Eindhoven University of Technology

MASTER

A semi-active damper with DC controller in a 3D DAF95 model

Clocquet, R.C.

Award date:1996

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A semi-active damper with DC controller in a

3D DAF95 model

R.C. Ciocquet

EUT, Faculty of Mechanical Engineering

Report No. WFW 96.022

Master’s thesis

Professor: Prof.dr.ir. J.J. Kok

Coaches: ir J.H.E.A. Muijderman

dr.ir. J.G.A.M. van Heck

ir. H.J. Giesen

Eindhoven, februari 1996

Eindhoven University of Technology (EUT)

Faculty of Mechanical Engineering

Department of Fundamentals of Mechanical Engineering

Section of Systems and Control

Abstract

The performance of a commercial vehicle suspension is determined by: the comfort of

the occupants and the cargo, the handling pïopeïtks, the required süspension wûïkifig

space and the dynamic tire force. A semi-active damper system with a model predictive

controller is developed to improve these performances. This controller uses a quarter

vehicle controller model and preview information of the road surface between the front

and the rear wheels. The investigation described here focuses on the implementation

and the testing of the developed semi-active damper system in an extended 3D DADS

(Dynamic Analysis Design System) model of a DAF95 tractor-semitrailer combination.

The semi-active suspension is used in the rear axle suspension of the tractor.

A step by step evolution is used to be sure about the correctness of the implementation

and the tests of the semi-active damper system in the DADS DAF95 model. A suitable

solution is searched among the possible solutions to realise a semi-active damper in

DADS. The chosen implementation of the semi-active damper with controller is tested

on a quarter vehicle model first. The simulation results of this semi-active quarter

vehicle DADS model are compared with the simulation results of the semi-active

quarter vehicle FORTRAN model. Next, the DADS DAF95 model is prepared for the

semi-active simulations. A controller which drives the DADS DAF95 model straight

ahead is developed, implemented and tested. The simulation results of the rear axle

behaviour of the DADS DAF95 model is compared with the simulation results of a

quarter vehicle model to see the differences between the simulation model and the

controller model. Finally, the semi-active damper system is applied to the DADS

DAF95 model. The problem is to get a suitable state for the controller model from the

3D DADS DAF95 simulation model.

1

Contents Introduction 1

1.1 Background information 1

1.2 Strategy 2

The redisitien of a semi-active damper in DABS 4 2.1 A small introduction to DADS 4

2.2 The realisation of a semi-active damper in DADS 5

The passive quarter vehicle 7

3.1 The passive quarter vehicle simulation model 7

3.2 The simulation model in DADS 8

The semi-active quarter vehicle 12

4.1 The direct calculation controller (DGG) 12

2.3 A UNIX script file 6

3.3 The comparison of two passive quarter vehicle implementations 10

4.2 The semi-active quarter vehicle in DADS and FORTRAN 13

4.3 The comparison of two semi-active quarter vehicle 15

implementations

The passive DAF95 tractor-semitrailer

5.1

5.2

5.3

The DAF95 tractor-semitrailer model in DADS

The controller used to drive the truck straight ahead

The comparison of the rear axle suspension of the DAF95

model with a quarter vehicle model

The implementation of the fixed semi-active damper 5.4

5.5 The simulation results

The semi-active DAF95 tractor-semitrailer

6.1

6.2

6.3 Some solutions

Cenchsions and Recommendations

7.1 Conclusions

7.2 Recommendations

The DAF95 model with direct calculation controller

The initial state for the controller model

18

18

20

22

24

25

28

28

29

31

33

33

34

11

8 Bibliography 36

9 Appendixes

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E

Appendix F

Appendix G

Appendix H

Road profile

A UNIX script file

Passive quarter vihicle model

Semi-active quarter vehicle model

Comparison of a quarter vehicle model with the rear axle

suspension of the DADS DAF95 model

Passice DADS DAF95 model

The initial state for the quarter vehicle controller model

from the DADS DAF95 model

Control schemes

... 111

Chapter 1 Introduction

1.1 Back ground information

The investigation described in this report is a part of the CASCOV project (Controller

Axle Suspension for Commercial Vehicles). The project partners are DAF trucks

N.V. , Monroe Belgium, Contitech Formteile GmbH, and Eindhoven University of

Technology. The purpose of this project is to develop an alternative rear axle

suspension for tractor-semitrailer combination. This suspension should i) improve the

ride comfort, 2) improve the handling properties, 3) decrease the vibrations, 4) decrease

the acceleration of the cargo, 5) improve the dynamic tire load and 6) decrease the

suspension working space of the vehicle. The comfort and the handling properties are

important for the drivers work environment. Decreasing the vibrations of the chassis

means a lighter construction of the chassis. Decreasing the acceleration of the cargo

implies a lighter transport packing of the cargo. The improvement of the dynamic tire

load results in a safer behaviour of the truck and a less road damage. The cargo lies

closer to the road surface when the suspension working space is smaller and therefore

the road behaviour of the truck will be improved and the volume of the semitrailer can

be edarged. The project is divided into three parts.

0 Passive system: improving the conventional rear axle suspension by using elements

with frequency dependent characteristics.

Adaptive system: improving the rear axle suspension by slowly adjusting the spring

and damper parameters dependent on the vehicle speed, the load and the type of

road.

Semi-active system: improving the rear axle suspension by using a semi-active

damper with a model predictive controller which uses preview of the road.

0

The main research of the third part of the CASCQV project is dedicated to design, to

develop and to test a controller with preview. This controller is developed and tested

1

in an ideal environment. Namely the quarter vehicle simulation model is identical to the

quarter vehicle controller model see figure 1.1 -a.

disturbance input

control input

'reality' 'reality' controlled o u i p

quarter.vehEle simulation model measured state

controller quarter vehicle controller d e l -control strategy

I

figure 1.1-a figure 1.1-b

A previous investigation, done in the same context, handles the creation of an

extensive 3D DAF95 model with a passive suspension in DADS (F. P. J. Bekkers [i]).

DADS is a program used to calculate the deterministic behaviour of non-linear

multibody systems in the time domain. This 3D DADS DAF95 model is created to

evaluate developed control strategies, but also to simulate large deterministic road

irregularities and handling properties during lane change manoeuvres in a quasi realistic

environment. The purpose of the investigation in this report is to replace the

conventional rear axle dampers of the tractor with semi-active dampers and a

controller in this DADS DAF95 model. This so called semi-active 3D DADS DAF95

model is created to test the developed controller in a quasi realistic environment, see

figure 1.1-b. The reaction of the controller on unmodelled dynamics is of great interest.

1.2 Strategy

Two types of road profiles can be distinguished: deterministic and stochastic

irregularities. The stochastic irregularities such as a brick paved road profile are

omitted. In the future the stochastic irregularities are tested in a 3D situation. The tests

in this investigation are carried out on 10 deterministic road profiles (see appendix A).

These road profiles are the same for the left and right wheels of the 3D DADS DAF95

model. For the sake of simplicity a quasi 2D situation is realised with the 3D DADS

DAF95 model to test the semi-active damper system.

2

Before the final implementation and tests of the semi-active damper with controller are

done on the DADS DAF95 model, the semi-active damper is verified on a rather

simple quarter vehicle model in DADS. A suitable solution to realise a semi-active

damper should be found in DADS first (chapter 2). The simulation results of the

passive quarter vehicle model in DADS are compared with the simulation results of the

same passive quarter vehicle model in FORTRAN (FORTRAN manual [7])(chapter 3).

Next, the simulation results of the semi-active quarter vehicle model in DADS are

compared with the simulation results of the semi active-quarter vehicle model in

FORTRAN (chapter 4). After this, the step to the 3D DADS DAF95 model is made.

The passive DADS DAF95 model is prepared for the semi-active application (chapter

5). After all these preparations the implementation of the damper with the controller is

done (chapter 6). Finally some conclusions are made and the recommendations for

further research are presented (chapter 7).

3

Chapter 2 The realisation of a semi-active damper in

This chapter starts with a short introduction of DADS. The second paragraph

discusses the realisation of the semi-active damper in DADS. A method to run ten

DADS simulations after each other is mentioned in the third paragraph.

2.1 A small introduction to DADS

DADS (Dynamic Analysis and Design System) is a computer simulation tool especially

for multibody systems (E.J. Haug [8], A. Sauren [12]), distributed by CADS1 Inc.

DADS has two ways to create a model:

- by a graphical user interface, the model is entered and organised into simple pre-

defined templates and windows.

- by a command line, the model is entered with commands.

The model is built up with rigid body elements which can make large non-linear

displacements in the 2D or 3D space. These bodies are connected with spring and

damper elements and/or with several joint elements. For the definition of external

forces or constraints several elements are available. These elements can be connected

to any arbitrary position on the rigid bodies. To complete the model, the user can use

specific elements such as tire elements, leaf spring elements, hydraulic elements and

control elements. For special needs, the user can create his own force and/or constraint

elements in the DADS user defined routines. These FORTRAN routines give the user

much freedom in creating a model. The models can be analysed with the next analysis:

the dynamic, the inverse dynamic, the kinematics and the static analysis. The

Dadsgraph and Animate modules can be used to visualise the system behaviour

(DADS manual [4] [5]) . The used DADS terminology is cursive written and gives the

4

inexperienced DADS user a helping hand in DADS. The DADS terminology is not

essential for the comprehension of this report.

