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Experimental results of a tire-burst controller for AHS
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Control Eng. Practice, Vol. 5, No.l !, pp. 1615-1622, 1997 Copyright © 1997 Elsevier Science Ltd Printed in ~ Britain. All rights r~m'v~l 00967-0661/97 $17.00+0.00
Pergamon
PII:S0967-0661 (97)10017-X
EXPERIMENTAL RESULTS OF A TIRE-BURST CONTROLLER FOR AHS S. Patwardhan*, H.-S. Tan* and M. Tomizuka**
*Partnersfor Advanced Transit and Highways (PATH), University of California at Berkeley, Berkeley, CA 94720, USA ([email protected]) **Department of Mechanical Engineering. University of California at Berkeley, Berkeley, CA 94720, USA
(Received June 1997; in final form July 1997)
Abstract: This paper investigates the problem of tire burst, and how to mitigate its adverse effects in an AHS environment. The problem is approached by first modeling the tire burst. A feed-forward controller is designed, based on inverting the nonlinear tire-burst dynamics for controlling the ear after the tire burst. The feed-forward term is approximated by the output of a second-order filter. The approximation also provides a way to characterize the feed-forward term for different road curvature and different tires (front/rear, left/right). Two different tire blow-out detection algorithms are discussed. This is followed by the experimental phase. Open-loop experiments were conducted to verify the tire-burst model. Closed-loop tests were then carried out to validate the automatic lane-following performance after a tire burst. The results have shown that the burst controller enables the car to follow the lane, even after a front tire blow-out. Copyright © 1997 Elsevier Science Ltd Keywords: Tires, automated guided vehicles, automotive control, fault-tolerant systems, feedback compensation, fault detection, vehicle dynamics, automobiles, feedforward compensation, automatic control
1. INTRODUCTION The two major goals of Automated Highway Systems (AHS) are to improve the throughput of a highway by overcoming human limitations, and to improve the highway safety by eliminating human errors. In an AHS vehicle, automatic lateral and longitudinal control systems would replace the driver for the steering and speed-control ftmetions. With the decrease in human involvement, devices such as sensors, controllers, actuators and communication links are required for automatic control, and are also responsible for the vehicle's safety. The system must detect failures that may induce hazards, and properly control the vehicle to mitigate any potentially hazardous situations. This paper concentrates on one of the most critical roadway failure scenarios, a tire blowout. First the tire-burst model developed in (Patwardhan et al., 1994) will be revisited. This will be followed by the design of a burst-detection algorithm and a tire-burst 1615
controller to compensate for the undesirable lateral displacements arising from a tire blowout. Finally, the results of tire-burst experiments will be presented. The experiments themselves can be broken into two phases: open-loop and closed-loop. The open-loop experiments validate the tire burst model, where/is the closed-loop experiments prove the effectiveness of the tire-burst control in an automatic lane-following environment. 2. BURST MODELING When a tire bursts, several changes occur in the car. These changes can be categorized as changes in the car geometry, changes in the operating conditions and changes in the tire-road characteristics (see Fig. 1). The changes in the geometry occur because the radius of one of the wheels suddenly decreases. Among other things, this changes the distribution of the suspension forces, and thus creates a force imbalance, as well as injecting disturbances into the pitch and roll dynamics of the car. Tire radius reduction also
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S. Patwardhan et al.
increases the moment arm of the forces acting on the tire about the king pin. Furthermore, the changes in the geometry lead to changes in the operating slip ratio of the car, as well as changes in the tire-road interaction characteristics, such as the tire rolling resistance and the comering stiffness. A list of the issues involved in the development of the vehicle tireburst model follows:
Tire Burst
"4 Vehicle Geometry
I-Interaction Roa jI ~\.
'-~ ]Operating [ [ Condition~
Force I Generation ~...\
Steering Command
'i - Vehicle Dynamics ~
~. Output
Fig. 1. Effects of a tire burst on vehicle behavior. 1. Time required for deflation: A tire burst being a rapid phenomenon, the heat loss from the tire air to the environment can be ignored. The tire air expands adiabatically. From the adiabatic expansion law ( P V ~ = Const. ), a relation between the deflation time and other tire parameters can be derived (Patwardhan 1994). For 7/ = 1.21, the relation looks like
Pt
4. Roll and pitch disturbances: Because of the sudden drop in the tire radius, the roll and pitch angles of the car change suddenly. 5. Increase in roll resistance: When the tire bursts, the tire shape changes dramatically. As the tire material passes in and out of the contact region, it experiences positive and negative bending. The energy spent in this bending comes from the increased roll resistance.
j-
]
3. Suspension force rearrangement: After the tire bursts, the suspension at the tire that has blown and that at the diagonally opposite point get stretched, whereas the remaining two suspensions are compressed. This effect changes the static force in each of the suspensions. The static components of the rearranged suspension forces can be computed from the equations of static force balance.
6. increased moment arm about king-pin: For a typical vehicle, the geometry of the king-pin (the axis about which the tires are pivoted to rotate) is constructed such that the tire-road interaction forces produce an optimal amount of turning moment around the king-pin axis, so as to produce a good driver feel. When a tire burst occurs, the moment arm of the road-tire interaction forces about the king-pin axis increases. As a consequence, (depending on the stiffness of the steering system), these moments tend to deflect the steering system. 7. Reduction in cornering stiffness: As the tire pressure decreases, the tire cornering stiffness decreases. Consequently, the cornering force under a tire burst reduces from its nominal value.
_ ldt = vi (P* + Pa) 0'71
~a
pl.21
(1) 3. TIRE-BURST CONTROLLER/DETECTOR DESIGN
0.5
Pa
where v i
volume of air inside the tire before burst
vf
volume of air inside the tire after burst
p
gauge tire pressure before burst
Pa
atmospheric pressure
Pa
Cq
air density at Pa time required for deflation area of the opening in the tire flow coefficient of the opening
Pt
a
T A
(P
variable
that
goes
linearly
from
+ P a ) to zero in t i m e 0 to T
For a typical tire, Eq. 1 gives a 0.5 sec deflation time for a 3cm diameter opening in the tire. 2. Tire radius reduction: After the tire bursts, the tire stiffness goes on decreasing as the tire pressure decreases. Consequently, the tire flattens out under the vehicle's weight till the steel rim hits the ground. As a result of radius change, the slip ratio at the contact point also changes.
