateral acceleration, we adopt the following rule for activating the switched

controllers.

(28)

Where LTRthr is a positive threshold that depends on the vehicle type and

parameters (for the simulations of this paper, LTRthr = 0.6 has been used).

6.2) Switched Rollover Prevention:

In the proposed multiple model/controller architecture shown in Figure 5, n

identification models are paired up with n locally robust controllers. For each

combination of h ∈ {h1, . . . , hp}, k ∈ {k1, . . . , kq}, and c ∈ {c1, . . . , cd}, a paired

local controller Ci ∈ {C1,C2, . . . ,Cn} is designed as discussed above; hence we

have,

(29)

P a g e | 27

which yields higher performance for the current values of h, k, and c. In the

execution of the proposed rollover scheme, the best model is identified based on the

2nd order roll plane model (20) and the corresponding controller Ci is used in rollover

prevention.

6.3) Numerical Analysis:

In this section, we investigate the performance of the CG estimation

algorithm, and its application in rollover prevention. The simulation results to be

presented assume the set of synthetic parameters given in Table 4.1. In the

numerical simulations we assume that the lateral vehicle parameters lv, Cv, Ch are

fixed and known, but roll dynamics parameters k, c, h are unknown. The rationale for

this is twofold; firstly it reduces the controller implementation complexity, thus helping

with exposing the benefits of the control approach discussed in this paper. Secondly,

the major parameters affecting roll dynamics behaviour are k, c and h, which

necessitates continuous monitoring of these parameters in rollover situations,

whereas the estimation of the lateral dynamics parameters can be achieved during

normal driving conditions, long before a rollover situation is likely to occur at freeway

speeds. With these in mind, we use the same fixed candidate model set as in

Section III-C. We emphasize that he simulated vehicle roll dynamics parameters of

h∗ = 0.51, k∗ = 36000, c∗ = 5000 are not in the fixed candidate model parameter set.

Motivated by the ease of exposition, we further assume that controller switching is

based on the estimated CG height only.

For the design of local controllers, we assume a peak vehicle speed of vmax =

30[m/s] (i.e. 108[km/h]), which represents typical freeway driving condition for a

compact passenger vehicle. The peak steering wheel input of _max = 100◦ (with

steering ratio of 1/18) is used to design the switched controllers such that, when the

vehicle is operating at _max and vmax, the condition (27) satisfied for each CG

height configuration, which is sufficient for mitigating rollover. We choose the

controller gains Kη as small as possible to minimize the control effort. The resulting 8

controller gains are calculated as follows:

(20)

For the numerical simulations, we use a typical obstacle avoidance

manoeuvre known as the Elk test with a peak driver steering input of magnitude λmax

= 100◦ and with an initial speed of v = 108[km/h]. The steering profile corresponding

to this manoeuvre and the resulting CG height estimation is shown in Fig. 6.4, where

P a g e | 28

the worst case CG height (i.e., hmax = 0.85[m]) is assumed until the initiation of the

steering manoeuvre. After the manoeuvre starts, the CG height has been estimated

to be 0.51[m] as seen from the figure. Fig. 6.5 depicts the resulting LTRd values for

the controlled and the uncontrolled vehicles. Clearly, the uncontrolled vehicle rolls

over as |LTRd| > 1 during the manoeuvre. Moreover, both of the robust (i.e., fixed

gain) and the switched adaptive controllers prevent rollover by keeping |LTRd| < 1.

However, the adaptive controller does it in a less conservative way which is

favourable. In Fig. 6.6 we compare the vehicle states of the controlled and the

uncontrolled vehicles, where we observe that due to smaller attenuation obtained by

the adaptive (switched) controller, the resulting states trajectories are closer to the

uncontrolled vehicle states as compared to the robust one. Again, this is favourable

as the adaptive controller causes smaller river intervention, and maintains a natural

response of the vehicle. Finally, Fig. 6.7 depicts the vehicle speed and the

normalized braking force variations for the controlled and the uncontrolled vehicles.

We observe that the adaptive controller results in much less controller actuation and

less drop in vehicle speed; this clearly shows the performance benefit of using the

suggested switched controller as compared to the fixed robust control alternative.

Figure 6.4: Steering input and the resulting CG height estimation [5]

P a g e | 29

Figure 6.5: LTRd for the controlled and uncontrolled vehicles.[5]

Figure 6.6: Vehicle states for the controlled and uncontrolled vehicles[5]

P a g e | 30

Figure 6.7: Vehicle speed and the normalized control force[5]

P a g e | 31

7. ACTIVE STEERING

We are interested in robust control design based on active steering actuators.

