John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

26
Dept. Of Mechanical and Nuclear Engineering, Penn State University Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover A Comparative, Experimental Study of Model Suitability to Describe Vehicle Rollover Dynamics for Control Design John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

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A Comparative, Experimental Study of Model Suitability to Describe Vehicle Rollover Dynamics for Control Design. John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University. Outline. Goals Analytical Vehicle Models Experimental Model Validation Conclusions. - PowerPoint PPT Presentation

Transcript of John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Page 1: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

A Comparative, Experimental Study of Model Suitability to Describe Vehicle Rollover Dynamics for Control Design

John T. CameronPennsylvania State University

Dr. Sean BrennanPennsylvania State University

Page 2: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

2/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Outline

1. Goals2. Analytical Vehicle Models3. Experimental Model Validation4. Conclusions

Page 3: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

3/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Goals

Examine various vehicle models to determine the effect that different assumptions have on: Model order Model complexity Number and type of parameters required

Experimentally validate the models to: Determine model accuracy Relate modeling accuracy to assumptions made Determine the simplest model that accurately

represents a vehicles planar and roll dynamics

Page 4: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

4/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Analytical Vehicle Models

Standard SAE sign convention

Page 5: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

5/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Analytical Vehicle Models Basic Assumptions Common to All Models

All models are linear Result:

• Small angles are assumed making cos(θ)≈1, sin(θ)≈0• Constant longitudinal velocity (along the x-axis)• The lateral force acting on a tire is directly proportional

to slip angle

• Longitudinal forces ignored• Tire forces symmetric right-to-left

sin1cos

sin1cos

tiretire CF

Page 6: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

6/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Analytical Vehicle Models

Model 1 – 2DOF Bicycle Model

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Page 7: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

7/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Analytical Vehicle Models Model 2 – 3DOF Roll Model

Assumes the existence of a sprung mass No x-z planar symmetry Originally presented by Mammar et. al., National Institute of

Research on the Transportations and their Security (INRETS), Versailles, France in 1999

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Page 8: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

8/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Analytical Vehicle Models Model 3 – 3DOF Roll Model

Assumes the existence of a sprung mass x-z planar symmetry Roll-steer influence Originally presented by Kim and Park, Samchok University,

South Korea, 2003

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Page 9: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

9/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Analytical Vehicle Models Model 3 (continued)

As a result of the assumption of roll steer, the external forces acting on the vehicle change accordingly

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Page 10: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

10/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Analytical Vehicle Models Model 4 – 3DOF Roll Model

Assumes a sprung mass suspended upon a massless frame x-z planar symmetry No roll steer influence Originally presented by Carlson and Gerdes, Stanford

University, 2003

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Page 11: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

11/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Analytical Vehicle Models Effect of assuming force equivalence

Slightly changes plant description (i.e. eigenvalues) Additionally, causes a higher gain in roll response from the

massless frame assumption

Page 12: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

12/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Model Fitting Procedures1. Experimentally determine the understeer gradient to find

the relationship between front and rear cornering stiffness values.

Considering both frequency and time domains*:

2. Determine estimates on cornering stiffness values by fitting of the 2DOF Bicycle Model (Model 1).

3. Determine estimates on roll stiffness and damping by fitting of Models 2 – 4.

* - Time domain maneuvers were a lane change and a pseudo-step

Page 13: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

13/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Time Domain Fit Results

101

0

5

10

15

Frequency Response, Steering Input to Yaw Rate, Mercury Tracer U =16.5 Cf =-22750 Cr =-19958.4561 K =38000 D =5000

w (rad/s)

Mag

(dB

)

101

-100

-50

0

w (rad/s)

Pha

se (d

eg)

MeasuredModel 1Model 2Model 3Model 4

101

15

20

25

30

35

40

Frequency Response, Steering Input to Lateral Acceleration, Mercury Tracer U =16.5 Cf =-22750 Cr =-19958.4561 K =38000 D =5000

w (rad/s)

Mag

(dB

)

101

0

50

100

150

w (rad/s)

Pha

se (d

eg)

MeasuredModel 1Model 2Model 3Model 4

Page 14: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

14/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Model Fitting Results Results for Steering Input to Lateral Acceleration

101

15

20

25

30

35

40

Frequency Response, Steering Input to Lateral Acceleration, Mercury Tracer U =16.5 Cf =-45500 Cr =-75562.5 K =53000 D =6000

w (rad/s)

Mag

(dB

)

101

0

50

100

150

w (rad/s)

Pha

se (d

eg)

MeasuredModel 1Model 2Model 3Model 4

Freq. Domain Fit

Page 15: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

15/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Model Fitting Results Results for Steering Input to Yaw Rate

101

0

5

10

15

Frequency Response, Steering Input to Yaw Rate, Mercury Tracer U =16.5 Cf =-45500 Cr =-75562.5 K =53000 D =6000

w (rad/s)

Mag

(dB

)

101

-100

-50

0

w (rad/s)

Pha

se (d

eg)