The primary aim of designing a controller for a tire blowout is that the lateral displacements of the car from the lane center line after a tire blowout should not exceed the lateral displacement limits set by the AHS operational requirements. Other considerations, such as passenger comfort, become secondary factors under the tire blow-out scenario. To keep the car within its lane boundary until it can safely be taken out of the mainstream traffic becomes vitally important from the viewpoint of hazard reduction. The automatic lane-following controller designed for the nominal operation would not be sufficient for the operation after a tire blowout. This paper describes a control strategy in which a burst controller takes over from the nominal controller after a tire burst (Patwardhan and Tomizuka, 1994) (see Fig. 2.). The switching between the controllers will be triggered by a burst-alarm. The most direct way of generating such a burst alarm is to use the tire pressure measurement. When the tire pressure drops below a certain threshold, a burst will be detected. Another way is to use a model-based fault-detection
Experimental Results of a Tire-Burst Controller for AHS algorithm, in which an observer is built to predict the pitch and roll rates of the car. These observed values, when compared with the actual measurements, generate a residue. The residue, will contain enough information to generate the burst alarm (Patwardhan, 1994). Nominal •__• Co..oiler I ;.
1617
where rout and r/n are the tire radius and the rim radius respectively; V is the actual vehicle velocity. Thus, the longitudinal control action is reduced because of a deliberate increase in the velocity measurement. Although this solution is implementation-specific, it serves as a guideline for a generic tire-burst controller. 2. Feed-forwar~l controller: By inverting the vehicle dynamics for the case of a tire burst, one can compute the ideal steering command that can keep the lateral displacement to zero after the tire burst. This term can be used as a feed-forward term for reducing the lateral displacements.
.l
1 |Enlergcney~ ~~] VEHICLE~-~
In this section, the dynamic equations of the car are considered for model inversion. The model inversion will be done for the specific case of tire-burst conditions. Consider the vehicle dynamics given by Eqs (3) and (4):
I Bursttime
m[3i - ~ + 0 F - OflA~ - AOf~ + qbfl~ + ckA~ Fig. 2. Tire-burst controller structure.
+~)'~'~ + / ~ + f l ~ + z~] + y ~ + ~ ] 4 4
(3)
3.1 Tire-burst controller As mentioned above, the controller based on the nominal vehicle model will not be sufficient to achieve the lane-following objective after a tire burst. Analysis also shows that merely redesigning the feedback term will not be sufficient to control the vehicle. Several schemes for burst controllers have been investigated in (Patwardhan, 1994), including intentionally bursting a symmetrically opposite tire to counteract the tire force imbalance produced by the burst of a single tire. The following subsections will discuss only the strategies that were successfully used for the closed-loop tire-burst experiments. 1. Engine toroue reduction: When a tire interacts with the road, it produces forces in the lateral as well as in the longitudinal direction. When other factors are kept constant, the total tire force generation capacity in the road-tire contact plane is roughly proportional to the vertical load on that tire. This indicates that the capacity of the tire to generate a lateral force gets reduced when the tire is generating a large amount of longitudinal force. Since a large steering force would be required during the tire-burst control, one can reduce the longitudinal force that the tire generates by reducing either the engine or the brake torque after a tire burst. In actual experiments, conducted under the University of California's PATH program, the engine torque was reduced by using a wheel speed sensor measurement to compute the vehicle speed, for closing the longitudinal control loop. After a front tire burst, the vehicle velocity measured by the wheel speed sensor located at the differential gear box is V. = 0.5 x ( ~ V + V),
(2)
i=1
i=1
m[j) + ~ - 0 ~ + 0flz~ + A O ~ - ~ f l ~ - ~Z~ - ~ Z ~ - ~2 - ~ +/3X~ + . A ~ - 0 ~ 1 4 4
(4)
= -Kwy ~ + mg(~ + ~)+ Z ~FPi + Z F(yi" i=1 i=1 These equations can be rewritten as: = al(X,Se,Sx)
fJ = b l ( X , S p , S x )
(5)
where :
x=[x
k
y
~
z
~ ~
4
~
o
0
c
4
i=1
i=1 4 i=1
The quantifies Ftxi and Ftyi are the tire forces in lateral and longitudinal direction. These are functions of state x , steering command 8=[81
62
63
64] T, time t, and the angular
velocities co = [col °22 co3 CO4]Tof the wheels (Patwardlmn et al., 1994; Peng, 1990). Angular velocities in turn depend on an another input to the car, the engine torque Te = [Tel "" Te4 ] T , where the indices 1..... 4 refer to the four wheels. Fpi are the suspension forces at the i th suspension that are
S. Patwardhan et al.
1618
functions of x , and time t (Patwardhan et al., 1994). All the other variables are defmed in the appendix. The time dependency of the forces arises because the tire stiffness changes as a function of time when one wants to model tire burst. As a result, Eq. (5) will be modified to :
= al(X'Sp'Sx) = a(xb't'd'Te) = b l ( X , S p , S x ) = b(Xb,t,~,Te) where x b = [x T
(6)
Xs
CG i
Yr
Controller Characterization
Va -----Q_-d Fig. 3. Defmition of system output. Consider Fig. 3. This figure defines the output of the lateral dynamics of the car. The output Yr of the system is defmed as the distance of the center of gravity (CG) of the car from the roadway center line. Point A is on the Ys axis extended. In the figure, Va ~ 5c. The velocity of point A with respect to the CG of the car is:
Yr = f i ; + V a S i n ( c - g d ) ~ J ' + J c ( g - E d )
(12)
Since the model inversion calls for the solution of transcendental equations, the computations cannot be done on-line. Fortunately, for controlling a tire burst, it is not required to perform these computations online. Instead, one can run the inversion algorithm offline, and store the corresponding control input trajectory. This trajectory will then be fed in as a feedforward trajectory once a tire burst is detected.
;Ys ,x
min[b(Xb,t,tS, Te) + a ( x b , t , t ~ , T e ) ( e - Cd) 6 +3~(~-- ~d)] 2 .
coT] T.
Car
gives the values of the steering command that are required for ideal lane-following. If such a solution of Eq. (10) is not possible, then one can find 8 that does the following minimization with constraint Eqs (ll)
•
A tire burst can happen at any place on a roadway, and the vehicle could be going on a straight road or on a curved road when this happens. Also, depending upon which tire has burst, the feedforward terms will be different. This calls for characterization of the feedforward term, based on the road curvature p and the index k of the burst tire. Figure 4 shows the plots of the feedforward term for different radii of curvature for an outer front tire burst. Fe~KlfoP~arfl tom1 0.01
(7)
The aim of any controller designed for tire bursts is to keep Yr as close to zero as possible. Note that the control input does not appear in the expression for Yr
-0.02
i -0.03 !
or ))r. Differentiation of Eq. (7) gives: ))r ~ 35 + 5~(C- ~) + A ( k - kd)
-0,(
o ~ -0.o4
(8) -0,o5
Substituting from Eq. (6) gives:
]Vr ~b(Xb,t,rY, T e ) + a ( x b , t , d , T e ) ( a - Cd) + x ( k - k d)
-0.06
For the case of ideal lane following, Yr - O. This also implies 3)r - 0 and j) = 0. When this value for ))r is substituted into Eq. (9),
b ( x b , t , ~ , T e ) + a ( x b , t , d , Te)(C- Cd)
(10)
+ k ( k - kd) = O. Solving Eq. (10) for d with the constraints: For 2 wheel steer: t~l = ~ 2 ;
For front wheel drive:
~ 3 = t~4 = 0; Tel = Te2 = cmd;
For 4 wheel steer: 61 = 6 2; 6 3 =c~ 4;
Actual"WWD tclm Approximate
--
(9)
Te3 = Te4 = 0; For rear wheel drive: Tel = Te2 = 0 ; (11) Te3 = Te4 = cmd; For four wheel drive: Tel = Ve2 = Te3 = Te4=cmd.