There are two types of active steering methods: full steer-by-wire and mechatronic-

angle-superposition types. Steer-by-wire actuators do not contain a physical steering

column between the steering wheel and the wheels; the steering torque is generated

solely by a servo motor based on the driver steering command. This enables steer-

by-wire actuators to be flexible and suitable for various vehicle dynamics control

applications. However, stringent safety requirements on such systems prevent them

from entering today’s series-production vehicles. Mechatronic-angle-superposition

type active steering actuators however have been recently introduced to the market.

They contain a physical steering column and act cooperatively with the driver, while

they permit various functions such as speed dependent steering ratio modification,

and active response to mild environmental disturbances. It is plausible that active

steering actuators will become an industry standard in the near future, due to their

capability of directly and most efficiently affecting the lateral dynamics of the car.

Active steering based lateral control methods can be perfectly transparent to the

driver and they are likely to cause the least interference with the driver intent unlike

the control approaches based on differential braking and active suspension.

Moreover, the use of active steering actuators do not result in a significant velocity

loss, therefore they are likely to enter the market initially for the high performance

vehicle segment[2].

In this paper we assume mechatronic-angle-superposition type steering

actuators with access to full state information. Although such active steering

actuators require inputs from the driver, for the sake of keeping the discussion as

simple as possible, in this paper we assume no internal actuator dynamics or delays

that might arise from driver interactions. It is however possible to account for the

effects of these in the controller design. Also our results can easily be extended to

the case of steer-by-wire actuators where driver interactions are of less importance.

We also assume in this paper that all the model parameters m,Jxx,Jzz, lv,

lh,Cv,Ch,k,h,c are known. This is an unrealistic assumption: yet our control design is

easily extended to account for uncertainty in these parameters which we

demonstrate by designing our controllers to be robust with respect to uncertainties in

vehicle speed v and center of gravity height h. As a side note, although we assumed

all the vehicle model parameters to be known, it is possible to estimate some of

these that are fixed (but unknown) using the sensor information available for the

control design suggested here; this however is outside the scope of this work (see

Akar et al., 2006).

7.1) State feedback controllers for robust disturbance attenuation:

In a later section, we will utilize the results obtained by Pancake, Corless and

Brockman (Pancake et al., 2000, 2006) to design controller gain matrices. (Pancake

et al., 2000, 2006) consider uncertain systems of the form

P a g e | 32

(21)

where q is some parameter vector (which can be time and state dependent) that

captures the plant nonlinearity/ uncertainty. The vector vector x(t) is the state at time

t and w(t) is a bounded disturbance input while u(t) is the control input and z1(t), . . . ,

zr(t) are the performance outputs. For each output z j (Pancake et al., 2000, 2006)

introduce a measure of performance measure g j which guarantees that the

magnitude of that output is less than or equal to g j times the peak value of the

magnitude of the disturbance. They present a controller design strategy which can

be used to minimize the performance level for one main output while keeping the

performance levels for the other outputs below some prespecified levels. In addition

the controllers in (Pancake et al., 2000) are robust in the sense that they ensure

performance in the presence of any allowable uncertainty which was taken into

account in the control design. The uncertainty in the plant is required to satisfy the

following condition.

Assumption 7.1.1 For each q and j = 1, . . . , r, the matrix

(22)

can be written as a convex combination of a finite number of matrices (called vertex

matrices)

Remark 1 Suppose that each of the matrices A(q ), B(q ), Bu(q ), Cj(q ), Dj(q ), Dju

(q) depend in a multi-affine fashion on the components of the M-vector q and each

element of q is bounded, that is,

Then, for all q , the matrix in (11) can be expressed as a convex combination of the

M matrices corresponding to the extreme values of the components of q ; these

vertex matrices are given by,

(23)

The following result from (Pancake et al., 2000, 2006) is useful in designing our

rollover prevention controllers.

THEOREM 7.1.2 Consider a nonlinear/uncertain system described by (9)-(10) and

satisfying Assumption 4.1. Suppose that there exist a matrix S = ST > 0, a matrix L

P a g e | 33

and scalars b1, . . .bN > 0 and m0,m1 j,m2 j ≥ 0, j = 1, . . . , r, such that the following

matrix inequalities hold

(24)

for all i = 1, . . . ,N and j = 1, . . . , r. Then the controller

u = Kx with K = LS−1 (25)

results in a closed loop nonlinear/uncertain system which has the following

properties:

(a) The undisturbed system (w = 0) is globally exponentially stable, that is, all state

trajectories decay exponentially.

