CHAPTER SUMMARY

ADAPTIVE CRUISE CONTROL

6.9 CHAPTER SUMMARY

The longitudinal controller in an ACC system has two modes of steady state operation:

1) speed control 2) spacing control

Steady state spacing control is called vehicle following. In the vehicle following mode, the longitudinal controller must ensure that the following two properties are satisfied:

1) Individual vehicle stability, in which spacing error converges to zero if the preceding vehicle travels at constant velocity

2) String stability, in which spacing error does not amplify as it propagates towards the tail of a string of vehicles.

An ACC system is “autonomous” - it does not depend on wireless communication or on cooperation from other vehicles on the highway. It only uses on-board sensors to accomplish its control system tasks. In the case of an autonomous controller, a constant inter-vehicle spacing policy cannot be used. This is because an autonomous controller can ensure individual vehicle stability but cannot ensure string stability in the case of the constant spacing policy. Instead the constant time-gap spacing policy in which the desired spacing is proportional to speed should be used. With the constant time-gap spacing policy, both string stability and individual vehicle stability can be ensured in an autonomous manner.

In addition to executing steady-state vehicle following, the longitudinal controller must also decide which type of steady state operation is to be used i.e. whether the vehicle should use speed control or vehicle following, based on real-time radar measurements of range and range rate. In addition, the controller must perform a number of transitional maneuvers, including transitioning from spacing control to speed control when the preceding vehicle makes a lane change, executing a “vehicle join” for closing in on a slower moving preceding vehicle, etc. These transitional maneuvers can be

executed based on controllers designed using R



R



diagrams. R



R



diagrams were discussed in section 6.7 of the chapter.

NOMENCLATURE

xi longitudinal position of ACC vehicle or of the ith vehicle in a string

xi ^or Vior V longitudinal velocity of the ith vehicle

1

1 

 

 _{i i}

i

i x x "

H

measured inter-vehicle spacing with "_i1 being the length of the preceding vehicle

des i

i

i x x_1L

G

spacing error of the ith vehicle

h value of time gap used in constant time gap controller

R range R range rate

Vp velocity of preceding vehicle

final

R , T, D constants used in the R



R



diagrams Tnet net combustion torque of the engine Tbr brake torque

Z

e engine angular speed

ca aerodynamic drag coefficient

R

gear ratio

reff effective tire radius

Rx rolling resistance of the tires

Je effective inertia reflected on the engine side m vehicle mass

REFERENCES

Choi, S.B. and Hedrick, J.K., “Vehicle Longitudinal Control Using an Adaptive Observer for Automated Highway Systems”, Proceedings of American Control Conference, Seattle, Washington, 1995.

Choi, S.B. and Devlin, P., “Throttle and Brake Combined Control for Intelligent Vehicle Highway Systems”, SAE 951897, 1995.

Fancher, P., Ervin, R., Sayer, J., Hagan, M., Bogard, S., Bareket, Z., Mefford, M. and Haugen, J., 1997, “Intelligent Cruise Control Field Operational test (Interim Report)”, University of Michigan Transportation Research Institute Report, No. UMTRI-97-11, August 1997.

Fancher, P. and Bareket, Z., 1994, “Evaluating Headway Control Using Range Versus Range-Rate Relationships”, Vehicle System Dynamics, Vol. 23, No. 8, pp. 575-596.

Hedrick, J.K., McMahon, D., Narendran, V.K. and Swaroop, D., “Longitudinal Vehicle Controller Design for IVHS Systems”, Proceedings of the 1991 American Control Conference, Vol. 3, pp. 3107-3112, June 1991.

Hedrick, J.K., McMahon, D. and Swaroop, D., “Vehicle Modeling and Control for Automated Highway Systems”, PATH Research Report, UCB-ITS-PRR-93-24, 1993.

Ioannou, P.A. and Chien, C.C., 1993, “Autonomous Intelligent Cruise Control”, IEEE Transactions on Vehicular Technology, Vol. 42, No. 4, pp. 657-672.

Rajamani, R., Hedrick, J.K. and Howell, A., “A Complete Fault Diagnostic System for Longitudinal Control of Automated Vehicles”, Proceedings of the Symposium on Advanced Automotive Control, ASME International Congress, November 1997.

Rajamani, R. and Zhu, C., 1999, “Semi-Autonomous Adaptive Cruise Control Systems”, Proceedings of the American Control Conference, June 1999.

Rajamani, R., Tan, H.S., Law, B. and Zhang, W.B., “Demonstration of Integrated Lateral and Longitudinal Control for the Operation of Automated Vehicles in Platoons,” IEEE Transactions on Control Systems Technology, Vol. 8, No. 4, pp. 695-708, July 2000.

R. Rajamani and S.E. Shladover, “An Experimental Comparative Study of Autonomous and Cooperative Vehicle-Follower Control Systems”, Journal of Transportation Research, Part C – Emerging Technologies, Vol. 9 No. 1, pp. 15-31, February 2001.

Reichart, G., Haller, G. and Naab, K, 1996, “Driver Assistance: BMW Solutions for the Future of Individual Mobility”, Proceedings of ITS World Congress, Orlando, October 1996.

Slotine, J.J.E. and Li, W., “Applied Nonlinear Control”, Prentice Hall, 1991.