-0,07
2
4
6
8
time {sac)
Fig. 4. Feed-forward terms: actual and approximate As a first step in the characterization of the controller, it is proposed to approximate the feedforward term by the output of a second-order filter, excited by a step input whose strength is a function of the radius of curvature of the roadway and the tire that has burst. The structure of this controller is shown in Fig. 5. When the tire burst occurs, a burst alarm will be generated by the burst-detection algorithm. The burst alarm will then be scaled according to the current radius of curvature p . The radius of curvature is assumed to be known here, because in IVHS, this information can be encoded in the roadway (Zhang et al., 1990). The scheme of Fig. 5 also has the advantage of addressing the scenario of a road curvature change when one of the tires has burst. Under such a
1619
Experimental Results of a Tire-Burst Controller for AHS curvature change, the feedforward filter input will be changed to a different value, which is the same as the value of the step if the burst had occurred on that patch of the roadway.
that
F~,i = C/o~i,i E {1,2} and F~, = CrOq,i ~ {3,4}.
Then, the vehicle lateral and roll dynamics can be simplified to
(2(Cfll+Crl2) I
2(C/+Cr)'
In the experiments, the feed-forward term is first computed off-line and then approximated by the step response of a second-order filter. Figure 6 shows the performance of the feed-forward controller when the car is traveling first on a straight road, followed by a curve that ends into a straight section when the outer front tire bursts midway through the curve.
=
mV
Y-L
-m~
+2C[
~Vjk
(13)
m 6
2(Cfll+Crl2) 2(Cfl2+Cr12) 2C/lI
~=
lzV
e+
lzV
Iz
(14)
6
~= 2(CI+Cr)zo ~ 2(Cfl,+Crl2)zo.k+kS~ip IxV
IxV
(15)
2I x
_b$~~+2C/zo6 . . . .
e+2~°+°, t Burst
I I !,,.l"="i
~
Controller
Bulrst time
road radius:
Fig.
5. Burst-controller
os
r
i
:
:
burst tire # : k
I
?....
!
•
.4 . i ,
. . .
i
,
,
;Curve. 76m radlu=
i
:
i
:. . . .
i i
_ ~-0,0~
p
j
structure.
~traight 0-1"=
21x
7
i i !......
i
r Straight :
, i I
i !
.
2
1
'~
j
_
.
-o.(
L
i
i
~
i
2
4
6
B
to time (see)
12
i
k
i
14
t6
18
20
Fig. 6. Feed-forward controller performance (simulation).
3.2 Tire-burst detection As soon as the tire burst occurs, the tire pressure drops. All other effects of the tire burst follow the drop in pressure. Other than the tire pressure itself, two of the most significant effects from the burstdetection viewpoint are the rolling and pitching of the vehicle. Consequently, there are two possible ways of detecting a tire burst and generating the burst alarm. 1. Tire oressure measurement: Tire pressure can be continuously monitored, and whenever it drops below a certain threshold, a burst alarm can be generated. In fact, such alarm systems have already been developed (Uemura et al., 1985). In (Uemura et al., 1985), the driver warning system consists of measuring the tire pressure once per revolution; on the other hand, in the experimental arrangement for the burst experiments (see Section 4 for details), the tire pressure was monitored continuotlsly. 2. Roll rate measurement: Consider a vehicle traveling at constant velocity v and having front and rear cornering stiffness c / and Cr respectively, such
Ix
where y, E and ~ are the lateral displacement, yaw angle and roll angle; m, I, and Ix are the mass and the moments of inertia about the yaw and roll axes; Ii and /2 are the distances of the vehicle's center of gravity from the front and rear axles; k is the sum of stiffness of the right (or left ) side suspension springs and b is the sum of the damping coefficients of the same two suspension dampers. An observer-based faultdetection scheme was built, with Eqs (13)-(15) as the plant. This observer was a simple pole-placement observer, using yaw-rate measurement. The simulation results are shown in Fig. 7. The figure shows the plots of the roll-rate error and the tire pressure (as a fraction of the nominal tire pressure). As far as the detection time is concerned, the two methods of burst detection compare quite well. However, the roll-rate error measurement can generate non-zero roll-rate error under excessive noise or disturbances, such as when the car drives over pot-holes and bumps. Consequently, this method has a higher probability of false alarms. In the experiments, the tire-pressure measurement method was used for detecting tire bursts. detection
o.~
.......
o.o6
~ .........
siganl
..................
p/pn
........
............ :=......
.......... i .............. !............... i............... i .............. ! ~
"6"
. . . . .
i. . . . .
2 . . . . .
L . . . . .
~. . . . .
2
"
! ...... L__
o.o,I ........................................................i.............. l r. In :
A rt)llrateerrot
i l~l~
0.75 0.50
.
.
/11
g 0.02 . . . . . . . . . . i .............. i . . - ~ - ~ . . ! .............. i ............. i./-.~/ . . . . . i~
.
.
.
.
....
0.25
0
°oo
-0.25
............... -0.04
1.00
............................. i............. i.............................. W
.............. ! .............................. ::............... i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i 2
4
i 6
time (s)
J 8
10
.0.50
12
Fig. 7. Tire burst detection. 4. EXPERIMENTAL SETUP Experiments were designed to verify the tire-burst vehicle model and the control algorithm.