(b) If the disturbance input is bounded, that is, kw(t)k ≤ rw for all t then, for zero initial

state, the performance outputs z1, . . . , zr of the closed loop system are bounded

and satisfy

(26)

for all t where

(27)

The scalars g1, . . . .gr are called levels of performance and can be

regarded as measures of the ability of the closed loop system to attenuate the effect

of the disturbance input on the performance outputs; a smaller g j means better

performance in the sense of increased attenuation. For a proof of the theorem, see

(Pancake et al., 2006).

Remark 2 Consider the situation in which the matrices Dj1 , . . . ,DjN are all zero for

some performance output z j. Then, for each i, inequality (14) is satisfied for some

m2j ≥ 0 if and only if it is satisfied with m2j = 0. Hence, if Dj1 , . . . ,DjN are all zero,

inequality (14) can be replaced with

(28)

In this case,

(29)

P a g e | 34

Also, using Schur complements, one can show that the above inequality is

equivalent to the following inequality which is linear in the variables S and m1 j.

(30)

Remark 3 Consider the closed loop system subject to a fixed bounded disturbance w

which satisfies kw(t)k ≤rw ,let

V(x) = xT Px (31)

and consider the bounded ellipsoid in state space defined by

(32)

The inequalities in (23) guarantee that whenever a state trajectory is outside of the

ellipsoid the time rate change of the Lyapunov function V is negative. From this one

can show that the ellipsoid is both invariant and attractive. Attractive means that all

state trajectories converge to the ellipsoid with increasing time. Invariance means

that if a state trajectory starts in the ellipsoid, it remains there forever; in particular, if

a trajectory starts at the origin, it will always be contained in the ellipsoid.

The inequalities in (24) guarantee that each performance output z j satisfies

(33)

Hence, if a trajectory starts within the ellipsoid, it must satisfy kz j(t)k ≤ g jrw for all t.

Otherwise, kz j(t)k is “eventually bounded” by g jrw .

7.2) Rollover Control Design:

We now apply the results described in the previous section to the rollover

prevention problem. We here present a design under the assumption that the plant

parameters are known and fixed.

7.2.1) Active steering PI controller with known plant parameters:

Our objective here is to superimpose an active steering control input u=dc on the

driver steering input dd to prevent rollover. Thus, the total steering input d to the

vehicle consists of two parts and is given by

(34) The driver input dd will be regarded as a disturbance input w. Recalling model (3),

our system is now described by

(35)

P a g e | 35

where x (t) ∈ R4 is the state at time t ∈ R, u(t) is a scalar control input and w(t) is a

scalar disturbance input. The matrices ˜A and ˜B are fixed and are as described as in

(3). We propose a proportional-integral (PI) type state feedback controller of the form

(36)

where the integrator state xI is the integral of the yaw rate tracking error:

(37)

The reference yaw rate y˙d is given by

˙d =d, (38)

for a constant gain a. Although this is a major simplification of the reference driver

intent, we chose this linear expression for the sake of simplicity. The resulting control

structure is depicted in Figure 7.1 below

Comment : The purpose of utilizing the integral action in the controller is to

guarantee that when driver input dd is constant, the corresponding steady state yaw

rate is given by y˙ =y˙d =add. This yaw rate will be large for large dd and will result in

a large steady state value of LTRd. To avoid this one could saturate y˙d at a certain

value such that, in steady state, ||LTR|| stays below 1, regardless of the driver input.

Figure 7.1: Flow diagram of the PI active steering controller [7]

We want the controller to keep the magnitude of LTRd small during transients with

reasonable control effort. In view of this, we introduce the following two performance

outputs:

z1 = LTRd = ˜C

z1 = C1x

z2 = D2uu,

(39)

P a g e | 36

Simulations: The model parameters used here are given in Table 7.1. They are

typical for a compact car. The steering ratio was assumed to be 1:18. In using

Theorem 7.1.2 to obtain a gain matrix K which minimizes the level of performance g1

for z1 subject to a specified level of performance g2 for z2, we used a simplified

version of the iterative solution algorithm described in the Appendix with N = 1. In the

numerical simulations presented here, we simulated an obstacle avoidance

maneuver that is commonly known as the elk-test. The maneuver takes place at a

speed of v = 140 km/h and with a peak steering magnitude of 100◦. The results of

the simulations are presented in Figure 7.2, which demonstrates the effectiveness of

the controller in preventing rollover in this dangerous maneuver by keeping the

magnitude of LTRd less than one. Notice that driver intervention of the controller as

measured by the difference in roll angles of the controlled and uncontrolled vehicles

show a slight difference, implying that the control action would probably be

undiscernible by the driver, which is favorable and was one of our aims.