2.2 The realisation of a semi-active damper in DADS.

The semi-active damper contains two non-linear damping characteristics namely a high

and a low damping characteristic. The damper force depends on the relative velocity

and the desired setting Sd. s d = 1 for a desired high damping characteristic and s d = O

for a desired low damping characteristic. However, the damper setting can not switch

from one setting to another setting instantaneously. The real setting s is a delayed

version of the desired setting sd. This delay is modelled with a first order filter. The

damper force is a linear interpolated force between the high and the low damping

characteristic dependent on the real setting s. See figure 2.1 and equations 2.1-2.3.

high & low damper char.

Fd(s=l)

Fd(sa.5)

Fd(s=O)

Fd = Sxfhi,h{V}+(l-S)xfiow{V} (2.1)

s = [-s+s,]/Z, (2.2) sd E {O?'}

Velocity [ d s ]

figure 2.1

zs in (2.2) is the time constant of the first order filter. €high and fi,, are respectively the

high and low damping characteristic. Fd is the damper force. v is the relative damper

velocity.

The main difficulties in realising a semi-active damper in DADS are:

- the implementation of the two damping characteristics and the linear interpolation

between them (equation 2.1).

- the implementation of the first order filter. An integration operator is necessary to

create a filter (equation 2.2).

There is one suitable way to realise a semi-active damper in DADS in spite of the

extended ability to connect FORTRAN files to DADS. The way to do so is by using

control elements and a user algebraic control element. The common use of control

5

elements is: to call in a state of the model with an input control element, to process it

by interlinked control elements, and to append it to the model by an output control

element. The user algebraic control element is an interlinked control element which

processes the control signals in FORTRAN. A user algebraic control element is used

to describe both damping characteristics (equation 2.1) because the damper model

parameters (oil pressures and surfaces) are easy to change in FORTRAN. The use of

control elements is a s~itable way to realise the first order filter (equation 2.2) because

of the possibility of using explicitfirst order control element in DADS. See figure 2.2

for the general implementation of the semi-active damper in DADS

input control element

rel. mi. chassis -axle ouiput control element user algebraic control element

damperforce damperforce

1 = v = relativevelocity 2 = sd = desiredsetting

desired setting settingfilter 3 = s = filteredsetting 4 = F, = damperforce

1st order input control element

figure 2.2

2.3 A UNIX script file

The created vehicle models in this report are tested on ten different road profiles see

appendix A. The simulation results of these DADS vehicle models are stored in a

binary file. This binary file contains a standard quantity of data. The bigger the model is

and the more accurate the analyses are the larger this binary file is. A lot of the stored

information is not used. Therefore a UNIX script file is created to run the next steps

ten times: a vehicle model with a specific road profile is calculated. The created binary

file is manipulated and only the interesting results are stored in a MATLAB file, after

which the binary file is deleted. See appendix B for details.

6

Chapter 3 The passive quarter vehicle

This chapter deals with a dynamic 2 degrees of freedom (2 dof) simulation model of

the rear axle suspension qf a DAF95 tractor. The reason to start with this model is:

this model is simple and the implementation of a fixed semi active-damper with

control elements in DADS is surveyable. The implementation with control elements

will be verified. The simulation results of this model in DADS is compared to the

simulation results of this model in FORTRAN. The first paragraph discusses the

simulation model. In the second paragraph the implementation of the simulation

model in DADS is described. The third paragraph discusses the comparison of the

simulation results of two implementations.

3.1 The passive quarter vehicle simulation model

As mentioned in the introduction of this chapter the simulation model represents the

dynamics of the rear axle suspension of a DAF95 tractor. The model contains a mass

that represents the rear axle (unsprung mass) and a mass that represents the chassis

(sprung mass). The suspension is modelled by the typical non-linear characteristics of

the damper and the air springs. The tire is modelled as a spring with a linear character

which generates only forces during compression to describe the tire lift-off effect. The

finite tire-road contact surface is included in the model by filtering the road surface

with a first order filter before it enters the spring (W. Foag [6]). This double mass

spring damper system is called a quarter vehicle model, see figure 3.1. The damper is

semi-active, which means that the damper can switch between a high damping

characteristic and a low damping characteristic. However, in this chapter the damping

is fixed to the high damping characteristic so, actually, it is a passive damper. The

system equations can be written in a state space notation, see figure 3.1 and equation

3.1-3.8. Remark the resemblance between equation 2.2 and 3.5.

7

Chassis

, Velocity [mis] '

Displacement [m]

Rear axle Tiresonna

Xl(t) =

X2(t) =

Xg(t) =

X4(t) =

X,(t) =

X6(t) = - - 7, - -

'd

I

roadprofile

figure 3.1

The state x(t) = [xl(t) xZ(t) x3(t) x4(t) x5(t) x6(t)l<. zs is the time constant of

the first order setting filter, T~ is the time constant of the first order Foag filter, v is the

speed of the vehicle and L is the tire-road contact length. Ten different road profiles

(x,(t,v)) are modelled to test the controller performance. These road profiles resemble

real situations, see appendix A.

3.2 The simulation model in DADS.

The passive quarter vehicle simulation model in DADS is derived from the quarter

vehicle of paragraph 3.1. The implementation in DADS is straightforward with

exception of the first order filter which filters the road profile. There are three bodies:

the chassis, the axle and the filtered road. The three bodies are connected with springs

8

by translational spring damper actuator elements which conform to figure 3.1. The

spring characteristics are realised by curves elements. The body that represents the

filtered road is a dummy body. This dummy body has no dynamic meaning. The

dummy body has a prescribed motion in time, realised with a driver element, and it

takes care of the connection point for the tire spring. This prescribed motion is the

filtered road height. The road profile is inserted with an user input control element.

This is a FOIITRm routine with the same function as an input control element. The

road profile is filtered by afirst order control element from which the output is applied

to the dummy body by the earlier mentioned driver element. The semi-active damper

with a fixed damper setting on high is implemented to compare the simulation results

of this DADS model with the simulation results of the same FORTRAN model. The

damper is created with the help of control elements which conform to paragraph 2.2.

See the control element scheme in figure 3.2.

inp. E i .

m l m2

3 ’ semi-passief.f 5 out b d.force

1 = xr(t,v) = roadheight 2 = x,(t) = filtered road height 3 = xq(t)-x3(t) = relativevelocity 4 = x5(t) = fixed damper setting 5 = Fd = damper force

damperforce

figure 3.2

rnl m2

The first input control element retrieves the value of the relative velocity between the

chassis and axle. The second input control element retrieves a constant with value one

to set the semi-active damper on the high damping characteristic. The user algebraic

control element calculates the damperforce depending on the relative damper velocity

and the fixed damper setting. The output control element applies this damperforce to

the chassis and the axle.

9

3.3 The comparison of two passive quarter vehicle

implementations.

roadprofile

similarity

The comparison is necessary to be sure about the choice of the implementation of the

fixed semi-active damper in the quarter vehicle simulation model in DADS. The

implementations are:

- The quarter vehicle implemented in FORTRAN.

- The quarter vehicle implemented in DADS with the fixed semi-active damper

realised with control elements.

There is only a small difference between the FORTRAN and DADS simulation results.

A summary of the similarity between the DADS and FORTRAN implementation is

given in table 3.1.

1 2 3 4 5 6 7 8

+ ++ ++ ++ ++ ++ ++ ++

Table 3.1 : Similarity ++ good, + rather good, I fair, - rather bad, -- bad.

Road profile 0.05

0 . 0 2

0.01

O .

0 . 5 0 .6 0.7 0 . 8 .o . o1

Time [SI

Suspension deflection 0.011

-0 .02 ‘ 0.5 0.6 O .7 0 . 8

Time [SI 1

figure 3.3

The road profile “standard brick” shows a different simulation result. The other nine

road profiles are similar. The road profile “standard brick” is the smallest obstacle so

the accuracy of the integration process is, in this case, important. The smaller the

10

problem is, the more accurate the solution should be and therefore the more accurate

the integration process should be. The differences between the filtered road profile in

DADS (thick line) and the filtered road profile in FORTRAN (thin line) are rather

small (see figure 3.3 Road profile). A disturbance of the filtered road profile causes

differences in the simulation results for the whole quarter vehicle model (see figure 3.3

Suspension deflection). The differences are due to the different integration processes.

The FORTRAN integration process uses a Runge-Kutta-Merson method and the

DADS integration process uses a variable integration process. The integration

tolerances in DADS and FORTRAN are the same. Reducing the integration tolerance

in DADS gives a result that corresponds with the FORTRAN simulation results.

Reducing the integration tolerance means a larger calculation time. Anticipating on the

3D DADS DAF9.5 model, the calculation time will increase tremendously. For the

extended simulation results see appendix C .