Swaroop, D., Hedrick, J.K., Chien, C.C. and Ioannou, P. “A Comparison of Spacing and Headway Control Laws for Automatically Controlled Vehicles”, Vehicle System Dynamics Journal, Nov. 1994, vol. 23, (no.8):597-625.

Swaroop, D. and Hedrick, J.K., “String Stability of Interconnected Dynamic Systems”, IEEE Transactions on Automatic Control, March 1996.

Swaroop, D., 1995, “String Stability of Interconnected Systems: An Application to Platooning in Automated Highway Systems”, Ph.D. Dissertation, University of California, Berkeley, 1995.

Swaroop, D. and Rajagopal, K.R., “Intelligent Cruise Control Systems and Traffic Flow Stability,” Transportation Research Part C: Emerging Technologies, Vol. 7, No. 6, pp.

329-352, 1999.

Swaroop, D. and Bhattacharya, S.P., “Controller Synthesis for Sign Invariant Impulse Response,” IEEE Transactions on Automatic Control, Vol. 47, No. 8, pp. 1346-1351, August, 2002.

Swaroop, D., “On the Synthesis of Controllers for Continuous Time LTI Systems that Achieve a Non-Negative Impulse Response,” Automatica, Feb 2003.

Texas Transportation Institute Report, “2001 Urban Mobility Study,” URL: mobility.tamu.edu United States Department of Transportation, NHTSA, FARS and GES, ‘‘Fatal Accident Reporting

System (FARS) and General Estimates System (GES),’’ 1992.

Watanabe, T., Kishimoto, N., Hayafune, K., Yamada, K. and Maede, N., 1997, “Development of an Intelligent Cruise Control System”, Mitsubishi Motors Corporation Report, Japan.

Woll, J., 1997, “Radar Based Adaptive Cruise Control for Truck Applications”, SAE Paper No. 973184, Presented at SAE International Truck and Bus Meting and Exposition, Cleveland, Ohio, November 1997.

Yanakiev, D. and Kanellakopoulos, I., 1995, “Variable time Headway for String Stability of Automated Heavy-Duty Vehicles”, Proceedings of the 34^th IEEE Conference on Decision and Control, New Orleans, LA, December 1995, pp. 4077-4081.

APPENDIX 6.A

This Appendix contains a proof of the result stated in section 6.6.1, namely that the magnitude of the transfer function

) ˆ s (

H

W O O

O G

G











 h s hs h s

s

i i

) 1

2

(

1 3

(6.36)

is always less than or equal to 1 at all frequencies if and only if ht2

W

. This Appendix is adapted from the original proof presented by Swaroop (1995).

Background Result:

Consider the following quadratic inequality in

Z

²:

2 0

4b c!

a

Z Z

(6.37)

We present the conditions on a ,

,

b c under which the above inequality holds for all values of

Z

².

¸ ¹

¨ ·

©

§  





a

c a

a b c b

a ^{4 2 4 2}

2 2 Z Z

Z Z

»»

¼ º

««

¬

ª ¸  

¹

¨ ·

©

§ ² ² ₂ ²

4 4

2 a

b ac a

a

Z

b

Hence

2 0

4b c! a

Z Z

if either

1) a

,

b

,

c

! 0

(6.38)

or

2) b0, a!0, c!0 and 4ac b² !0 i.e. b² ac4 0 (6.39)

Calculations:

Consider the transfer function

O O W

O G

G











 hs hs h s

s s H

i i

) 1 ˆ (

) ˆ

(

_{3 2}

1

Substituting s j

Z

,

) 1

( ) ) (

(

_{2 2}

Z W O Z Z

O

O Z Z

h h j

h j j

H

   



(6.40)

2 2 2

2 2

2 2 2

) 1

( )

| ( ) (

| O Z Z O W Z

O Z Z

h h j h

H

   



1

| ) (

|

H j

Z d

œ

2 2 2

2 2 2

2

O ( O Z ) Z ( 1 O W Z )

Z  d 

h

 

h



h

œ



²

^{2 2}

²



^{2 2 2}

⁰

4 2

2h

Z 

h

 W

h

 WO

h

Z  O

h

t

W

(6.41)

Comparing with the background result in equations (6.38) and (6.39) 1) If b!0

0 2

2 ²

2 h h !

h

W OW

Hence

OW W 2 1

2

! 

h

This is possible for small

O

if and only if h!2

W

2) If b0 and b²  ac4 0

0 4

) 2 2

(

h²

 W

h

 OW

h^{2 2}

 W

²h²

O

²h²



After simplifying

2 2

2 2

4 8

4 4

h h

h h

W W

W O W





 

) 2 ( 4

) 2

(

²

h h

h





 

W W O W

Since

O

must be positive, this implies h!2

W

Replacing the strict inequality in equation (6.37) with a simple inequality, it follows that ht2

W

. From (1) and (2), ht2

W

is a necessary condition. It also follows that if ht2

W

is satisfied, then one can find a

!0

O

such that

|

H

(

j

Z ) | d 1

. Thus ht2

W

is both a necessary and sufficient condition for ensuring that the transfer function H

ˆ s ( )

has a magnitude less than or equal to 1 at all frequencies.

Chapter 7

LONGITUDINAL CONTROL FOR VEHICLE