Table 7.1: Fixed model parameters [7]

It is of particular interest for us to see how the suggested controllers affect the

vehicle path. To do this, we note that the coordinates (x, y) of the vehicle CG relative

to the road satisfy

x = v cos(+) ,

y = v sin(+) ,

where we choose the initial coordinates (x(0), y(0)) to be zero. In Figure 7.3 the CG

trajectories of the controlled and the uncontrolled vehicles are compared along with

the remaining states. We observe from trajectory plots that control action causes a

small divergence from the uncontrolled vehicle path during the first half of the

P a g e | 37

maneuver while preventing rollover; in a real driving situation, the driver would time

the second half of the maneuver based on the speed and location of the vehicle.

Also similar to the roll angle variation, the remaining state plots of the controlled

vehicle are close to those of the uncontrolled vehicle during the maneuver.

Figure 7.2: Comparison of the controlled (with fixed model) and uncontrolled vehicles. [7]

Figure 7.3: Comparison of the controlled (with fixed model) and uncontrolled vehicle states and trajectories. [7]

P a g e | 38

Figure 7.4: Comparison of the robustly controlled and the uncontrolled vehicles (v = 70km/h, peak = 150◦, and h =

0.45m). [7]

Figure 7.5: Comparison of the trajectories and states of robustly controlled and the uncontrolled vehicles (v =

70km/h, peak = 150◦, and h = 0.45m). [7]

P a g e | 39

8. ROPS (Rollover Occupant Protection Systems)

8.1) The Concept:

Grzebieta et al (2009) demonstrated a “proof of concept” how roof crush

intrusion into the occupant compartment can be prevented using an innovative

externally retrofitted rollover load distribution device. It was developed based on an

understanding of how vehicles roll and roofs crush during rollover. It incorporates a

roll “hoop” placed in line with the major radius of the vehicle changing and improving

the vehicle geometry. Figure 8.1 demonstrates via sketches the concept of this

process.

Grzebieta et al (2009) presented rollover crash test results of a U.S.

manufactured production SUV with a seat belted Hybrid III anthropomorphic test

dummy (ATD) subjected to two rolls on the Jordan Rollover System (JRS). A second

production SUV of the same make and model was fitted with the HALO™ Prototype

1 and was then subjected to the same dynamic rollover crash test using the JRS test

rig. Injury measures from the ATD, crush and crush velocity from various locations in

the retrofitted vehicle during testing were noted and compared to the measurements

from the production vehicle. Roadway impact loads measured in both vehicles were

compared to each other and to the Volvo XC90, the current best-performing rollover

crashworthy production vehicle. Results showed that when both roof crush and

vehicle’s centre of gravity fall is prevented by the geometry change of the HALO™

Prototype 1 retrofit system, the ATD injury measures and road impact loads are

significantly reduced.

8.2) Test Apparatus:

8.2)1. The JLS:

The JRS is shown in Figure 8.2. The Vehicle Body is mounted on the Rotating

Cradle and then fitted into the Support Towers. The Road Surface is moved to the

far end (not shown) of the Track. The Support Tower’s release mechanism and the

Road Surface trigger are synchronized to achieve the prescribed test parameters.

The Road Surface moves down the track at the prescribed speed and the Vehicle

Body is rotated and released to meet the Road Surface at the prescribed angle and

roll rate, and arrested after each roll. Detailed descriptions of capabilities and

operation of the JRS are published elsewhere.

The protocol used to test the HALO™ prototypes was performed with at least

2 passenger side leading rolls at 18 mph (29 kph) roadbed speed, a 222 °/sec

vehicle angular rate, a 4 inch (10.2 mm) drop height and a 10° impact pitch angle,

most of these parameters are more severe than those recommended by Friedman

and Grzebieta (2009). If there was a third roll conducted, the road speed was 15

mph (24 kph) and the pitch angle was 5°, with the same drop height and equivalent

angular rate. The vehicles were equipped with Hybrid III 50th percentile dummy

P a g e | 40

belted in the driver‟s seat. For each roll, the dynamic peak roof crush was tabulated,

the end of test residual roof crush, and dynamic peak roof crush speed at the pillars

and roof header

Figure 8.1: Top row: Vehicle‟s CG drops during rollover and then rises again;

Bottom row: Hoop maintains vehicle‟s CG at constant height, thus reducing

roof load [1]

P a g e | 41

Figure 8.2: Photograph of the major components of the JRS[1]

8.2.2) HALO™ Prototype 2 Development and Testing:

The second prototype of the HALO™ was a much more intricate design with multiple

attachment points, a fully integrated interior B-pillar to B-pillar reinforcement and a

fully redesigned exterior front. This prototype worked very well in reducing roof crush

as shown in Figure 8.3. The vehicle struck the ground at 147° on the near side and

cleanly rolled over the far side with very little apparent damage. The dummy was

only lightly loaded during the test. The test results for prototype 2 are shown in Table

8.1.