11

Chapter 4 The semi-active quarter vehicle

This chapter deals with the modelling of the semi-active quarter vehicle and with the

explanation of the semi-active system controller. Simulations are carried out with

both the DADS and the FORTRAN implementation of the vehicle model. The

simulation results are compared to be sure about the accuracy of the DADS

implementation. In the first paragraph the direct calculation controller proposed by

J.H.E.A. Muijdeman [ I 11 is discussed. The second paragraph considers both the

implementation in DADS and in FORTRAN. Finally, the arising differences between

the DADS and FORTRAN simulation results are discussed.

4.1 The direct calculation controller (DCC)

The purpose of the direct calculation controller is to improve comfort and handling

properties of the DAF95 tractor-semitrailer. The controller uses a quarter vehicle

controller model. This quarter vehicle controller model is similar to the simulation

model described in paragraph 3.1. Comfort and handling properties of the vehicle are

translated into measurable quantities. The performance criterion of the controller is a

weighted sum of the measurable quantities: the maximum absolute vertical chassis

acceleration, the tire lift-off time and the crossing of the suspension deflection bounds.

The controller assumes that the road surface between the front and the rear axle of the

tractor is known by reconstruction of this road surface from measurements at the

vehicle (R.G.M. Huisman [9]). The quotient of the length over which the road profile

is known, the wheel base length of the DAF tractor (3.5 [m]) and the vehicle speed is

called the preview interval (=3.5/v). The prediction simulation results of 26 quarter

vehicle control models with the state of the quarter vehicle simulation model at t as

initial condition is calculated over the preview interval [t , t+3.5/v]. The preview

interval is divided in six subintervals (see figure 4.1).

12

figure 4.1

In each subinterval the damper setting can be either 1 or O. A quarter vehicle

controller model is needed to calculate all the 26 different possible damper setting

sequences (6 subintervals and 2 settings). The damper setting sequences are unique

binary numbers from O00000 up to 1 1 1 1 1 1. The controller determines the optimum

damper setting sequence over the preview interval [t , t + 3.5 / v] by considering the

performance criterion for each damper setting combination. The first bit of the

optimum damper setting sequence will be applied to the quarter vehicle simulation

model, the other five are discarded. The whole procedure is repeated at the beginning

of every new subinterval. The direct calculation controller is still in development. At

first sight, the six subintervals are a balance between a small number of subintervals

and a limited accurate solution versus a large number of subintervals and a large

calculation time. Basically, it is a straightforward implementation of a Model Predictive

Controller (M. Morari [ 101)

4.2 The semi-active quarter vehicle in DADS and

FORTWAN,

The semi-active quarter vehicle simulation model in DADS is the same as the passive

quarter vehicle simulation model in paragraph 3.2 but now there is a controller

involved to calculate the optimum damper setting. The control scheme of figure 3.2 is

extended with some extra control elements. The DCC is completely implemented in

FORTRAN and is linked to DADS with the help of the user algebraic control element

(see figure 4.2). This DCC requires the actual state of the DADS quarter vehicle

simulation model. The prediction, simdation of the 26 quarter vehicle control models

are calculated with a FORTRAN NAG integrator. The FORTRAN NAG integrator is

synchronised to the DADS integrator.

13

state

equilibrium state

static equi. state

F, controller

yes -new setting

\L setting

figure 4.3

1 = x,(t,v) = roadheight 2 = x,(t) = filtered roadheight 3 = x,(t) = axlevelocity 4 = x,(t) = chassisvelocity 5 = x,(t) = axle position 6 = x,(t) = chassisposition 7 = x5(t)-x,(t) = relativevelocity 8 = Fd = damper force 9 = Sd = disered setting 10 = x,(t) = fiiteredsetting

figure 4.2

The controller in the user algebraic control element does a few

things before starting the direct calculation controller (see figure

4.3). The DCC needs a relative state with respect to the static

equilibrium. The static equilibrium of the quarter vehicle

simulation model is defined at 0.5 seconds (ti = 0.5). Before ti

is reached the desired setting is 1. The first time when t 2 ti an

initialising step is made. The next time when t 2 ti the relative

state is compared with the state at ti . The ideal point of time to

calculate the DCC is the moment at which a new subinterval

starts (t, + n x 3.5/(6 x v)

DADS it is impossible to call the user algebraic control element

at a specific point of time. The time when the control element

scheme is calculated depends on the DADS integration process.

DADS calculates a new damper setting when DADS calls the

user algebraic control element for the first time in a new

subinterval (see figure 4.4, t + At). The damper setting

calculated on this time is held for the rest of the time within that

subinterval when DADS calls the user algebraic control

n = 1,2,3 ,...... ). However, for

14

element. This is a less accurate implementation with regard to the FORTRAN

implementation. The FORTRAN implementation of the quarter vehicle simulation

model gives the opportunity to realise an exact calculation of the subintervals and the

moment of calculating the DCC (see figure 4.4).

roadprofile 1 2 3 4 5 6 7 8 9

similarity + ++ ++ ++ ++ ++ ++ + ++

old subinterval t t+At new subinterval

10

++

'iontroller'

old subinterval t controller t new subinterval FORTRAN - 7 7 7

actual state at t

calculation time of simulation model +

figure 4.4

The integration of the FORTRAN simulation model stops exactly at the end of a

subinterval after which the controller is calculated. The simulation will restart the

calculation exactly at the beginning of a new subinterval with a new damper setting and

with the state at time (t) as the initial state.

4.3 The comparison of two semi-active quarter vehicle

implementations.

The comparison of the DADS with the FORTRAN implementation is necessary to

verify the accuracy of the DADS semi-active quarter vehicle simulation model. The

results of the FORTRAN model and the results of the DADS model are almost

identical. A summary of the similarity between the DADS and FORTRAN

implementation is given in table 4.1.

15

The differences are caused by the sensitivity of the direct calculation controller. A

small test indicates that the controller is sensitive for small variations of the initial state.

Chapter 6 will explain more of the sensitivity of the controller. The sensitivity of the

direct calculation controller depends on the difference between the DADS and

FORTRAN integrator and the differences between the FORTRAN and DADS

implementations of the controller. The difference between the DADS and FORTRAN

iritegrator is described in paragraph 3.3. The remedy is to reduce the integration

tolerance, this will increase the calculation time. The FORTRAN and DADS

implementations of the controller are different as mentioned in the previous

paragraphs. The FORTRAN implementation calculates the subintervals exactly

[t, t + 3.5/(6 x v)] . The DADS implementation calculates the subinterval depended on

the time of calling the user algebraic controller element by DADS. The fault made

with the DADS implementation is At (see figure 4.4). The fault made with the DADS

implementation is directly dependent on the integration tolerance. Reducing the

integration tolerance will improve the fault At, but the calculation time will increase.

The difference in the FORTRAN (thin line) and the DADS (thick line) damper setting

is clear to see in the simulation results of the road profile called “wave 2” (see figure

4.5).

Chassis acceleration 2 0 [ I

5 e 10 €

.o o E 0 -10

<

Y

E c

e, e

2 -20 ‘ 1 0.5 1 1.5 2

Time [SI

100

80

5 60

e, 40 Y

$ c4 20

-2 0 O

u.5 1 1.5 2 Time [s]

Damper force I

16

Fortran damper setting

Time [s]

DADS damper setting 1

0.8

" 0 . 6 -

I bo C .- g 0.4 rn

0.2

O 0 .5 1 1.5 2

figure 4.5

The different damper settings take place at 1.4 seconds. The small differences in the

damper forces are clear and it will cause some differences to the complete simulation

model. Anticipating on the DADS DAF95 model, reducing the integration tolerance

to improve the fault At , will increase the calculation time tremendously. For the

extended simulation results see appendix D.

17

Chapter 5 The passive DAF95 tractor-semitrailer model

This chapter deals with the verification of an extended 30 model of a DAF95 tractor-

semitrailer in DADS. Before the model is used to simulate, the model is verified. In

the first paragraph a first impression of the extended model is given, especially about

the rear axle suspension. The second paragraph discusses some controllers with the

aim of keeping the tractor-semitrailer driving straight ahead. The third paragraph

discusses the comparison of the DADS DAF95 model with the quarter vehicle model.

The fourth paragraph considers the implementation of the fixed semi-active damper

in the DADS DAF95 model. The fifih paragraph discusses both the simulation results

of the original DADS DAF95 model and the sirnulation results of the DADS DAF95

model with the fixed semi-active damper.

5.1 The DAF95 tractor-semitrailer model in DADS

The 3D model of a DAF95 tractor-semitrailer in DADS is created by F.P.J. Bekkers

[i]. It is a model with 33 bodies and 34 degrees of freedom. A linearisation of a DADS

model can be performed by DADS on any time point. The created system matrix of

the linear equivalent first order state space model has a square dimension of 68. The

most important bodies related to the dynamic behaviour of the tractor-semitrailer are

represented in figure 5.1.