1620
S. Patwardhan et al.
4.1 Open-loop experiments The open-loop experiments for model validation were conducted on an AMC-Concord sedan. The car was driven with a fixed steering angle, and one of the tires was burst at a pre-selected speed. A water jet was installed on the front bumper, that would leave a trail on the pavement of the test site, so that the vehicle's trajectory could be recorded and compared with the simulation outputs. One of the biggest hurdles in conducting the experiments was to create a tire blowout in a controlled manner. This was achieved by installing an air release valve on the wheel which was operated by a remote-controlled device powered by a small battery. An important consideration in this design was to have a valve opening about an inch in diameter, a size slightly greater than the rupture area for a typical tire burst. This arrangement ensured that the air in the tire was released within a short time span, characteristic of a typical fire blow-out. This approach would create a situation close to a fire burst, without actually rupturing the tire. One tire could then be used more than once in the experiments. As shown in Fig. 8, eight holes were drilled in the rim of the wheel. The total area of these eight holes was slightly more than the area of a one-inch diameter hole. Flexible tubing connected these openings to a release valve at the center of the wheel. The valve was designed as a two-stage release valve, with the first stage being an off-the-shelf solenoid pneumatic valve. The second stage was a pneumatic cylinder that operated on the air from the tire itself. This cylinder in turn operated the latch of the valve flap. The first stage solenoid valve was powered by a small battery on the wheel, and triggered by a radio receiver that would receive trigger signals from a radio transmitter operated by the driver. Another radio transmitter-receiver pair was used in the experiment to transmit the tire pressure measurement back to the car. The steering lock mechanism of the car was modified to secure the steering at a constant angle during the tests.
measuring scheme and a steering actuator. A magnetic-marker-based roadway reference system was used (Zhang et al., 1990) to measure the lateral displacement in real time. Magnets were installed every 1 meter along the center line of the test track. Magnetometers were mounted on the front bumper of the vehicle, and the magnetic field strengths in the vertical and horizontal directions were translated into the vehicle's lateral displacement by using calibration tables. A DC servo motor was used for the steering actuator to realize the steering commands. The ffmal configuration for the experiment, shown in Fig. 9, was realized on a PONTIAC 6000 STE sedan. This vehicle was also equipped with a throttle actuator, and a wheel speed sensor. These were used for the longitudinal velocity control.
Fig. 9. Tire burst: experimental arrangement. 5. EXPERIMENTAL RESULTS AND INTERPRETATIONS
5.1 Open-loop experiments The open-loop experimental results were superimposed on the simulation results from the open-loop fire-burst vehicle model. Figure 10 (Fig. 11) shows such a plot for the front (rear) wheel burst experiment. Front Tire Burst 16
/
14
//J
~-
\ E>cmfiment "
12
/
/ ~
~ ~
\
Flexibh 'c' Tubing !
\
.,,.~) \\
\
m
/,
10 EI
E E
/ \,\
.~,/
"L L ) j / ........ ~-~
/
i :
,o \ .... d Tire
../ 50
10O
150 200 X in meters
/
250
300
350
Fig. 8. Tire burst: experimental arrangement.
Fig. 10. Front tire-burst experiment (open-loop).
4.2 Closed-loop experiments
The plots show excellent agreement between experiments and simulations for transient behavior, immediately after the tire burst. This verifies the validity of the tire-burst model from the closed-loop controller design viewpoint. The transient region is
Besides the experimental arrangement described above, two additional components were needed for the closed-loop experiments: a lateral displacement-
Experimental Results of a Tire-Burst Controller for AHS followed by integrator drift, which is caused by the double integrator characteristics of the open-loop vehicle, being integrated over a long time and thus magnifying any small discrepancies between the model and vehicle states.
1621
by the longitudinal controller is actually Fro=20.01 mph (given by Eq. (2)). Finally, Fig. 15 shows the tire pressure measurement. Feodforfnud tern1 (L~'nph teat)
Rear Tire B e r t 30 ............
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . . . . . .
2.=
2C
• ........
- ......
:
";~o
I
0011 o
5o
""
lOO 15o 200 250 L~tgllodlnel dlltanco along track (m)
I
/ 350
3O0
Fig. 13. Closed-loop tire burst experiment (feedforward term). 50
1 O0
150 200 x in meters
250
300
350
Fig. 11. Rear tire-burst experiment (open-loop).
Burld Comrohr Pedormlnce (20mph r u t )
2SI
i
5.2 Closed-loop experiments The closed-loop experiments were conducted for a front-tire-burst scenario with co = 2rad / s, ~"= 0.5. Results of the experiment are shown in Figs 12-15.
~15
i ~k~Carluv~lrackwltho~burllcontrbller
1
I
0"2 l . . . .
k
I~v~ (~h ~or..) ....................
.....
4. i z . . . .
3
........ ,.;~.~.
t.)
. . . . . . 50
,
.
i
:
I
i
i
!
'
50
Wlt~ut Burst ~ l k J r
i
100 150 200 250 Longitudinal dlltanco along track (m)
300
350
Fig. 14. Closed-loop tire burst experiment (vehicle speed).
i
I :.: .,,:,, ... ,.:: .......... 100 150 200 250 Longitudinal distance =long track (m)
i
i
: * ~
WithOgt Burst CoNroller -o.~
i
...........
T o
:Ln ! L T t
Burst ~ v ~ u t cont;)
Burst Co*ltroller PedormaPce (20mph test)
o t
i 8 . . . ~ikh ~ . )
Tire pressure (w#h burst controller case).
3(3
300
25
350
:¸ !
2G
Fig. 12. Closed-loop tire burst experiment (lateral displacement) These figures compare the results, with and without the burst controller. It can be seen that without the tire-burst controller, the lateral deviations of the car reach the sensor limit, and the car goes out of control (see Fig. 12). With the burst controller, although the ride quality and tracking error worsen after the tire burst, the car does not reach the lateral sensor limit, and does not leave the track. Figure 13 shows the feed-forward term. As the road curvature changes, the input to the feed-forward block gets scaled and in turn, the feed-forward term changes. This term becomes non-zero only after a tire burst has been detected. Figure 14 shows the vehicle velocity. The velocity set-point for the longitudinal control during the experiment was 20mph, but the vehicle tracks to about 15mph after the burst because the velocity seen
i
:
.......
t
o
10
Longitudinal dlatance along track (m)
Fig. 15. Closed-loop tire burst experiment (tire pressure).
6. CONCLUSIONS This paper has investigated the problem of tire burst, and how to mitigate its adverse effects in an AHS environment. The problem was approached by first modeling the tire burst. A feed-forward controller was
S. Patwardhanet al.
1622
designed, based on inverting the nonlinear tire-burst dynamics for controlling the car after the tire burst. The feed-forward term was approximated by the output of a second-order filter. The approximation also provided a way to characterize the feed-forward term for different road curvatures and different tires (front/rear, left/right). Two different tire-blow-out detection algorithms were discussed. This was followed by the experimental phase. Open-loop experiments were conducted to verify the tire-burst model. Closed-loop tests were then carried out to validate the automatic lane-following performance after a tire burst. The results have shown that the burst-controller enables the car to follow the lane, even after a front tire has blown out. ACKNOWLEDGMENT This work was performed as part of the Partners for Advanced Transit and Highway (PATH) program, prepared under the sponsorship of the State of California; Business, Transportation and Housing Agency; Department of Transportation (Caltrans).