MeasuredModel 1Model 2Model 3Model 4

Freq. Domain Fit

Page 16: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

16/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Model Fitting Results Results for Steering Input to Roll Rate

101

-5

0

5

10

15

Frequency Response, Steering Input to Roll Rate, Mercury Tracer U =16.5 Cf =-45500 Cr =-75562.5 K =53000 D =6000

w (rad/s)

Mag

(dB

)

101

-100

-50

0

50

100

w (rad/s)

Pha

se (d

eg)

MeasuredModel 2Model 3Model 4

Freq. Domain Fit

Page 17: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

17/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Model Fitting Results Inconsistency in roll rate measured response does not

appear at lower speeds

Better sensors are required to clarify inconsistencies in data – especially lateral acceleration and roll rate

100

101

-10

0

10

Frequency Response, Steering Input to Roll Rate U =8.9 Cf =-45500 Cr =-75560 K =53000 D =6000

w (rad/s)

Mag

(dB

)

100

101

-500

-450

-400

-350

-300

-250

w (rad/s)

Pha

se (d

eg)

measuredModel 2Model 3Model 4

Page 18: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

18/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Remarks on Model Validation

As a result of overall accuracy and simplicity, Model 3 was chosen for further investigation. This entails: The development of model-based predictive

algorithms for rollover propensity The development of control algorithms for rollover

mitigation

Page 19: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

19/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Conclusions

A relatively simple dynamic model is capable of modeling both the planar and roll dynamics of a vehicle well under constant speed conditions.

Relatively accurate measurements may be taken with inexpensive sensors The dynamics are seen even with commercial grade

sensors Important for industry because such sensors are typically

found in production vehicles

Extra care should be taken when model fitting in the time domain

Page 20: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

20/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Time Response Tests Pseudo-Step Response, 8.9 m/s, 0.09 rad amplitude, FR Params

1 1.5 2 2.5

0.02

0.04

0.06

0.08

0.1Step, Steering vs. Time

Time (s)

Ste

erin

g A

ngle

(rad

)

1 1.5 2 2.50

0.05

0.1

0.15

0.2

0.25

0.3Yaw Rate vs. Time

Time(s)

Yaw

Rat

e (ra

d/s)

MeasuredModel 1Model 2Model 3Model 4

1 1.5 2 2.5

0

0.2

0.4

0.6

0.8

1

1.2

Lat. Accel. vs. Time

Time (s)

Lat.

Acc

el. (

m/s

2 )2.5 3 3.5 4

0

0.02

0.04

0.06

0.08

0.1

Steering vs. Time

Time (s)

Ang

le (r

ad)

2.5 3 3.5 4

0

0.05

0.1Roll Rate vs. Time

Time (s)

Rol

l Rat

e (ra

d/s)

Page 21: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

21/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Time Response Tests Pseudo-Step Response, 8.9 m/s, 0.09 rad amplitude, TR Params

1 1.5 2 2.50

0.02

0.04

0.06

0.08

0.1Step, Steering vs. Time

Time (s)

Ste

erin

g A

ngle

(rad

)

1 1.5 2 2.50

0.05

0.1

0.15

0.2

0.25

0.3

Yaw Rate vs. Time

Time(s)

Yaw

Rat

e (ra

d/s)

MeasuredModel 1Model 2Model 3Model 4

1 1.5 2 2.5

0

0.5

1

Lat. Accel. vs. Time

Time (s)

Lat.

Acc

el. (

m/s

2 )

2.5 3 3.5 40

0.02

0.04

0.06

0.08

0.1

Steering vs. Time

Time (s)

Ang

le (r

ad)

2.5 3 3.5 4

-0.02

0

0.02

0.04

0.06

0.08

0.1Roll Rate vs. Time

Time (s)

Rol

l Rat

e (ra

d/s)

Page 22: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

22/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Time Response Tests Lane Change Maneuver, 17.8 m/s, Right-to-Left, then Left-to-Right,

FR

0 2 4 6 8-0.04

-0.02

0

0.02

0.04Lane Change, Steering Angle vs. Time

Time (s)

Ang

le (r

ad)

0 2 4 6 8

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Yaw Rate vs. Time

Time(s)

Yaw

Rat

e (ra

d/s)

2 4 6 8

-0.5

0

0.5

Lat. Accel. vs. Time

Time (s)

Lat.

Acc

el. (

m/s

2 )

MeasuredModel 1Model 2Model 3Model 4

0 2 4 6 8

-0.04

-0.02

0

0.02

0.04

Steering Angle vs. Time

Time (s)

Ang

le (r

ad)

0 2 4 6 8

-0.1

-0.05

0

0.05

0.1

Roll Rate vs. Time

Time (s)

Rol

l Rat

e (ra

d/s)

Page 23: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

23/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Time Response Tests Lane Change Maneuver, 17.8 m/s, Right-to-Left, then Left-to-Right,

Time

0 2 4 6 8-0.04

-0.02

0

0.02

0.04Lane Change, Steering Angle vs. Time

Time (s)

Ang

le (r

ad)

0 2 4 6 8

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Yaw Rate vs. Time

Time(s)

Yaw

Rat

e (ra

d/s)

0 2 4 6 8

-0.5

0

0.5

Lat. Accel. vs. Time

Time (s)

Lat.