,." ...... ~. , ". "._. __, , , , .,,, , _,i_ . ..... .. ." ,

figure 5.1

18

These rigid bodies are: the occupants, the cabin, the front wheels and axle, the engine,

the chassis, the rear wheels and axle, the trailer (2x), and the trailer wheels and axles

(3x). Two bodies and a torsion spring in between are used to describe the torsion

flexibility of the semitrailer. The engine is suspended with springs and dampers from

the chassis and so is the cabin with the occupants. The tractor rear axle suspension is

discussed in more detail because of the importance in this report. The mechanical

construction of the tractor rear axle suspension with coupling-rods and roil stabilisers

is realised with constraints and joints. The roll stabiliser is constructed with two bodies

and in between is a stiff rotational spring damper actuator. The four airsprings and the

two dampers are realised with translational spring damper actuators and so are the

suspension bumps (F.P.J. Bekkers [2])(see figure 5.2).

Point of interest Semi-active damper

' '. ; . . ': Rollstabilizer

Airsprings body

--Right wheel body

...- Left wheel body

side-view top-view

figure 5.2: Real construction with DADS bodies.

The triads (affixed points on the bodies), used to implement the original damper, lie

straight above each other, the dampers stand straight up, see figure 5.2. These points

are also the points of interest of the DADS DAF95 model with respect to the quarter

vehicle model.

19

5.2 The controller used to drive the truck straight ahead

/ I semi-active dampers with the direct calculation

controller. The road profile offered to the right tires is

the same as the road profile offered to the left tires.

- 1 20

0 0.90 .- c 61 0.60 P 9 :I_j~

O 30

O The differences between the left and right side O 40 80 120 160

(dampers) should be decreased with the help of a

controller that drives the DADS DAF95 straight

Times [SI

figure 5.3

ahead. The mass of the DADS DAF95 model is asymmetrically distributed with respect

to the left and right side. An extra petrol tank is constructed on the left side of the

tractor. Therefor the DADS DAF95 model has a driving deviation to the left side when

the driving wheel is fixed (see figure 5.3). This driving deviation is undesirable. Two

controllers were already developed to drive the DADS DAF95 model along a

prescribed path. The purpose of these controllers are to simulate the lane change

manoeuvre and to determine the handling properties of the DADS DAF95 model. The

lane change manoeuvres are simulated on a flat road profile. The first controller is a

trajectory prescribed path controller (T. v. d. Broek [3]). This controller makes use of

the inverse dynamics of the front axle in the x-y surface. The second controller is a PI

controller (W. Vos [13]). The PI controller is implemented on the DADS DAF95

model. The controller results obtained with the DADS DAF95 model and the ‘negative

wave’ road profile are unstable (see figure 5.4). The integrator winds up when the

front tires are free of the ground (see figure 5.5, t = 5 [s]).

Driving direction Front tire force -1 50 - E 100

E u

$ 50

O

.e ,- e 3 40

-50 20

6 7 7 5 5 Time [ s] 8

-100 6

Times Is]

figure 5.4 figure 5.5

20

And when the tires touch the ground the controlled steer angle is too great to manage

(t = 5.5 [s]). Both controllers don’t take care of the possibility that the tractor-

semitrailer is out of control when the front tire-road contact decreases in consequence

of a too extreme road profile. Extreme road profiles are ‘wave 1 ’, ‘wave 2’, ‘negative

wave’ and ‘traffic hump 2’. In a good PI controller an anti windup system (K. Aström

[ 141) is involved. A Conditional integration is implemented. The integral stops updatkg

when the tire force is almost zero. At the moment the tires touch the ground the

integration process should be reset. This is impossible during the integration process of

DADS. Therefor the integration process is restarted but without any success. The

discontinuity is impossible to offer by the DADS integration process.

The only reason to use an integrator in this case

(controller to drive straight ahead) is to suppress the

offset. The mean offset of the DAF95 model on the

road is 0.3 [mm]. That is why a P controller is

implemented to the DADS DAF95 model. But it is

also implemented because of its simplicity of tuning

and the less tax on the integration process of DADS.

The worst controller results are realised with the

DADS DAF95 model and the ‘negative’ road profile

Driving direction zo

-10-

-154 5 6 7 8

Time [ s]

figure 5.6

(see figure 5.6). Even these controller results are good with respect to the desired

performances. The P controller is not so tightly tuned so it can resist the unstable

moments after the tires touch the ground. A small summary of the controllers is given

in table 5.1 -a and a summary of the performance of the P controller is given in table

5.1-b.

implemented yes no Yes ‘yes’

table 5.1-a

controller I fixed I TPPC I PI I conditional PI I P

Yes

lTSUltS I

Fig. 5.3 - Fig. 5.4 - Fig 5.6

21

road profile

max(amp) [mm]

5.3 The comparison of the rear axle suspension of the

DAF95 model with a quarter vehicle model

1 2 3 4 5 6 7 8 9 1 0

0.05 0.6 0.85 0.6 0.5 0.6 3.1 3.8 0.5 17

A quarter vehicle model is built to compare with the rear axle suspension of the DADS

DAF95 model. The comparison gives more insight into the DADS DAF95 model and

its differences with the quarter vehicle controller model. The unmodelled dynamics of

the quarter vehicle model are of a great interest. The FORTRAN quarter vehicle is

supposed to resemble the rear suspension of the DADS DAF95 model. The quarter

vehicle, described in paragraph 3.1 with the original suspension damper characteristic

is used. This model is expanded with some missing characteristics with regard to the

DADS DAF95 rear axle suspension. The lowest suspension bump at -0.09 [m] and the

upper suspension bump at O. 14 [m] are added to the airspring characteristic as very

stiff springs. The tire model is supplied with a linear damper. See figure 5.7. for the

expanded quarter vehicle model. This expanded quarter vehicle model with semi active

damper will be used as the controller model in the next chapter.

I Chassis

VelociW [mis] Displacement [m] I Rear axle I

hs~lacmsnt Iml r Filter ( l e order) I

roadprofile

figure 5.7

22

The modelled dynamics, especially the front axle suspension of the tractor and the axle

suspension of the semitrailer, influence the simulation results of the rear suspension of

the tractor of the DADS DAF95 model. The influences of the front axle suspension of

the tractor and the axle suspension of the semitrailer are the most important because of

their low frequency and their great amplitude. These influences are clear visible in the

comparison of the rear suspension of the passive DADS DAF95 modei and a quarter

vehicle model. A general impression of the comparison is made in table 5.2

roadprofile 1 2 3 4 5 6 7 8

sim3asity ++ ++ k ++ ++ ++ + + 9 10

+ k

The trends of the quarter vehicle simulation model are nearly the same as the

simulation results of the rear axle suspension of the DADS DAF95 model. In general:

the influences of the tractor front axle and the semitrailer rear axles are bigger when

the vehicle speed is lower and when the obstacles are more intensive. An intensive road

profile is recognisable by its height and its shape. Intensive road profiles are : “Wave

I”, “Wave 2” ,”Negative wave” and “Traffic hump 2”. Three of the 10 simulation

results are discussed on the basis of the rear axle suspension deflection of the tractor of

the DADS DAF95 model and on the basis of the axle suspension of the quarter vehicle

mode!.

A good similarity between the quarter vehicle

model (thin line) and the DADS DAF95 model Suspension deflection

150 $1

-

- -100 ‘ 4 5 6 7

Time [SI

(thick line) is visible in the simulation results of

the road profile called “Traffic hump 1” (#2)

(see figure 5.8). The small influences of the

front axle of the tractor of the DADS DAF95

figure 5.8 (‘just before the obstacle). Until that time the

quarter vehicle model has no disturbance.

23

Suspension deflection ‘ h 150 I

Time [SI

figure 5.9

A good example of the influences of the front

axle of the tractor and the rear axles of the

semitrailer of the DADS DAF95 model (thick

line) are clear to see in the simulation results of

the road profile called “Traffic hump 2” (#3).

Before the quarter vehicle and the rear axle

suspension of the tractor reaches the obstacle

the simulation results of the DADS DAF95

model are influenced by the front axle

suspension of the tractor. A dip of the suspension deflection caused by the rear axle

suspension of the semitrailer is performed at about 7.8 seconds. A combination of the

low vehicle speed and the rather intensive obstacle makes these influences happen (see

figure 5.9).

Suspension deflection 2 0 0 1 I

-200 L I 4 5 6 7

Time [SI

figure 5.10

A rather good similarity between the quarter

vehicle model (thin line) and the DADS

DAF95 model (thick line) is clear to see in the

simulation results of the road profile called

“wave 1” (#7). The influences of the

suspension bumps are visible at 140 [mm] and

90 [mm]. They introduce high frequency

vibration in the chassis and the rest of the

model. After hitting the suspension bumps the

DADS DAF95 model has a smaller transient suspension deflection with respect to the

quarter vehicle model. This causes some time deviation between the simulations. (see

figure 5.10). For the extended simulation results see appendix E.

5.4 The implementation of the fixed semi-active damper

The two passive dampers in the DADS DAF95 model will be exchanged by two fixed

semi-active dampers. The semi-active dampers are fixed on the high damping

characteristic. The implementation in DADS DAF95 model is rather similar to the

implementation of the semi-active damper in the DADS quarter vehicle model. The

24

control scheme, see appendix H, has great resemblance with the control scheme of

figure 3.4. The differences of the original damping characteristic and the high damping

characteristic are visible in figure 5.1 1.