Patwardhan, S. and M. Tomizuka (1994). Feedforward controller design using nonlinear model inversion for automobile tire burst, Proc. of ASME Winter Annual Meeting, Chicago. Patwardhan, S., M. Tomizuka, W. Zhang and P. Devlin (1994). Theory and experiments of tire blow-out effects and hazard reduction control for automated vehicle lateral control system, Proc. of American Control Conference, Baltimore. Peng, H. and M. Tomizuka (1990). Vehicle Lateral Control for Highway Automation, Proc. American Control Conference, San Diego, pp 788-794. Uemura, Y., et al. (1985). Tire Pressure Warning System, Tenth Int. Technical Conf on Experimental Safety Vehicles, Oxford, England, July 1-4, pp. 288-294. Zhang, W., R. Parson and T. West (1990). An intelligent roadway reference system for vehicle lateral guidance/control, Proc. of American Control Conference, San Diego. APPENDIX
REFERENCES Patwardhan, S. (1994). Fault detection and tolerant control for lateral guidance of vehicles in automated highways, University of Calif. Berkeley, PATH Publication, UCB-ITS-PRR-9417.
Definition of variables for Eqs (3) and (4): x,y,z, Displacement and rotations about the three body fixed coordinate axes. O,O,c Road gradient and superelevation A,y angles Wind drag coefficient in x direction gwx Wind drag coefficient in y direction Kwy
Control Eng. Practice, Vol. 5, No.l !, pp. 1615-1622, 1997 Copyright © 1997 Elsevier Science Ltd Printed in ~ Britain. All rights r~m'v~l 00967-0661/97 $17.00+0.00
Pergamon
PII:S0967-0661 (97)10017-X
EXPERIMENTAL RESULTS OF A TIRE-BURST CONTROLLER FOR AHS S. Patwardhan*, H.-S. Tan* and M. Tomizuka**
*Partnersfor Advanced Transit and Highways (PATH), University of California at Berkeley, Berkeley, CA 94720, USA ([email protected]) **Department of Mechanical Engineering. University of California at Berkeley, Berkeley, CA 94720, USA
(Received June 1997; in final form July 1997)
Abstract: This paper investigates the problem of tire burst, and how to mitigate its adverse effects in an AHS environment. The problem is approached by first modeling the tire burst. A feed-forward controller is designed, based on inverting the nonlinear tire-burst dynamics for controlling the ear after the tire burst. The feed-forward term is approximated by the output of a second-order filter. The approximation also provides a way to characterize the feed-forward term for different road curvature and different tires (front/rear, left/right). Two different tire blow-out detection algorithms are discussed. This is followed by the experimental phase. Open-loop experiments were conducted to verify the tire-burst model. Closed-loop tests were then carried out to validate the automatic lane-following performance after a tire burst. The results have shown that the burst controller enables the car to follow the lane, even after a front tire blow-out. Copyright © 1997 Elsevier Science Ltd Keywords: Tires, automated guided vehicles, automotive control, fault-tolerant systems, feedback compensation, fault detection, vehicle dynamics, automobiles, feedforward compensation, automatic control
1. INTRODUCTION The two major goals of Automated Highway Systems (AHS) are to improve the throughput of a highway by overcoming human limitations, and to improve the highway safety by eliminating human errors. In an AHS vehicle, automatic lateral and longitudinal control systems would replace the driver for the steering and speed-control ftmetions. With the decrease in human involvement, devices such as sensors, controllers, actuators and communication links are required for automatic control, and are also responsible for the vehicle's safety. The system must detect failures that may induce hazards, and properly control the vehicle to mitigate any potentially hazardous situations. This paper concentrates on one of the most critical roadway failure scenarios, a tire blowout. First the tire-burst model developed in (Patwardhan et al., 1994) will be revisited. This will be followed by the design of a burst-detection algorithm and a tire-burst 1615
controller to compensate for the undesirable lateral displacements arising from a tire blowout. Finally, the results of tire-burst experiments will be presented. The experiments themselves can be broken into two phases: open-loop and closed-loop. The open-loop experiments validate the tire burst model, where/is the closed-loop experiments prove the effectiveness of the tire-burst control in an automatic lane-following environment. 2. BURST MODELING When a tire bursts, several changes occur in the car. These changes can be categorized as changes in the car geometry, changes in the operating conditions and changes in the tire-road characteristics (see Fig. 1). The changes in the geometry occur because the radius of one of the wheels suddenly decreases. Among other things, this changes the distribution of the suspension forces, and thus creates a force imbalance, as well as injecting disturbances into the pitch and roll dynamics of the car. Tire radius reduction also
1616
S. Patwardhan et al.
increases the moment arm of the forces acting on the tire about the king pin. Furthermore, the changes in the geometry lead to changes in the operating slip ratio of the car, as well as changes in the tire-road interaction characteristics, such as the tire rolling resistance and the comering stiffness. A list of the issues involved in the development of the vehicle tireburst model follows:
Tire Burst
"4 Vehicle Geometry
I-Interaction Roa jI ~\.
'-~ ]Operating [ [ Condition~
Force I Generation ~...\
Steering Command
'i - Vehicle Dynamics ~
~. Output
Fig. 1. Effects of a tire burst on vehicle behavior. 1. Time required for deflation: A tire burst being a rapid phenomenon, the heat loss from the tire air to the environment can be ignored. The tire air expands adiabatically. From the adiabatic expansion law ( P V ~ = Const. ), a relation between the deflation time and other tire parameters can be derived (Patwardhan 1994). For 7/ = 1.21, the relation looks like
Pt
4. Roll and pitch disturbances: Because of the sudden drop in the tire radius, the roll and pitch angles of the car change suddenly. 5. Increase in roll resistance: When the tire bursts, the tire shape changes dramatically. As the tire material passes in and out of the contact region, it experiences positive and negative bending. The energy spent in this bending comes from the increased roll resistance.
j-
]
3. Suspension force rearrangement: After the tire bursts, the suspension at the tire that has blown and that at the diagonally opposite point get stretched, whereas the remaining two suspensions are compressed. This effect changes the static force in each of the suspensions. The static components of the rearranged suspension forces can be computed from the equations of static force balance.
6. increased moment arm about king-pin: For a typical vehicle, the geometry of the king-pin (the axis about which the tires are pivoted to rotate) is constructed such that the tire-road interaction forces produce an optimal amount of turning moment around the king-pin axis, so as to produce a good driver feel. When a tire burst occurs, the moment arm of the road-tire interaction forces about the king-pin axis increases. As a consequence, (depending on the stiffness of the steering system), these moments tend to deflect the steering system. 7. Reduction in cornering stiffness: As the tire pressure decreases, the tire cornering stiffness decreases. Consequently, the cornering force under a tire burst reduces from its nominal value.