Figure 8.3: HALO™ Prototype 2; No noticeable deformation to the roof structure[1]

P a g e | 42

Table 8.1: Test results for the HALO™ Prototype 2. [1]

P a g e | 43

9. CASE STUDIES

Several of the government and police agencies have vehicle fleets. For

example, in 2008, the U.S. Border Patrol had over 33,000 vehicles. In 2008, the non-

profit “People Safe in Rollovers Foundation”, held a Rollover Summit in Washington

D.C. to share ideas on how to keep people safe in rollovers. One of the speakers

was Dr. David Garcia, a victim of roof crush in his Ford Escort. In his testimony at the

Oversight Committee Hearing on Passenger Vehicle Roof Strength on June 4, 2008,

he talked about two fellow Americans who were also victims of rollover crashes.

9.1) U.S. Border Patrol Vehicles:

David Webb was a 35 year-old Border Patrol agent out on a routine call when

the right rear tire of his 1997 Chevrolet Tahoe blew out. This caused him to lose

control and his SUV rolled over. He sustained a fractured skull and never regained

consciousness. Figure 8.1 shows the vehicle with roof deformation at the driver-side

A-pillar, after the crash. It is worth noting that the aftermarket roll cage in the rear for

detainees was the section of the vehicle that did not crush.

Figure 9.1: Government vehicle rollover victim David [1]

The other victim was 30 year-old Border Patrol agent, Luis Pena, Jr. Mr. Pena

was amnesic to the event, but speculates that he may have tried to avoid hitting

either a horse or cattle when his 2003 Ford F-250 XL rolled over. His injuries

included vertebral dislocation with spinal cord injury, rendering him quadriplegic.

Figure 9.2 shows the roof crush at the driver-side A and B-pillars.

P a g e | 44

Figure 9.2: Government vehicle rollover victim Luis[1]

On June 6, 2008, Mr. Pena, presented his case to the current Chief and

Assistant Chief of the Border Patrol. The Chief and Assistant Chief were shocked to

know that the vehicles they provide for their agents were potentially unsafe. By law

the Border Patrol is required to order only American-made vehicles. Mr. Pena was

informed that he is the only Border Patrol Agent who has ever survived a rollover;

there were 7 other Border Patrol Agents who had died in rollovers in the previous 1½

years.

9.2) U.S. Marine Transport Van:

On June 10, 2001, a solo highway traffic collision involving a 1996 Ford 15

passenger Club Wagon owned by the U.S. Government resulted in fatal injuries to

two of the U.S. Marine occupants and minor- to-major injuries to 12 others.

A volunteer driver departed Camp Wilson in route to Laughlin, Nevada, with

15 Marine Corp passengers. The Ford Club Wagon Van had a tire blow out, which

caused a loss of control and vehicle rollover. This vehicle sustained multiple impacts

to the roof, rear and both sides. There was a significant impact to the right roof and

upper right side which caused significant intrusion into the right side of the

passenger compartment. This major impact to the roof had a principal direction of

force from top to bottom and right to left. Figure 9.3 shows the marine transport van

after the crash; the exterior view is on the left and the interior view from the rear is on

the right.

P a g e | 45

Figure 9.3: Military vehicle fleet - U.S. Marine transport van case study [1]

Commercial Vehicle Fleets:

Some of the largest commercial vehicle fleets are managed by the Oil, Gas

and Mining industry (OGM). Some fleets have as many as 30,000 vehicles across

the globe. The majority of the fleets are made up of light truck vehicles (i.e., SUV,

pickup, van). These global companies provide vehicles, including fleets of 12 and 15

passenger vans, for use at and traveling to and from these sites.

These global companies recognize the need for occupant protection for their

personnel as a result of their duty of care to provide a safe work environment. Most

of the companies have some form of requirement for Rollover Occupant Protection

Systems (ROPS) installed on their vehicles because of their concerns regarding roof

crush. The types of ROPS structures used vary widely among the companies and to

some degree is a function of location, availability, expertise and terrain at the site.

For many years these systems have been primarily fitted internally to the vehicles.

With the recent introduction of Side Curtain Airbags, these internal ROPS have

become a problem. The OGM industry began looking for a solution that was external

to the vehicle and would not interfere with the Side Curtain Airbags. In addition, any

proposed ROPS design must maintain payload capacity and fuel economy.