Original & high damping char.

60

-10’ I -2 -1 O 1 2

Velocity [ d s ]

figure 5.1 1

The dashed dotted line represents the high damping characteristic, the continuous line

represents the original damping characteristic. The high damping characteristic is much

higher and so the damper response will be more quickly stabilised than the original

damper response.

5.5 The simulation results

The simulation results of the DADS DAF95 model with the original damper are

compared with the simulation results of the DADS DAF95 model with a fixed semi-

active damper. The question is: are, with respect to the performance criterion of the

DCC, the simulation results of the DADS DAF95 model with a fixed semi-active

damper better than the DADS DAF95 model with the original damper. The criterion of

the controller is a weighted sum of the maximum absolute vertical chassis acceleration,

the tire lift-off time and the crossing of the suspension deflection bounds. A general

impression of the comparison is made in the table 5.3.

25

roadprofile 1 2 3 4 5 6 7 8 9

improvement k Zk f - - k + + --

The first impression is that the model wiîh the fixed semi active damper improves the

simulation results with respect to the performance criterion of the DCC. The

improvements silown in table 5.3 have a big resemblance tc the intensity of their road

profiles. Road profile “Railway crossing” is a rather flat obstacle. The excitation

caused by this road profile is rather soft, so the improvement reached with the fixed

semi-active damper is small. The road profiles “wave 1 and wave 2” are intensive road

profiles, and therefore their excitation causes a rather great improvement. The

simulation results of both models on the road profile “wave 1” are shown in figure

io .t

5.12)

Tire force 150 1

Suspension deflection

Time [SI figure 5.12-a

Chassis acceleration 30 I

y 20 . E 10 .o o z 2 -10

E Y

al o 2 -20 I

4 5 6 7 -30 ‘ Time [SI

figure 5.12-c

-150 4 5 6 7

Time [s]

figure S. 12-b

Diff. left - right damper 2 0 1 I

1

E - 0

-1

- <li 1

4 5 6 7

- $

Time [SI figure 5.12-d

The thick line represents the DADS DAF95 model with fixed semi-active damper, The

thin line represents the DADS DAF95 model with original damper. Figure 5.12-a

shows the rear tire force. The general tendency is the same, but the tire force of the

26

DADS DAF95 model with fixed semi-active damper has smaller peaks. The tire lift-off

time, the time when the tire force is zero, decreases. Figure 5.12-b shows the rear axle

suspension deflection. The differences between both dampers is great. The time of the

crossing of the suspension deflection bounds decreases. The complete deflection of the

model with fixed semi-active damper stabilises faster. Figure 5.12-c shows the vertical

chassis acceleration. The high frequency vibrations caused by the suspension bumps of

the DADS D M 9 5 model with original darnper are visible at 4.7 seconds and at 5.5

seconds. The chassis acceleration of the DADS DAF95 model with the fixed semi-

active damper is less spiky and the maximum and minimum acceleration decreases. The

improvement of the fixed semi-active damper against the original damper is great with

respect to the performance criterion of the DCC. The differences between the left and

right side of both models with respect to the rear axle are shown in table 5.4.

r~adproaile 1 2 3 4 5 6 7 8

improvement - k 1i - - k + + 9 io -- k

The differences shown in table 5.4 have a big resemblance with the intensity of their

road profiles. A soft road profile like “railway crossing” has a small difference. An

intensive road profile like “wave 1” has a great difference between the left and right

side. The differences realised on road profile “wave 1” are rather big (see figure 5.12-

d). The desired 2D situation of the 3D DADS DAF95 model doesn’t succeed well.

Therefore, two DC controllers will be implemented on the semi-active DADS DAF95

model in the next chapter, one DCC for the right side and one DCC for the left side.

For the extended simulation results see appendix F.

27

Chapter 6 The semi-active DAF95 tractor-semitrailer

The implementation of the semi-active damper system in the quartercar model

succeeded and the passive DADS DAF95 model is prepared. Here the implementation

of the semi-active damper system with a direct calculation controller in the DADS

DAF95 model is considered. The first paragraph discusses the implementation of the

direct calculation controller. The second paragraph describes the problem to get a

suitable state for the controller model from the simulation model. The third

paragraph gives some common solutions to solve this problem.

The implementation of the direct calculation controller on the DADS DAF95

simulation model is almost the same as the implementation of the direct calculation

controller on the quarter vehicle simulation model in DADS. Although the road

profiles for the left and right wheels are identical, the differences between the left and

right damper velocity are not negligible. Therefore a separate controller is implemented

for the left and right damper. The position and the velocity at t of the left semi-active

damper connection points of the DADS model are used as initial condition for the

controller model of the left controller, and the position and velocity of the right semi-

active damper connection points of the DADS model are used as initial condition for

the controller model of the right controller. The prediction results of the quarter

vehicle controller model with the 26 different damper setting sequences predict the

behaviour over the preview interval [t , t+3.5/v]. The used quarter vehicle controller

model is the extended quarter vehicle model with suspension bumps and a tire damper

(see figure 5.7). In paragraph 5.3 we saw the resemblance between simulation results

of the extended quarter vehicle model and the rear axle suspension of the DADS

DAF95 model. Because the DADS DAF95 tire model doesn’t use something like a

finite road contact, the filtered road profile (x6) used as a finite road contact in the tire

28

model of the quarter vehicle controller model is explicit constructed. The implemented

control scheme (see appendix H) of the two semi-active dampers and controllers on

the DADS DAF95 model is similar to the implemented control scheme on the semi-

active quarter vehicle simulation model.

5.2 The initid condition for the controller modell.

At the beginning of every new subinterval an initial condition has to be determined for

the quarter vehicle controller model from the DADS DAF95 simulation model. The

position and the velocity of the connection points of the semi-active dampers are

chosen as the initial condition. This initial state is a relative state with respect to the

static equilibrium of the DADS OAF95 model which conform to figure 4.3. The front

wheels reach the beginning of the obstacle at 4 seconds; the static equilibrium of the

DADS DAF95 model is defined at 3.9 seconds (tl = 3.9 [SI, see figure 4.3). First, the

prediction results (simulation results of the quarter vehicle controller model) are

determined with the relative rear axle state from the DADS DAF95 model at t = 3.9 [SI as initial state.

Axle dis. 1

-0.2' ' I 4 4.5 5 5 . 5 6

Time [SI

figure 4 . I-a figure 6.1-b

29

In this case the response of the quarter vehicle controller model resembles the

behaviour of the rear axle suspension of the DADS DAF95 model. Figure 6.1-a and

6.1-b shows respectively the left rear axle position and the left rear axle velocity

[x,(t) and x3(t)]. The fat dashed line represents the simulation results of the semi-

active DADS DAF95 simulation model on road profile “wave 1” and the thin

continuous h e represents the results of the quarter vehicle controller model. These

results of the quarter vehicle controller model are here called the natural prediction

results of the quarter vehicle controller model. The unmodelled dynamics causes some

small differences between the 3D DADS DAF95 model and the quarter vehicle

controller model.

Axle dis. 0.6[[/

Axle vel.

-0.1‘ I 3.8 4 4.2 4 . 4 4 . 6

Time [SI

figure 6.2-a figure 6.2-b

If the initial condition of the quarter vehicle controller model is taken from the DADS

DAF95 model at a non static equilibrium state, then the prediction of the quarter

vehicle controller model shows a transient response with regard to the simulation result

of the rear axle suspension of the DADS DAF95 model. Figure 6.2-a and 6.2-b show

respectively the left rear axle position and the left rear axle velocity [xl (t) and x,(t)]. If

the initial state is taken from the actual state of the DADS DAF95 model at 4.295

seconds, the thin dashed dotted line represents the prediction results of the quarter

vehicle and the fat dashed line represents the simulation results of the semi-active

30

DADS DAF95 simulation model. A small deviation of the axle position with regard to

the natural prediction results causes a transient response of the velocity of the axle.

This prediction result is comparable with the underdamped response of a mass spring

damper system to a step function. The cause is the stiff tire spring and the small tire

damper. The direct calculation controller uses this transient prediction result to

determine the optimal damper setting sequence. The damper setting (the first bit of a

binzy Uiznper setting sequence number between O and 63) is based on the moment

when this undesired transient prediction result is at worst. These calculated desired

damper settings are therefore useless. For the total state comparison see appendix G.

6.3 Some solutions

The main purpose of a controller model is to predict the responses of the DADS

DAF95 rear axle suspension during the preview interval. The problem is how to get a

suitable initial state for the controller model from the DADS DAF95 simulation model.

Three possible solutions are:

1. a controller model which describes the vehicle dynamics better, for instance a half

vehicle controller model instead of a quarter vehicle controller model. Such a half

vehicle controller model describes not only the tractor rear axle dynamics but also

the influences of the tractor front axle suspension and the axle suspension of the

semitrailer. This solution has some disadvantages. There is no preview in front of

the front axle suspension so the road surface in front of the vehicle is unknown.