_ ldt = vi (P* + Pa) 0'71
~a
pl.21
(1) 3. TIRE-BURST CONTROLLER/DETECTOR DESIGN
0.5
Pa
where v i
volume of air inside the tire before burst
vf
volume of air inside the tire after burst
p
gauge tire pressure before burst
Pa
atmospheric pressure
Pa
Cq
air density at Pa time required for deflation area of the opening in the tire flow coefficient of the opening
Pt
a
T A
(P
variable
that
goes
linearly
from
+ P a ) to zero in t i m e 0 to T
For a typical tire, Eq. 1 gives a 0.5 sec deflation time for a 3cm diameter opening in the tire. 2. Tire radius reduction: After the tire bursts, the tire stiffness goes on decreasing as the tire pressure decreases. Consequently, the tire flattens out under the vehicle's weight till the steel rim hits the ground. As a result of radius change, the slip ratio at the contact point also changes.
The primary aim of designing a controller for a tire blowout is that the lateral displacements of the car from the lane center line after a tire blowout should not exceed the lateral displacement limits set by the AHS operational requirements. Other considerations, such as passenger comfort, become secondary factors under the tire blow-out scenario. To keep the car within its lane boundary until it can safely be taken out of the mainstream traffic becomes vitally important from the viewpoint of hazard reduction. The automatic lane-following controller designed for the nominal operation would not be sufficient for the operation after a tire blowout. This paper describes a control strategy in which a burst controller takes over from the nominal controller after a tire burst (Patwardhan and Tomizuka, 1994) (see Fig. 2.). The switching between the controllers will be triggered by a burst-alarm. The most direct way of generating such a burst alarm is to use the tire pressure measurement. When the tire pressure drops below a certain threshold, a burst will be detected. Another way is to use a model-based fault-detection
Experimental Results of a Tire-Burst Controller for AHS algorithm, in which an observer is built to predict the pitch and roll rates of the car. These observed values, when compared with the actual measurements, generate a residue. The residue, will contain enough information to generate the burst alarm (Patwardhan, 1994). Nominal •__• Co..oiler I ;.
1617
where rout and r/n are the tire radius and the rim radius respectively; V is the actual vehicle velocity. Thus, the longitudinal control action is reduced because of a deliberate increase in the velocity measurement. Although this solution is implementation-specific, it serves as a guideline for a generic tire-burst controller. 2. Feed-forwar~l controller: By inverting the vehicle dynamics for the case of a tire burst, one can compute the ideal steering command that can keep the lateral displacement to zero after the tire burst. This term can be used as a feed-forward term for reducing the lateral displacements.
.l
1 |Enlergcney~ ~~] VEHICLE~-~
In this section, the dynamic equations of the car are considered for model inversion. The model inversion will be done for the specific case of tire-burst conditions. Consider the vehicle dynamics given by Eqs (3) and (4):
I Bursttime
m[3i - ~ + 0 F - OflA~ - AOf~ + qbfl~ + ckA~ Fig. 2. Tire-burst controller structure.
+~)'~'~ + / ~ + f l ~ + z~] + y ~ + ~ ] 4 4
(3)
3.1 Tire-burst controller As mentioned above, the controller based on the nominal vehicle model will not be sufficient to achieve the lane-following objective after a tire burst. Analysis also shows that merely redesigning the feedback term will not be sufficient to control the vehicle. Several schemes for burst controllers have been investigated in (Patwardhan, 1994), including intentionally bursting a symmetrically opposite tire to counteract the tire force imbalance produced by the burst of a single tire. The following subsections will discuss only the strategies that were successfully used for the closed-loop tire-burst experiments. 1. Engine toroue reduction: When a tire interacts with the road, it produces forces in the lateral as well as in the longitudinal direction. When other factors are kept constant, the total tire force generation capacity in the road-tire contact plane is roughly proportional to the vertical load on that tire. This indicates that the capacity of the tire to generate a lateral force gets reduced when the tire is generating a large amount of longitudinal force. Since a large steering force would be required during the tire-burst control, one can reduce the longitudinal force that the tire generates by reducing either the engine or the brake torque after a tire burst. In actual experiments, conducted under the University of California's PATH program, the engine torque was reduced by using a wheel speed sensor measurement to compute the vehicle speed, for closing the longitudinal control loop. After a front tire burst, the vehicle velocity measured by the wheel speed sensor located at the differential gear box is V. = 0.5 x ( ~ V + V),
(2)
i=1
i=1
m[j) + ~ - 0 ~ + 0flz~ + A O ~ - ~ f l ~ - ~Z~ - ~ Z ~ - ~2 - ~ +/3X~ + . A ~ - 0 ~ 1 4 4
(4)
= -Kwy ~ + mg(~ + ~)+ Z ~FPi + Z F(yi" i=1 i=1 These equations can be rewritten as: = al(X,Se,Sx)
fJ = b l ( X , S p , S x )
(5)
where :
x=[x
k
y
~
z
~ ~
4
~
o
0
c
4
i=1
i=1 4 i=1
The quantifies Ftxi and Ftyi are the tire forces in lateral and longitudinal direction. These are functions of state x , steering command 8=[81
62
63
64] T, time t, and the angular
velocities co = [col °22 co3 CO4]Tof the wheels (Patwardlmn et al., 1994; Peng, 1990). Angular velocities in turn depend on an another input to the car, the engine torque Te = [Tel "" Te4 ] T , where the indices 1..... 4 refer to the four wheels. Fpi are the suspension forces at the i th suspension that are
S. Patwardhan et al.
1618
functions of x , and time t (Patwardhan et al., 1994). All the other variables are defmed in the appendix. The time dependency of the forces arises because the tire stiffness changes as a function of time when one wants to model tire burst. As a result, Eq. (5) will be modified to :
= al(X'Sp'Sx) = a(xb't'd'Te) = b l ( X , S p , S x ) = b(Xb,t,~,Te) where x b = [x T
(6)
Xs
CG i
Yr
Controller Characterization
Va -----Q_-d Fig. 3. Defmition of system output. Consider Fig. 3. This figure defines the output of the lateral dynamics of the car. The output Yr of the system is defmed as the distance of the center of gravity (CG) of the car from the roadway center line. Point A is on the Ys axis extended. In the figure, Va ~ 5c. The velocity of point A with respect to the CG of the car is:
Yr = f i ; + V a S i n ( c - g d ) ~ J ' + J c ( g - E d )
(12)
Since the model inversion calls for the solution of transcendental equations, the computations cannot be done on-line. Fortunately, for controlling a tire burst, it is not required to perform these computations online. Instead, one can run the inversion algorithm offline, and store the corresponding control input trajectory. This trajectory will then be fed in as a feedforward trajectory once a tire burst is detected.
;Ys ,x
min[b(Xb,t,tS, Te) + a ( x b , t , t ~ , T e ) ( e - Cd) 6 +3~(~-- ~d)] 2 .
coT] T.