P a g e | 46

10. GLOBAL SCENARIO

10.1) ESC (Electronic Stability Control):

Available in many new cars, this technology helps drivers maintain control of

their vehicle during extreme steering maneuvers by keeping the vehicle headed in

the driver's intended direction, even when the vehicle nears or exceeds the limits of

road traction.

When drivers attempt an extreme maneuver (for example, to avoid a crash or

because a curve’s severity has been misjudged), they may experience unfamiliar

vehicle handling characteristics as the vehicle nears the limits of road traction. The

result is a loss of control. This loss usually results in either the rear of the vehicle

"spinning out," or the front of the vehicle "plowing out."

A professional driver, with sufficient road traction, could maintain control in an

extreme maneuver by using various techniques, such as countersteering

(momentarily turning away from the intended direction). It would be unlikely,

however, for an average driver to properly apply countersteering techniques in a

panic situation to regain vehicle control.

Spinning out: In the ESC-equipped car, the ESC system immediately detects that the

vehicle’s direction is changing more quickly than appropriate for the driver’s intended

direction. ESC momentarily applies the right front brake to alter the direction of the

vehicle back to the correct path. The rear of the non-ESC equipped trailing car also

begins to slide or spin out as it enters the left curve. However, in the case of the non-

ESC equipped vehicle, it continues to spin out, and ends up off the road.

Plowing out: In the ESC-equipped vehicle, the ESC system immediately detects that

the vehicle’s direction is changing less quickly than appropriate for the driver’s

intended direction. ESC momentarily applies the left rear brake to alter the direction

of the vehicle back to the correct path. The front of the non-ESC equipped trailing car

also begins to slide or plow out as it enters the left curve. However, in the case of the

non-ESC equipped vehicle, it continues to plow out and runs off of the road.

How ESC works:

Electronic Stability Control (ESC) uses automatic braking of individual wheels

to prevent the heading from changing too quickly (spinning out) or not quickly

enough (plowing out). ESC cannot increase the available traction, but maximizes the

possibility of keeping the vehicle under control and on the road during extreme

maneuvers by using the driver’s natural reaction of steering in the intended direction.

ESC happens so quickly that drivers do not perceive the need for steering

corrections. If drivers do brake because the curve is more or less sharp than

anticipated, the system is still capable of generating uneven braking if necessary to

correct the heading.

P a g e | 47

ESC systems exist under many trade names, including Vehicle Stability

Control (VSC), Electronic Stability Program (ESP), and Vehicle Stability

Enhancement (VSE). Some of its common names exit as follows:

Electronic Stability Program (ESP) - Audi, VW, Saab, Daimler, Chrysler

Vehicle Stability Control (VSC) - Toyota, Lexus

Vehicle Stability Assist (VSA) - Honda, Acura

Advance Trac - Ford, Lincoln

StabiliTrak - General Motors, Saturn

Vehicle Dynamic(s) Control (VDC) - Subaru, Nissan

Dynamic Stability Control (DSC) - Mazda, BMW, Rover

Dynamic Stability and Traction Control (DSTC) – Volvo

10.2) Rollover Air Bags:

In addition to protecting drivers’ or passengers’ heads during a side-impact

crash, some side-impact head air bags, or "curtains," can also protect occupants

from injury and ejection during a rollover crash. This is important because ejection

causes most injuries and fatalities in rollover crashes - most people who are killed

are not wearing safety belts to hold them in place.

Not all side-impact head air bags are designed to deploy as rollover air bags.

Check with your dealer and vehicle manufacturer for the availability of side-impact

head air bags that can also operate as rollover air bags.

How rollover air bags work?

If a rollover is detected, the side-impact head air bags are typically triggered in

combination with safety belt retractors to remove slack from the safety belt and keep

the occupant firmly in the seat. Most side-impact head air bags deploy downward

from the overhead roof rail, very close to the side windows. In many cases the

rollover sensing system can determine an imminent rollover when the roll angle is

very small and all four wheels are still on the ground.

When deployed as rollover air bags, side-impact head air bags will stay

inflated longer to help protect the heads of the occupants during the rollover. They

also keep the occupants of the outboard seats from being thrown from the vehicle.

The combination of these air bags and properly worn safety belts can significantly

reduce the chance of ejection.

Figure 10.1: Rollover Air bags [14]

P a g e | 48

11. INDIAN SCENARIO

Active Suspension is being used by[15]:

Audi - R8

BMW Sedans

Rolls Royce - Phantom

Bentley GT

Mercedez Benz - CL, CLS, E, GL, M, R, S, SL

Jaguar - S-Type, XJ, XK

Land Rover - Range Rover, Range Rover Sport

Volvo - S60, V70

Some of the ESC operated vehicles sold in India:

Electronic Stability Program (ESP) - Audi, VW

Vehicle Stability Control (VSC) – Toyota

Vehicle Stability Assist (VSA) - Honda

Advance Trac - Ford

Dynamic Stability and Traction Control (DSTC) – Volvo

12. FUTURE ASPECTS

There are hundreds of truck rollovers every year. They not only cause

significant loss of life and injuries, but damage to vehicles, property and goods.