The exactness of the prediction of the tractor front axle behaviour during the

preview interval depends on the assumed road surface in front of the tractor front

wheels. Furthermore a half vehicle controller model asks much more calculation

time than a quarter vehicle controller model and the calculation capacity of a

practical controller is limited.

2. a quarter vehicle controller model with an adaptive character to suppress the

unmodelled dynamic influences. An identification method for instance with respect

to the chassis mass, the tire spring and tire damper of the quarter vehicle model can

be used. Both, the effective mass just above the rear suspension and the tire model

31

3.

of the DADS DAF95 model are not well known and cause indirectly the transient

response. The identification is rather useless because the effective mass just above

the rear axle suspension of the DADS DAF95 model fluctuates to much during the

preview interval. This fluctuation is mainly caused by the movement of the tractor

front axle suspension and the axle suspension of the semitrailer.

an extra simulation model (quarter vehicle model) which generates perfect states

for the quarter vehicle controller model. The corisequence is, there is EO feedback

from the DADS DAF95 model. The influences of the front axle suspension of the

tractor and the axle suspension of the semitrailer and all the other unmodelled

dynamics are ignored. Only the reconstruction of the road over the preview interval

is used by the controller.

32

Chapter 7 Conclusions and

7.1 Conclusions 1.

2.

3.

4.

5.

6.

Recommendations

For special needs, the user can use a very extended ability to connect FORTRAN

files to DADS. In spite of this extended ability, there is only one suitable way to

realise a semi-active damper in DADS. The way to do so is by control-elements

and a specific control element which links FORTRAN to DADS.

The semi-active damper with the direct calculation controller is implemented and

accurate tested on a quarter vehicle simulation model in DADS. The DADS

simulation results correspond with the simulation results realised with the same

model in FORTRAN in spite of the less accurate DADS implementation of the

controller.

Two controllers were already developed to drive the DADS DAF95 model along a

prescribed path. But they don’t take care of the lift-off effect of the tractor front

wheels. The developed, implemented and tested proportional controller which

drives the tractor-semitrailer combination straight ahead is simple and the

controlling results are satisfying in spite of the lift-off effect of the tractor front

wheels.

The resemblance of the quarter vehicle model responses and the rear axle

suspension responses of the 3D model are rather big. The non-linear characteristics

of the dampers and the springs of the quarter vehicle model are the same as the

DADS DAF95 model.

A rather big performance improvement can be achieved on the investigated road

profiles if the original damping characteristic is replaced by the high damping

characteristic in the passive DADS DAF95 model.

The direct calculation controller is rather sensitive for small fluctuations of the

initial state. The actual state from the simulation model as an initial condition for

33

the controller model causes a transient response of the controller model. This

transient response is undesirable with regard to the direct calculation controller.

7.2 Recommendations

I. The step from a quarter vehicle simulation model to an extended 3D DADS

DAF95 model is rather big. A half vehicle model (6dof) with the non-linear

damper and spring characteristics in FORTRAN give the same insight as the

3D DADS DAF95 model in a simpler way. The implementation of the direct

calculation controller is easier because there are no typical DADS

implementations involved. The problem of unmodelled dynamics is similar.

To succeed the realisation of the direct calculation controller in the “reality”,

the robustness of the controller strategy should be improved andor the

controller model should predict a better simulation result of the DADS DAF95

rear axle suspension during the preview interval.

A.

11.

The controller is rather sensitive for small fluctuations of the initial

state. The robustness of the controller strategy is possibly to improve.

Maybe a relative acceleration can be used in the performance criterion,

or a relative weighage between the 26 prediction results can be

inspected. Maybe the optimal moment of changing the setting can be

determined in stead of a fixed number of subintervals on which the

setting is changed. Maybe the simulation results of a controller model

with only the high and the low damper characteristic over the preview

interval give an insight in the moment of changing the damper setting.

The initial condition of the controller model from the simulation model

needs more attention. A possible solution can be realised with the help

of the quarter vehicle controller model and an Extended Kalman Filter.

The solution is a combination of the solutions 2 and 3 described in

paragraph 6.3. The simulation results of the expanded quarter vehicle

(see figure 5.7) equalise the simulation results of the rear axle

suspension of the DADS DAF95 model (see table 5.2). An extended

B.

34

Kalman Filter estimates the state (also the initial state for the controller

model) of the quarter vehicle model and identifies the parameters.

These parameters are for instance the mass of the chassis, the tire

stiffens and tire damping. The purpose of the parameter identification is

to make the controller model independent. The mean chassis mass

(think about the cargo fluctuations in reality) and the mean tire stiffens

and tire uamping (think about the tire wear in reality) can be identiîied

and applied to the controller model. This extended Kalman filter should

not correct for unmodelled dynamics.

35

Chapter 8 Bibliography

Bekkers F.P.J., Modülar based vehicle modelling. 3 3 modular base6 tractor semi

trailer models to predict the dynamic behaviour on handling and deterministic

road irregularities. Master’s thesis, Report No. TUE/W/WFW/95-078

Bekkers F.P.J., Modular based vehicle modelling. Supplement: Main component

description. Master’s thesis, Report No. TUEíW/WFW/95-078

Broek T v.d., Inverse simulations in vehicle dynamics, Report No.

T ~ J E N W I ‘ ~ 1 - 1 14

DADS Reference manual revision 7.5 Vol 1

DADS Reference manual revision 7.5 Vol 2

Foag W., Regelungstechnische konzeption einer Aktiven FKW-federung mit

“Preview”. VDI-Verlag, 1990.Fortschr.-Ber. VDI Reihe 12 Nr. 139, ISBN 3-18-

143912-6

FORTRAN manual, Pitman, The Professional Programmers Guide to

FORTRAN 77, University of Leicester department of Physics

Haug E. J., Computer aided kinematics and dynamics of mechanical systems.

Vol 1 Basic methods. The University of Iowa, 1985.

Huisman, F.E. Veldpaus, H.J.M. Voets, and J.J. Kok. An optimal continuous

time control strategy for active suspensions with preview. Vehicle System

Dynamics, 22:43-55, 1993

Morari M., C. E. Garcia, D.M. Prett. Model Predictive Control: Theory and

Practice, a survey (1989). California Institute of Technology.

Muijderman J.H.E.A., personal communication

Sauren A., Multibody dynamica, TUE Lecture nr. 45550

Vos W. A., Handeling Voertuigreactie op spoorvorming, Eindhoven University

of Technology, WOCíVTIpu95.52

Aström K.J., Wittenmark B. and S .B. JGrgensen. ( 1990) “Process Control”

Kompendium, Lund Institute of Technology.

36

Appendix A Road profiles

This appendix deals with the ten different roadprofiles. These different roadprofiles are

related to real situations. These ten different road profiles are exactly modelled in a

FORTRAN file. Both the DADS models and the FORTRAN models make use of this

FORTRAN file.

A B v others [ml Em1 [kmhl

A w

1. Standard brick 4-L 0.105 0.065 80

2. Traffic hump1 & \ 0.6 1.4 20 C=O.1

3. Traffic hump2 AT\ 1.0 2.25 15 C=0.25

A B A IcJ(c-JIcJI

4. Scraped road 1 0.07 60

5. Scraped road2 IA r 0.07 60 A

6. No lid of well 0.6 0.1 40 M

A - 7. Wave1 'n 25.0 0.5 80 sinus2

A - 8. Wave2 ~n 7.5 0.2 80 sinus2

9. Railway cross. 25 Tongelre

Al

Appendix B UNIX script file

The UNIX script file listed below is created to simplify the execution of a model with

IO different roadprofiles and to reduce the lage binary-file with all the slxu!attion

results to a matlab-file containing only the interesting results. This script file is

executed by the command:

sun3% run-dads-all model-def

The script file works as follows:

- The needed files are checked on there existence. These files are the curves.cmd,

ndads3d, model.def and dads2matlab.

- The curves.cmd file is a file which contains the commands to plot the

interesting curves in the dadsgraph postprocessor.

- The ndads3d file is a new executable of DADS with the user defined

FORTRAN routines linked at it.

- The model.def file contains the model such as DADS uses it. The model is

dependent on the number of roadprofile and the vehicle speed. Both are

changed by changing the symbols speed and obstacle in the model.def file.

- The dads2matlab file is used by GAWK which translates the contents of a

DADS ASCII output file to a MATLAB file.

- The needless files, are deleted. Especially the MATLAB-files and the log-file can

cause some trouble.

- The definition file (.de0 is loaded by the standard DADS executable.

- The symbols speed and the number of the roadprofile are set.

- The model is saved in a formatted file. A definition-file and a formatted-file are files

which are used by DADS to store the model in. The formatted-file has a format to

execute a calculation. The definition-file has a format to assemble a model.

B1

- The calculation with the formatted file is started by the new DADS executable. The

DADS-sum produces usually an information-file (.in0 with information of the

calculation process and a binary-file (.bin) with all the results of the total model.

- The dadsgraph postprocessor loads the binary-file and the command-file

curves.cmd. This command-file possess the interesting states of the model.

- The created m i e s are saved in a data-file (.dat) with an ASCII-format.