Car
gives the values of the steering command that are required for ideal lane-following. If such a solution of Eq. (10) is not possible, then one can find 8 that does the following minimization with constraint Eqs (ll)
•
A tire burst can happen at any place on a roadway, and the vehicle could be going on a straight road or on a curved road when this happens. Also, depending upon which tire has burst, the feedforward terms will be different. This calls for characterization of the feedforward term, based on the road curvature p and the index k of the burst tire. Figure 4 shows the plots of the feedforward term for different radii of curvature for an outer front tire burst. Fe~KlfoP~arfl tom1 0.01
(7)
The aim of any controller designed for tire bursts is to keep Yr as close to zero as possible. Note that the control input does not appear in the expression for Yr
-0.02
i -0.03 !
or ))r. Differentiation of Eq. (7) gives: ))r ~ 35 + 5~(C- ~) + A ( k - kd)
-0,(
o ~ -0.o4
(8) -0,o5
Substituting from Eq. (6) gives:
]Vr ~b(Xb,t,rY, T e ) + a ( x b , t , d , T e ) ( a - Cd) + x ( k - k d)
-0.06
For the case of ideal lane following, Yr - O. This also implies 3)r - 0 and j) = 0. When this value for ))r is substituted into Eq. (9),
b ( x b , t , ~ , T e ) + a ( x b , t , d , Te)(C- Cd)
(10)
+ k ( k - kd) = O. Solving Eq. (10) for d with the constraints: For 2 wheel steer: t~l = ~ 2 ;
For front wheel drive:
~ 3 = t~4 = 0; Tel = Te2 = cmd;
For 4 wheel steer: 61 = 6 2; 6 3 =c~ 4;
Actual"WWD tclm Approximate
--
(9)
Te3 = Te4 = 0; For rear wheel drive: Tel = Te2 = 0 ; (11) Te3 = Te4 = cmd; For four wheel drive: Tel = Ve2 = Te3 = Te4=cmd.
-0,07
2
4
6
8
time {sac)
Fig. 4. Feed-forward terms: actual and approximate As a first step in the characterization of the controller, it is proposed to approximate the feedforward term by the output of a second-order filter, excited by a step input whose strength is a function of the radius of curvature of the roadway and the tire that has burst. The structure of this controller is shown in Fig. 5. When the tire burst occurs, a burst alarm will be generated by the burst-detection algorithm. The burst alarm will then be scaled according to the current radius of curvature p . The radius of curvature is assumed to be known here, because in IVHS, this information can be encoded in the roadway (Zhang et al., 1990). The scheme of Fig. 5 also has the advantage of addressing the scenario of a road curvature change when one of the tires has burst. Under such a
1619
Experimental Results of a Tire-Burst Controller for AHS curvature change, the feedforward filter input will be changed to a different value, which is the same as the value of the step if the burst had occurred on that patch of the roadway.
that
F~,i = C/o~i,i E {1,2} and F~, = CrOq,i ~ {3,4}.
Then, the vehicle lateral and roll dynamics can be simplified to
(2(Cfll+Crl2) I
2(C/+Cr)'
In the experiments, the feed-forward term is first computed off-line and then approximated by the step response of a second-order filter. Figure 6 shows the performance of the feed-forward controller when the car is traveling first on a straight road, followed by a curve that ends into a straight section when the outer front tire bursts midway through the curve.
=
mV
Y-L
-m~
+2C[
~Vjk
(13)
m 6
2(Cfll+Crl2) 2(Cfl2+Cr12) 2C/lI
~=
lzV
e+
lzV
Iz
(14)
6
~= 2(CI+Cr)zo ~ 2(Cfl,+Crl2)zo.k+kS~ip IxV
IxV
(15)
2I x
_b$~~+2C/zo6 . . . .
e+2~°+°, t Burst
I I !,,.l"="i
~
Controller
Bulrst time
road radius:
Fig.
5. Burst-controller
os
r
i
:
:
burst tire # : k
I
?....
!
•
.4 . i ,
. . .
i
,
,
;Curve. 76m radlu=
i
:
i
:. . . .
i i
_ ~-0,0~
p
j
structure.
~traight 0-1"=
21x
7
i i !......
i
r Straight :
, i I
i !
.
2
1
'~
j
_
.
-o.(
L
i
i
~
i
2
4
6
B
to time (see)
12
i
k
i
14
t6
18
20
Fig. 6. Feed-forward controller performance (simulation).
3.2 Tire-burst detection As soon as the tire burst occurs, the tire pressure drops. All other effects of the tire burst follow the drop in pressure. Other than the tire pressure itself, two of the most significant effects from the burstdetection viewpoint are the rolling and pitching of the vehicle. Consequently, there are two possible ways of detecting a tire burst and generating the burst alarm. 1. Tire oressure measurement: Tire pressure can be continuously monitored, and whenever it drops below a certain threshold, a burst alarm can be generated. In fact, such alarm systems have already been developed (Uemura et al., 1985). In (Uemura et al., 1985), the driver warning system consists of measuring the tire pressure once per revolution; on the other hand, in the experimental arrangement for the burst experiments (see Section 4 for details), the tire pressure was monitored continuotlsly. 2. Roll rate measurement: Consider a vehicle traveling at constant velocity v and having front and rear cornering stiffness c / and Cr respectively, such
Ix
where y, E and ~ are the lateral displacement, yaw angle and roll angle; m, I, and Ix are the mass and the moments of inertia about the yaw and roll axes; Ii and /2 are the distances of the vehicle's center of gravity from the front and rear axles; k is the sum of stiffness of the right (or left ) side suspension springs and b is the sum of the damping coefficients of the same two suspension dampers. An observer-based faultdetection scheme was built, with Eqs (13)-(15) as the plant. This observer was a simple pole-placement observer, using yaw-rate measurement. The simulation results are shown in Fig. 7. The figure shows the plots of the roll-rate error and the tire pressure (as a fraction of the nominal tire pressure). As far as the detection time is concerned, the two methods of burst detection compare quite well. However, the roll-rate error measurement can generate non-zero roll-rate error under excessive noise or disturbances, such as when the car drives over pot-holes and bumps. Consequently, this method has a higher probability of false alarms. In the experiments, the tire-pressure measurement method was used for detecting tire bursts. detection
o.~
.......
o.o6
~ .........
siganl
..................
p/pn
........
............ :=......
.......... i .............. !............... i............... i .............. ! ~
"6"
. . . . .
i. . . . .
2 . . . . .
L . . . . .
~. . . . .
2
"
! ...... L__
o.o,I ........................................................i.............. l r. In :
A rt)llrateerrot
i l~l~
0.75 0.50
.
.
/11
g 0.02 . . . . . . . . . . i .............. i . . - ~ - ~ . . ! .............. i ............. i./-.~/ . . . . . i~
.
.
.
.
....
0.25
0
°oo
-0.25
............... -0.04
1.00
............................. i............. i.............................. W
.............. ! .............................. ::............... i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i 2
4
i 6
time (s)
J 8
10
.0.50
12
Fig. 7. Tire burst detection. 4. EXPERIMENTAL SETUP Experiments were designed to verify the tire-burst vehicle model and the control algorithm.