For preventing these rollover many organizations have been set up across the

world to train the drivers as well as to provide technological details (that has been

discussed in the paper) to various automobile companies.With implementation of the

rollover prevention techniques there will be declination of loss of properties and

goods, also casualties will see a negative slope.

Some organizations, namely DECA and VicRoads are doing a great job in

this. Not only these preventive measure are being applied, but also small vehicles

equipped with tilting vehicle technologies are being made in Australia. So that people

can have a safe transport without fear of losing life.

The Heavy Vehicle Rollover Prevention Program provides organisations with

information to run their own training and awareness presentations for staff. The

presentation is an important part of understanding what causes crashes and how, by

working together, they can be prevented.

The Heavy Vehicle Rollover Prevention Program is now available in a

packaged eight part series ideal for training, toolbox sessions and refreshers. These

specialised videos, complete with training notes and selected pictures, can be

purchased through the following link at Training Snippets.

Organisations can run their own presentation by using the following tools:

Tool1: Prevention guide. This booklet has information to guide users on how to

implement the program using the various tools. It also discusses key issues and

P a g e | 49

solutions to deploy the program, and how to maintain and monitor the program to

evaluate its effectiveness.

Tool 2: Program presentation. The presentation illustrates the main safety concerns

and learnings from the program. Regardless of the transport task, the information is

relevant and allows you to customise for your own transport operation. The

presentation may be reproduced in its entirety, but no part should be removed. Due

to embedded video links contained within the presentation to view, click 'save,' then

proceed.

Tool 3: Program video The video explains the issues, uses realistic models to

demonstrate scientific explanations, and shares real life experiences from people in

the industry. The video is divided into 8 segments.

Part 1 of 8 - Creating your own code of behaviour

Part 2 of 8 - Understanding the problem

Part 3 of 8 - Centre of gravity

Part 4 of 8 - Centrifugal force

Part 5 of 8 - Dynamic loads

Part 6 of 8 - Expect the unexpected

Part 7 of 8 - Putting it all together

Part 8 of 8 - If you do go over

Tool 4: Code of behaviour. A code of behaviour is an opportunity to allow everyone

to have their say, to see the problems others face, and to collectively provide a

workable solution to that issue. This should be developed from the framework

provided, but you need to add or customise it to suit your particular freight task

issues.

It’s not a driver or management-driven objective - everyone can be involved,

even members of the community. It has been shown to work best if you involve, but

not direct, people to identify and deliver solutions. It is a self imposed code of

behaviour - you own it and you maintain it. Please feel free to discuss with your local

Transport Safety Services (TSS) officers if you require information or advice in

developing a code.

Tool 5: Information bulletinThe information bulletin is an overview of some key points

in preventing rollovers. It can be used as a flyer to introduce people to the concepts

of the program, or as a handout during the delivery of the program. It may be

reproduced as required but only in its entirety.

Tool 6: Example truck models The models complement the presentation and

reinforce the concepts raised. By using scale models you can easily and clearly

demonstrate the effects of different loads and different configurations with loads.

P a g e | 50

13. CONCLUSION

We have presented a methodology for the design of vehicle rollover

prevention systems using active steering actuators. By introducing the load transfer

ratio LTRd, we obtain a system performance output whose value provides an

accurate measure for determining the onset of rollover. Our rollover prevention

system is based upon recent results from Pancake, Corless and Brockman, which

provide controllers to robustly guarantee that the peak value of the performance

output of an uncertain system does not exceed a certain value. Simulation results

are presentedto illustrate the benefits of the proposed approach. Future work will

proceed in several directions. We shall extend the methodology to include differential

braking, active suspension and combinations thereof to refine our rollover prevention

strategy, and analyze the resulting control allocation problem. We shall also examine

the efficacy of our controllers in the presence of conditions which can result in a

tripped rollover. As an alternative approach we shall also investigate a gain

scheduled control approach based on locally valid fixed models and LMI based

controllers as described in this paper. In another possible extension of the

synthesis procedure we shall look into the use of more complex vehicle and/or

tire models with the LMI algorithm.

A second strand of work will investigate refinement of the synthesis

procedure. In particular, we shall investigate whether convergence and feasibility

conditions can be developed to determine the existence of control gains to achieve

certain pre-specified performance parameters j.

