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# IMECE05 Presentation - PowerPoint PPT Presentation

Stability at the Limits. Yung-Hsiang Judy Hsu J. Christian Gerdes Stanford University. did you know…. Every day in the US, 10 teenagers are killed in teen-driven vehicles in crashes 1 Loss of control accounts for 30% of these deaths

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Presentation Transcript

### Stability at the Limits

Yung-Hsiang Judy Hsu

J. Christian Gerdes

Stanford University

November 10, 2005

• Every day in the US, 10 teenagers are killed in teen-driven vehicles in crashes1

• Loss of control accounts for 30% of these deaths

• Inexperienced drivers make more driving errors, exceed speed limits & run off roads at higher rates

• In 2002, motor vehicle traffic crashes were the leading cause of death for ages 3-33.2

To understand how loss of control occurs, need to know what determines vehicle motion

1 National Highway Traffic Safety Administration. Traffic safety facts (2002)

2 USA Today. Study of deadly crashes involving 16-19 year old drivers (2003)

2

SIDE VIEW

• Motion of a vehicle is governed by tire forces

• Tire forces result from deformation in contact patch

• Lateral tire force is a function of tire slip

Contact Patch

Ground

BOTTOM VIEW

a

Fy

3

maximum tire grip

Linear

Saturation

Loss of control

4

• Normally, we operate in linear region

• Predictable vehicle response

• But during slick road conditions, emergency maneuvers, or aggressive/performance driving

• Enter nonlinear tire region

• Response unanticipated by driver

5

Imagine making an aggressive turn

• If front tires lose grip first, plow out of turn (limit understeer)

• may go into oscillatory response

• driver loses ability to influence vehicle motion

• If rear tires saturate, rear end kicks out (limit oversteer)

• may go into a unstable spin

• driver loses control

• Both can result in loss of control

6

We’d like to design a control system to

• Stabilize vehicle in nonlinear handling region

• Make vehicle response consistent and predictable for drivers

• Communicate to driver when limits of handling are approaching

7

• Identify tire operating region

• Vehicle/Tire models

• Tire parameter estimation

• Produce stable, predictable response

• Feedback linearizing controller

• Driver input saturation

• Simulation results

8

Bicycle model

• 2 states: β and r

• Nonlinear tire model (Dugoff)

• Steer-by-wire

Assume

• Small angles

• Ux constant

9

Sum forces and moments:

Dugoff tire model:

-C

10

• Find f: use GPS/INS

• Find Fyf: SBW motor give steering torque

• Estimate C f and 

• LS fit to linear tire model

• NLS fit to Dugoff model

• Compare residual of fits to tell us if we’re in the nonlinear region  estimate 

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• Begin estimating  after entering NL region

• C f estimate is steady

15

• Desired vehicle response

• Track response of bicycle model with linear tires

• Be consistent with what driver expects

• When tires saturate, compensate for decreasing forces with steer-by-wire input

• One input f; two states ,r

• Could compromise between the two

• Or, track one state exactly

16

• Nonlinear control technique

Applicable to systems that look like:

• Use input to cancel system nonlinearities.

In our case,

• Apply linear control theory to track desired trajectory:

17

• Ramp steer from 0 to 4o at 20 m/s (45 mph) in 1 s

• Controller results in exact tracking of linear tire model yaw rate trajectory

18

• Ramp steer from 0 to 6o at 20 m/s (45 mph) in 1 s

• FBL works well up to physical capabilities of tires

19

• Road naturally saturates driver’s steering capability often unexpectedly

• Here, we safely limit steering capability in a predictable, safe manner

• Why do we need it?

• Prevents vehicle from needing more side force than is available

• Keeps vehicle in linearizable handling region

• Saturation algorithm

• If  < th, driver commands are OK

• If ¸th, gradually saturate driver’s steering capability

20

• Ramp steer from 0 to 6° at 20 m/s (45 mph) in 1 s

• Tracks linear model yaw rate, then saturates input

• Reduced sideslip

21

• Relative importance of  vs. r

• Which produces a more predictable response?

• differential drive

• rear steering

22

• Overall approach

• Sense tire saturation and actively compensate for them with SBW inputs

• Algorithm can characterize tires (C, ) using GPS-based f and estimates of Fyf,

• Make vehicle response more predictable

• Up to capabilities of tires, controller tracks linear yaw rate trajectory

• Reduces sideslip

• Current work

• Estimate C,  on board in real-time

• Implement overall controller on research vehicle

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• Simulate control system on more complete vehicle model

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• input: ramp steer from 0 to 5° at 45 mph in 0.5 s

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Case 1: Both tires are linear (f¸ 1 and r¸ 1)

Case 2: Both tires saturating (f < 1 and r < 1)

27

Case 3: front is nonlinear, rear is linear (f¸ 1 and r < 1)

Case 4: front is linear, rear is nonlinear (f¸ 1 and r < 1)

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• Define new inputs v1 and v2

to represent system as

29

SISO algorithm:

30

• Model Fyf as:

• Substitute into system equations:

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• Choose new input

cr = 200

c = 50

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• Find f:Use GPS/INS to measure r and f and estimate 

• Find Fyf: Estimate tm from steering geometry, model tp as

and use disturbance torque estimate from SBW system to find Fyf

• Estimate :

• Using least squares

34

• P1: Ramp steer from 0 to 9° in 24 s at V = 31 mph

35

• Motivation

• Background

• Controller design

• Feedback linearization

• Driver input saturation

• Validation on complex model

• Conclusions

37

• electronically actuate steering system separately from driver’s commands

• decouple underlying dynamics from driver force feedback

Conventional steering

Steer-by-wire

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Lineartire model

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Nonlineartire model

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• Ramp steer to from 0 to 4o at 45 mph in 0.5 s

41

• Find f: GPS/INS measures , r, V

• Find Fyf: SBW motor give steering torque 

• Estimate C f and  from (Fyf, f) data

• LS fit to line

• NLS fit to Dugoff

Compare fit errors to tell us if in nonlinear region

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