- "his data-file is manipulated by the GAWK application. GAWK needs 2 file with

commands, the dads2matlab-file . These commands are applied to every line of the

data-file. The results are stored in a MATLAB-file (.m).

- The files not needed anymore are deleted. These files are the formatted-file the

binary -file the information-file and the data-file.

- An log-file is created to store in all the results normally sent to the screen.

B2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . run-dads-al1 ............................

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

# ! /bin/sh

# k is the directory to run the DADS sum in. This is a temporary # disk. The available space in this directory suppose to be greater

# then the space used by DADS.

#k=$ { PWD)

k=/usr/tmp

if [ !

then

fi if [ !

then

fi if [ !

then

fi

if [ !

then

-r ${PWD)/curves.cmd ]

echo The curves.cmd file isn\'t readable

exit

echo The $1 file isn\'t readable exit

-f ${PWD>/ndads3d I

echo The ndads3d file doesn\'t exist

exit

-r ${HOME)/bin/dads2matlab I

echo The ${HOME)/bin/dads2matlab file isn\'t readable exit

fi echo

echo mfiles='ls *.m'

fm3files='ls ${k)/*.fm3'

datfiles='ls ${k)/*.dat' inffiles='ls ${k)/*.inf'

binfiles='ls ${k}/*.bin'

logfiles='ls log' echo

echo "Remove the files ? "

echo

echo $mfiles echo Sfm3files

echo $datfiles

echo Sinffiles

echo $binfiles

echo Slogfiles echo

echo " (y/n) "

read input

B3

case $input in

y) rm -f *.m ${k}/*.bin ${k}/*.inf ${k}/*.dat ${k}/*.fm3;;

n) echo "Sorry no execution !";exit

esac echo

echo A log file is created.

echo

dads -nomenu -3 > log <i done

load hierarchy $1

set symbol speed 80/3.6 set symbol obstakel 1

save formatted ${k}/steen.fm3

done ndads3d >> log << done

${k}/steen

${k}/steen ${k}/steen

${k}/steen done

dadsgraph -nomenu >> log << DONE

open ${k}/steen.bin cmd curves.cmd

write curve ${k}/steen.dat exit n

DONE gawk -f ${HOME}/bin/dads2matlab ${k}/steen.dat > steen.m

rm ${k}/*.bin ${k}/*.inf ${k}/*.dat ${k}/*.fm3

dads -nomenu -3 zz log << done

load hierarchy $1 set symbol speed 20/3.6

set symbol obstakel 2

save formatted ${k}/verkeerl.fm3

etc. etc.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . curves.cmd . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

curve curve

curve

curve

curve

curve

curve curve

"road: z " road

tirespring: for" tireforce

"spring : dis" suspension-deflection

"spring:vel" demper-velocity

"MASS2 : ZDD" massa-zdd "node-8 demperforce

"node-9 Ir set-d

" node-1 O " set

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . dads2matlab . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

((NF == 7) && (tell == o ) ) {

nrec=$l; teller=l ;

tell=O

print "B= [ ''

>

((NF == 2 ) && ($1 ! = "x-axis:") && ($1 != "y-axis:") && (tell == O ) ) {

teller += 1:

}

((NF == 2 ) && ($1 ! = "x-axis:") && ($1 ! = "y-axis:") & & (teller i nrec+l) && (tell ==

0 ) ) I print $0

1

((teller == nrec+l) && (NF == 2 ) && (teil == O ) ) {

print $0 " I ; " tell=2 ;

1

((NF == 7) && (tell ! = O ) ) {

nrec=$7 ; teller=l;

tell+=l print " B ( : , "tell") = [ "

((NF == 2) && ($1 ! = "x-axis:") && ($1 != "y-axis:") && (tell ! = O ) ) {

teller += 1;

1

((NF == 2) && ($1 ! = "x-axis:") && ($1 ! = "y-axis:") && (teller i nrec+l) && (tell ! =

0 ) ) I print $2

>

((teller == nrec+i) && (NF == 2 ) && (tell ! = O)) {

print $2 " 1 ; "

1

B5

Appendix C Passive quarter vehicle model

This appendix compares the simulation results of the quarter vehicle models in DADS

with the quarter vehicle model in FORTRAN. The qurter vehicle models with a

passive damper are:

- the quarter vehicle model implemented in FORTRAN.

- the quarter vehicle model with the fixed semi-active damper realised with control

elements implemented in DADS.

Only the simulation results of the passive quarter vehicle models on the roadprofile

“Standard brick” are enclosed in this appendix. The simulation results of the quarter

vehicle models on the roadprofile “Standard brick” shows the small differences

between the DADS and FORTRAN integrator. The simulation results of the quarter

vehicle models on the other nine roadprofiles are identical.

DADS -fortran -

2 E c \

O

cd

o o

.- U

8 -2

4

Standard brick

o f

-

Road profile

3 0 . 0 4

u 0 . 0 3 Y

g 0.02

9 a O

o cd - 0.01

- 0 . o1 ' J 0 . 5 0 . 6 0.7 0 . 8

Time [SI

Suspension deflection 0 . 0 1 i I

- 0 . 0 2 I 0 .5 0 . 6 0 . 7 0.8

Time [SI

Chassis acceleration 21 I

-4 ' I 0.5 0 .6 0.7 0 .8

Time [SI

3 0 0

250

2 200

tL" 100 25 o 150 2

50

n

Tire force

Y

0 . 5 0 . 6 0 . 7 0 . 8 Time [SI

Damper velocity

7 0 . 5 . E u

.- 2 0 o O o 3

> - 0 . 5 -

-1 1 I - 0.5 0 . 6 0 . 7 0 . 8

Time [SI

Damper force 40 i

-10 0.5 0 . 6 0 . 7 0 . 8

Time [SI

c2

Appendix D Semi active quarter vehicle model

This appendix compares the simulation results of the quarter vehicle model with semi-

active damper and direct calculation controller in DADS and the same semiactive

quarter vehicle model in FORTRAN. Only the simulation results of the semi-active

quarter vehicle models on the road profile “Wave 2 are enclosed in this appendix. The

simulation results of the quarter vehicle models on the road profile “Wave 2” shows

the small differences between the DADS and FORTRAN implementation.

Dl

0.2 n

-0.15 E

g 0.1 3

n

Y E a,

3

.? O. 05 n

DADS - fortran ~

Road profile

ö.5 1 1.5 2 Time [s]

Suspension deflection I._.I

-0.2' I

0.5 1 1.5 2 Time [SI

Chassis acceleration I

-20 ' I

0.5 1 1.5 2 Time [s]

Fortran damper setting

300

250

2 200 3 a, 150 2 ;4" 100

CI 50

Wave 2

Tire force

u.5 1 1.5 2 Time [SI

Damper velocity

- 3 L I I

0.5 1 1.5 2 Time [SI

Damper force 100 I

8 0

E 6 o a, 40

20

O -20 ' 0.5 1 1.5 2

Time [SI

DADS damper setting 1 1

0.8 0.8 I - 0 . 6 I - 0 . 6

M c .e 0 0.4 5 0 . 4 co co 0.2 0.2

n

M E

.3

n n ö.5 1 1.5 2

U

0.5 1 1.5 2 Time [SI Time [SI

D2

Appendix E Comparison of a quarter vehicle model with the

rear axle suspension of the DADS DAFBS model

This appendix compares the simuiation results of the rear axle suspension of the DADS

DAF95 model with the quarter vehicle model in FORTRAN. Both models contain the

original dampers. The road profile in the DADS DAF95 model is not exactly called in,

so figure “Road profile” gives only an indication of the road profile of the DADS

DAF95 model with regard of the quarter vehicle road profile. Of course, the

roadprofiles applied to both models are exactly the same. The Chassis acceleration of

the DADS DAF95 model is plotted with respect to the chassis body situated between

the front axle and rear axle. This chassis acceleration is not the chassis acceleration

straight above the rear axle suspension. So the comparison is misleading with regard to

the chassis acceleration of the quarter vehicle model.

El

DAF95- 2d0f -

* 0.4-

2 0 . 2 - 2 n O -

- .-

Traffic hump 1

z y 150. 0

h

O

150 1.5

100- 1 1- Y 5 0.5- n -

x

O

.+ * o

-0.5-

-1. >

D

0 9

30 15 - 2 10 2 0 . E Y

* o ; Y 0 10-

c4

c 5 O .3

O

-10

3 0

-5 2

E2

qh

0 .8

n -0.6 E

s CI

0.4 o cj 3

20.2 n n

DAF95- 2d0f -

Road profile

: ,fl,, , ~

" 4 5 6 7

Time [SI

Sumension deflection I

150 n 2 100 Y 3 50 E $ 0

ci

cd 3

2 -50 -100

4 5 6 7 Time [SI

Chassis acceleration 20 I I

-20 ' I 4 5 6 7

Time [SI

Traffic hump 2

Tire force 250 1

200

150 E a g 100 lL

50

O ' / I 4 5 6 7

Time [SI

Damper velocity 2 i

/ W

-2 ' 4 5 6 7

Time [SI

Damper force 40 - 30

20 o g 10 lL

O

-10 ' 4 5 6 7

Time [s]

E3

DAF95- 2dof

c a,

Wave 1

0 3

Road profile

2

4 5 6 7 Time [s]

c

600

500

400

a, 3 0 0 2 Y

2 200 100

O

Tire force

4 5 6 7 Time [SI

Damper velocity

41-----7 Suspension deflection

200 I

-200' I 4 5 6 7

Time [s]

-4 I 4 5 6 7

Time [SI

Chassis acceleration - 6o 3

Damper force I

3 0

g 20 Y

0 10

-10 -40 I

4 5 6 7 Time [SI

-20 I 4 5 6 7

Time [SI

E4

Appendix F Passive DADS DAF95 model

This appendix deals with the comparison of the simulation results of the DADS

DAF95 mode! with the original damper (pass.) a d the DADS DAF95 rnodel with the

fixed semi-active damper (semi-p.). The road profile of the quarter vehicle model in

DADS is not exactly called in, so figure “Rear wheels left” gives only an indication of

the road profile of the DADS models.