Acc

el. (

m/s

2 )

MeasuredModel 1Model 2Model 3Model 4

0 2 4 6 8

-0.04

-0.02

0

0.02

0.04

Steering Angle vs. Time

Time (s)

Ang

le (r

ad)

0 2 4 6 8

-0.1

-0.05

0

0.05

0.1

Roll Rate vs. Time

Time (s)

Rol

l Rat

e (ra

d/s)

Page 24: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

24/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Experiments Performed Determination of Understeer Gradient

Understeer gradient is a constant indicating the additional amount of steering necessary to maintain a steady-state turn per g of lateral acceleration (e.g. units are rad/g)

Provides a relationship between the front and rear cornering stiffness‘

Lateral acceleration was measured on a 30.5 m radius circle at 6.7, 8.9, and 11.2 m/s

r

f

f

rus C

WCW

K

22

r

f

f

rus C

WCWK

22 fusr

ffr CKW

CWC

2

Page 25: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

25/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Model Fitting Procedure Step 1 – Determine understeer gradient

Plotting additional steering angle vs. lateral acceleration, the understeer gradient is simply the slope of the line

y = 0.045x + 0.018R2 = 0.9965

0.024

0.026

0.028

0.03

0.032

0.034

0.036

0.125 0.175 0.225 0.275 0.325 0.375 0.425

Lat. Accel (g's)

Add

ition

al A

ngle

(rad

)

Page 26: John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

Dept. Of Mechanical and Nuclear Engineering, Penn State University

26/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover

Analytical Vehicle ModelsPaper Model Order Method of validation Who are they withWilliams, 1995, Nonlinear control of roll moment distribution… NL 2DOF No roll dynamics included, only a "roll moment factor" Georgia Institute of TechnologyRosam, 1997, Development and simulation of a novel roll… ? No model or Free Body Diagram Given University of BathDarling, 1998, An Experimental Study of a Prototype… ? No model or Free Body Diagram Given University of BathFeng, 1998, Automatic Steering Control of Vehicle Lateral... 2 & 3DOF Errors in published formulation PATH

Feng, 2000, Decoupling Steering Control For Vehicles… 2 & 3DOF Errors in published formulation PATHKrishnaswami, 1998, A Regularization Approach To Robust… 2DOF Not enough information given UMTRIWielenga, 1999, A Method for Reducing On Road Rollover… 3DOF Model formulation not given DynomotiveChen, 1999, A Real Time Rollover ThreatIndex For SUV's coupled 2DOF Decoupled approach UMTRIChen, 2001, Differential Braking Based Rollover Prevention… 3DOF Parameters difficult to obtain UMTRIKitajima, 2000, Control For Integrated Side Slip Roll 8DOF*, 3DOF Equations complex, not enough information given UMTRIEger, 2003, Modeling of rollover sequences 2DOF Covers tripped rollovers University of Karlsruhe, GermanyKueperkoch, 2003, Novel Stability Control Using SBW… 3DOF Not relevant to our study Bosch CorporationRossetter, 2003, A Gentle Nudge Towards Safety… 2DOF Not relevant to our study StanfordTakano, 2003, Study on a vehicle dynamics model for… 3DOF Errors in published information Tokyo University of Ag. and Tech.Oh, 2004, The Design of a Controller for the SBW System 9DOF Model formulation not given Hyundai/Hanyang University

Paper Model Order Comments Who are they withSharp, 1993, On the design of an active control system for a… 3DOF Complex formulation, parameters are difficult to obtain Cranfield Institute of TechnologyChen, C, 1998, Steering Control of High-Speed Vehicles 2DOF Not relevant to our study PATHMammar, 1999, Speed Scheduled Vehicle Lateral Control 3DOF Nicely derived, but no experimental validation. Includes a Evry University, France

mathematical proof on its model matching abilities.Cole, 2000, Evaluation Of Design Alternatives For Roll Control… 3DOF Model is developed through a software package University of NottinghamHyun, 2000, Vehicle Modeling And Prediction Of… NL 8DOF Not relevant to our study Texas A&MIkenaga, 2000, Active Suspension Control Of Ground… 7DOF No description of lateral dynamics Texas ArlingtonManning, 2000, Coordination Of Chassis Control Systems NL 5DOF Not enough information given University of Leeds, UKKim, 2003, Investigation Of Robust Roll Motion Control… 3DOF Clean presentation, parameters given, model worked Samchok University, South KoreaSprague, 2002, Automated stability analysis of a vehicle… 6DOF Model formulation not given Exponent Failure Analysis AssociatesHuh, 2002, Monitoring System Design For Estimating... 4DOF No roll dynamics included, only lateral weight transfer Samchok University, South KoreaCarlson, 2003, Optimal rollover prevention with SBW and diff… NL4DOF, L3DOFAll work done in simulation Stanford

Models With Experimental Validation

Models Not Experimentally Validated