On the practical side of this work, we have scheduled with our industrial

partners an evaluation of our control design in real production vehicles. We are also

looking into extending these ideas to railroad vehicles.

Figure 13.1: Comparison of the trajectories and states of robustly controlled and the uncontrolled vehicles (v0 =

140km/h, peak = 120◦, and h = 0.375m). [7]

P a g e | 51

Figure 13.2: Comparison of continuous and switched robust controllers at a non critical maneuver (v = 140km/h,

peak = 50◦, and h = 0.375m). [7]

a

REFERENCES: 1. Bozzini S., Jimenez J., et. al., “Commercial, Police, and Military Vehicle Rollover

Protection and Evaluating the Effectiveness of Geometry and Retrofit Rollover

Testing”, Safety Engg. International, Icrash Conference September 23, 2010 –

Washington DC.

2. Active Front Wheel Steering, International Quality and Productivity Center,

Published on: May 16, 2008

3. “A methodology for the design of robust rollover prevention controllers for

automotive vehicles using differential braking”. Publication Date: March 15, 2009.

4. Richier M., Lenain R., et. al. “Rollover Prevention System Dedicated to ATVs on

Natural Ground”, Applied Mechanics and Materials, Vol. 162 (2012) pp 505-514.

5. Shorten R., Solmaz S., et. al., “Center of Gravity Estimation and Rollover

Prevention Using Multiple Models & Controllers”, US Patent no: US

2009/0024269 A1, Publication date: January 22, 2009.

6. Sellami Y., Imine H., et. al., “Rollover Risk Prevention of Heavy Vehiles by

Reliability Based Analysis”, 10th International Symposium on Heavy Vehicle

Transport Technology. HV Paris 2008.

7. Solmaz S., Corless M, et. Al., “A Methodology for the Design of Robust Rollover

Prevention Controllers for Automotive Vehicles with Active Steering”,

International Journal of Control, Vol 1.00, No. 00, November 23, 2006.

8. http://www.bp.com/liveassets/bp_internet/china/bpchina_english/STAGING/local_

assets/downloads_pdfs/r/Rollover_Awareness_Presentation_v2.pdf

9. http://en.wikipedia.org/wiki/Rollover

10. http://www.pmcpsc.com/img/Convoy%20Safety.ppt

11. Carlson C. R. and Gerdes J. C., “Optimal Rollover Prevention with Steer by Wire

and Differential Braking”, Proceedings of IMECE’03, 2003 ASME International

Mechanical Engg. Congress and Exposition, November 16-21, 2003,

Washington DC.

12. Ungoren A. Y. and Peng H., “Evolution Of Vehicle Dynamic Control for Rollover

Prevention”, December 31, 2003.

13. Chen B.C. and Peng H., “Differential Braking based Rollover Prevention for

SUV”, Vehicle System Dynamics, Vol. 36, No. 4-5, November 2001, pp 359-389.

14. http://www.safercar.gov/Vehicle+Shoppers/Rollover/Rollover+Air+Bags

15. http://www.edmunds.com/car-technology/suspension-iii-active-suspension-

systems.html

b

BIBLIOGRAPHY: Nagy S., Baranyi P., et. al., “Rollover Prevention of a Heavy Vehicle via TP model

based H∞ Control Design Approach”, 2008.

Griffin A., et. Al., “Active Suspension Systems”, June 5, 2005.

Rowell J. D., “Safety or Profit: Ford’s Rollover Protection System”.

Nagai M., Yoshida H., et. Al. “Study on Car Body Tilting System using Variable

Link Mechanism”, JSME International Journal, Series C., Vol.47, No.2, 2004.

Bose Suspension System, 2004.

Hac A., “Rollover Stability Index Including Effects of Suspension Design”, SAE

2002 – 01- 0965.

c

ANNEXUTRE: DECA – Rollover prevention and stability program -

http://www.youtube.com/watch?v=BEZ5UattxI4

ESP - http://www.youtube.com/watch?v=IbWb9vKmNKc

Center of gravity - http://www.youtube.com/watch?v=yWWbAr9iLZg

Dynamic Loads - http://www.youtube.com/watch?v=N9BdtLBz9lg

Centrifugal force - http://www.youtube.com/watch?v=zBWYMThAq-Q

Creating your own code of behaviour -

http://www.youtube.com/watch?v=DrerkwhZmw0

Bose suspension - http://www.youtube.com/watch?v=eSi6J-QK1lw

ABS - http://www.youtube.com/watch?v=ngKSirE7zJA

Tilting vehicle technology http://tiltingvehicle.com/