F1

0.6

20.58

.i 0.56

.o 0.54 8 0.52

Y

W cj - U

.* 0 -5-

3 -10

2 -15

U

cj I.i

a, o

pass. ~ semi-p. - Scraped road 2

-

-

Rear wheels left I

n

E E Y

~

J

!

0.5 4 5 6 7

Time [SI

c 0.5' 0

o .3 U

o - .

Suspension deflection 201 A '

-80 I I

4 5 6 7 Time [SI

Chassis acceleration I

I -20 '

4 5 6 7 Time [s]

Diff. left - right damper

.3 v) W a 3

Tire force 100

80

y 60

8 40 c4

20

O

z a,

4 5 6 7 Time [SI

2

" 1 3 .=" o o 0 a, - k -1

-2

Damper velocity

------l 4

4 5 6 7 Time [SI

Damper force - 30

20.

-10 ' I 4 5 6 7

Time [SI

Driving direction l 7

I -0.02 ' 4 5 6 7

Time [SI 4 5 6 7

Time [SI

F2

pass. - semi-p. - Wave 1

Rear wheels left 1.2

0.2' I 4 5 6 7

Time [SI

Suspension deflection

Tire force 150 I

4 5 6 7 Time [s]

Damper velocity

-150 ' I 4 5 6 7

Time [SI -4 I I 4 5 6 7

Time [SI

Chassis acceleration 3 0 1

Damper force 40

;*i <, 20 30 y 10 z e & 20

cd g 10 3 -10 L

2 -20

.- O 0 0 *

a o O

- 3 0 ' I 4 5 6 7

Time [SI

Diff. left - right damper

-1 I I

4 5 6 7 Time [SI

-10 I 4 5 6 7

Time [SI

Driving direction

-3 I 4 5 6 7

Time [SI

F3

O.

- Y E o . v)

3 - o . cd o .- U 5 o .

O.

- v)

- Y E $

pass. - semi-p. -

O----

Rear wheels left

4 5 6 7 Time [SI

Suspension deflection I

4 5 6 7 Time [s]

Chassis acceleration I

Railway crossing

Tire force

40 1

15 I 4 5 6 7

Time [SI

Damper velocity l 7

4 5 6 7 Time [SI

Damper force 2 5 -

-6 ' I 4 5 6 7

Time [SI 4 5 6 7

Time [SI

Diff. left - right damper - 61 i

(li .3

Driving direction 0 . 8

3 0.6 E y 0 .4

8 0 . 2 O .e U

-0.21 I 4 5 6 7

Time [SI

F4

Appendix G The initial state for the quarter vehicle

controller model from the DADS DAF95 model

This appendix deals with the problem to get a suitable initial state for the quarter

vehicle controller model from the rear axle suspension state of the DADS DAF95

simulation model. The stars represent the states of the semi-active DADS DAF95

simulation model. The thick dashed line represents the simulation results of the semi-

active DADS DAF95 simulation model. The thin continuous line represents the

response of the quarter vehicle on the actual state of the DADS DAF95 model started

at 3.9 seconds. These simulation results, here called the natural simulation of the

quarter vehicle, are rather the same with respect to the semi-active DADS DAF95

simulation results. The thin dashed dotted line represents the response of the quarter

vehicle on the actual state of the DADS DAF95 model started at 4.295 seconds.

GI

Daf95- 2dof

0.6

0.5

0.4

0 . 3 - Y E 2 v, 0.2

0 -

-0.1

-0.2

0.5

Y

.3

fl\ -

-

I

f o - l : J ' '

-

-0.5

Axle vel. 4

1

n

4 0 E Y

3 g -1

-2

-3

1

0.8

-0.6 I

Y

* 0

* 0.4

0.2

O

3

2

1 - UI

E O Y

g -1 - -2

-3

-4 4 4.5 5 5.5 6

Time [SI

Setting

4 4.5 5 5.5 6

0.5

0.4

0.1

O

Chassis dis.

4 4.5 5 5.5 6 Time [SI

Chassis vel.

4 4.5 5 5.5 6 Time [SI

Filtered road

/ i \ i \ (/ \

\ \ \ i

I I w , \\ m 4 4.5 5 5.5 6

/ i \ i \ (/ \

\ \ \ i

I I w , \\ m 4 4.5 5 5.5 6

Time [SI Time [SI

G2

Daf95- 2dof

Axle dis. Chassis dis. 0.6

0.5

0.4

E 0 . 3

0.2

0.1

O

- Y

v)

-0.1 3 . 8 4 4.2 4.4 4.6

2

1.5 - v)

. 1 E Y

s - 0.5

Time [s]

Axle vel.

O 3 . 8 4 4.2 4.4 4.6

Time [SI

1

0 . 8

- 0.6 I

Y

* 0

* 0.4

0.2

O 3 .

0.5

0.4

0 . 3

- 0.2 E

0.1 i

z o -0.1

-0.2

-0.2 3 . 8 4 4.2 4.4 4.6

Time [SI

Chassis vel. 2*5*

-0.51 3 . 8 4 4.2 4.4 4.6

Time [SI

Filtered road

I 0.4

E 0 . 3 Y

5 .3

g 0.2-

//

O-./ ra 01 ' 3 . 8 4 4.2 4.4 4.6

Time [SI

G3

Daf95- 2dof -

/ I / -

/ 0.1 -

n

E

-0.21 - c 4m

Y

Axle vel. Chassis vel. 1.4

1.2

1

70.8

0.6

n v1

E

:: i

0.4

0.2 4.

G4

Appendix H Control schemes

This appendix deals with the control schemes as implemented in the DADS DM95

model.Page H1 represents the control scheme with the fixed semi-active damper. - 1 = -

2 = -

6 = -

- - - 7 = x,(t) -

8 = xj(t)-x6(t) = 9 = Fd -

10 = x,(t)-X6(t) = 11 = Fd - 12 = s ,=1 - 15 = Xj(t) - 16 = s d = l - 19 = x,(t) -

-

- -

- - -

y - position front axle steer angle x - position rear axle road profile relative left damper velocity left damper force relative right damper velocity right damper force disered setting filtered setting disered setting filtered setting

Page H2 represents the control scheme with the semi-active damper and direct

calculation controller. - I = -

2 = - 3 = -

- - - 4 = x,(t) -

5 = X6(t) -

6 = x,(t)-x,(t) = 7 = Fd -

9 = Xj(t) - 10 = x,(t) - 11 = x,(t) - 12 = x,(t) - 13 = x4(t) -

15 = Fd - 16 = sd - 17 = x,(t) -

18 = x,(t) - 19 = xi(t) - 20 = x,(t) -

21 = x,(t) -

-

- - - 8 = 'd - -

-

-

-

14 = x,(t)-x,(t) = -

- - - -

- -

The names of the blocks and the numbers

y- position front axle steer angle x - position rear axle road profile filtered road profile relative left damper velocity left damper force disered setting left filtered setting left z -position rear axle left side z -position chassis left side z - velocity rear axle left side z - velocity chassis left side relative right damper velocity right damper force disered setting right filtered setting right z - position rear axle right side z - position chassis right side z - velocity rear axle right side z -velocity chassis right side

of the nodes agree with the names and

numbers used in the implementation. They gives the reader only an indication of their

functions.

Ï

H1

,

E i

input vooras

input vel.

chassis achteras left damper

force

10 DAF skyh0ek.f

dampetforce Block3 11 ,

x t4

set filter 19 , right

right right

inp. 16

road b K-factor driver

input 1 vooras

b 1 6- set filter 17 right

6 , chassis achteras

left I

DAF95 sa.f Block2

damperforce right

_.

DAF95 sa.f Block2

dam perforce set filter

left

inp.

achteras right

inp.

chassis right

inp. 20 direct calc. -

z 18

Z -19 r+

--+ DAF95sa.f Block5

x w

dz achteras right

7 +

controller -- right

I I

, inp.

I inp.

chassis

inp.

ach teras left

DAF95 sa.f Block4

direct calc. controller

left

inp. dz

chassis left

out damper

force left

inp. dz

chassis right

out damper

force right