1620
S. Patwardhan et al.
4.1 Open-loop experiments The open-loop experiments for model validation were conducted on an AMC-Concord sedan. The car was driven with a fixed steering angle, and one of the tires was burst at a pre-selected speed. A water jet was installed on the front bumper, that would leave a trail on the pavement of the test site, so that the vehicle's trajectory could be recorded and compared with the simulation outputs. One of the biggest hurdles in conducting the experiments was to create a tire blowout in a controlled manner. This was achieved by installing an air release valve on the wheel which was operated by a remote-controlled device powered by a small battery. An important consideration in this design was to have a valve opening about an inch in diameter, a size slightly greater than the rupture area for a typical tire burst. This arrangement ensured that the air in the tire was released within a short time span, characteristic of a typical fire blow-out. This approach would create a situation close to a fire burst, without actually rupturing the tire. One tire could then be used more than once in the experiments. As shown in Fig. 8, eight holes were drilled in the rim of the wheel. The total area of these eight holes was slightly more than the area of a one-inch diameter hole. Flexible tubing connected these openings to a release valve at the center of the wheel. The valve was designed as a two-stage release valve, with the first stage being an off-the-shelf solenoid pneumatic valve. The second stage was a pneumatic cylinder that operated on the air from the tire itself. This cylinder in turn operated the latch of the valve flap. The first stage solenoid valve was powered by a small battery on the wheel, and triggered by a radio receiver that would receive trigger signals from a radio transmitter operated by the driver. Another radio transmitter-receiver pair was used in the experiment to transmit the tire pressure measurement back to the car. The steering lock mechanism of the car was modified to secure the steering at a constant angle during the tests.
measuring scheme and a steering actuator. A magnetic-marker-based roadway reference system was used (Zhang et al., 1990) to measure the lateral displacement in real time. Magnets were installed every 1 meter along the center line of the test track. Magnetometers were mounted on the front bumper of the vehicle, and the magnetic field strengths in the vertical and horizontal directions were translated into the vehicle's lateral displacement by using calibration tables. A DC servo motor was used for the steering actuator to realize the steering commands. The ffmal configuration for the experiment, shown in Fig. 9, was realized on a PONTIAC 6000 STE sedan. This vehicle was also equipped with a throttle actuator, and a wheel speed sensor. These were used for the longitudinal velocity control.
Fig. 9. Tire burst: experimental arrangement. 5. EXPERIMENTAL RESULTS AND INTERPRETATIONS
5.1 Open-loop experiments The open-loop experimental results were superimposed on the simulation results from the open-loop fire-burst vehicle model. Figure 10 (Fig. 11) shows such a plot for the front (rear) wheel burst experiment. Front Tire Burst 16
/
14
//J
~-
\ E>cmfiment "
12
/
/ ~
~ ~
\
Flexibh 'c' Tubing !
\
.,,.~) \\
\
m
/,
10 EI
E E
/ \,\
.~,/
"L L ) j / ........ ~-~
/
i :
,o \ .... d Tire
../ 50
10O
150 200 X in meters
/
250
300
350
Fig. 8. Tire burst: experimental arrangement.
Fig. 10. Front tire-burst experiment (open-loop).
4.2 Closed-loop experiments
The plots show excellent agreement between experiments and simulations for transient behavior, immediately after the tire burst. This verifies the validity of the tire-burst model from the closed-loop controller design viewpoint. The transient region is
Besides the experimental arrangement described above, two additional components were needed for the closed-loop experiments: a lateral displacement-
Experimental Results of a Tire-Burst Controller for AHS followed by integrator drift, which is caused by the double integrator characteristics of the open-loop vehicle, being integrated over a long time and thus magnifying any small discrepancies between the model and vehicle states.
1621
by the longitudinal controller is actually Fro=20.01 mph (given by Eq. (2)). Finally, Fig. 15 shows the tire pressure measurement. Feodforfnud tern1 (L~'nph teat)
Rear Tire B e r t 30 ............
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . . . . . .
2.=
2C
• ........
- ......
:
";~o
I
0011 o
5o
""
lOO 15o 200 250 L~tgllodlnel dlltanco along track (m)
I
/ 350
3O0
Fig. 13. Closed-loop tire burst experiment (feedforward term). 50
1 O0
150 200 x in meters
250
300
350
Fig. 11. Rear tire-burst experiment (open-loop).
Burld Comrohr Pedormlnce (20mph r u t )
2SI
i
5.2 Closed-loop experiments The closed-loop experiments were conducted for a front-tire-burst scenario with co = 2rad / s, ~"= 0.5. Results of the experiment are shown in Figs 12-15.
~15
i ~k~Carluv~lrackwltho~burllcontrbller
1
I
0"2 l . . . .
k
I~v~ (~h ~or..) ....................
.....
4. i z . . . .
3
........ ,.;~.~.
t.)
. . . . . . 50
,
.
i
:
I
i
i
!
'
50
Wlt~ut Burst ~ l k J r
i
100 150 200 250 Longitudinal dlltanco along track (m)
300
350
Fig. 14. Closed-loop tire burst experiment (vehicle speed).
i
I :.: .,,:,, ... ,.:: .......... 100 150 200 250 Longitudinal distance =long track (m)
i
i
: * ~
WithOgt Burst CoNroller -o.~
i
...........
T o
:Ln ! L T t
Burst ~ v ~ u t cont;)
Burst Co*ltroller PedormaPce (20mph test)
o t
i 8 . . . ~ikh ~ . )
Tire pressure (w#h burst controller case).
3(3
300
25
350
:¸ !
2G
Fig. 12. Closed-loop tire burst experiment (lateral displacement) These figures compare the results, with and without the burst controller. It can be seen that without the tire-burst controller, the lateral deviations of the car reach the sensor limit, and the car goes out of control (see Fig. 12). With the burst controller, although the ride quality and tracking error worsen after the tire burst, the car does not reach the lateral sensor limit, and does not leave the track. Figure 13 shows the feed-forward term. As the road curvature changes, the input to the feed-forward block gets scaled and in turn, the feed-forward term changes. This term becomes non-zero only after a tire burst has been detected. Figure 14 shows the vehicle velocity. The velocity set-point for the longitudinal control during the experiment was 20mph, but the vehicle tracks to about 15mph after the burst because the velocity seen
i
:
.......
t
o
10
Longitudinal dlatance along track (m)
Fig. 15. Closed-loop tire burst experiment (tire pressure).
6. CONCLUSIONS This paper has investigated the problem of tire burst, and how to mitigate its adverse effects in an AHS environment. The problem was approached by first modeling the tire burst. A feed-forward controller was
S. Patwardhanet al.
1622
designed, based on inverting the nonlinear tire-burst dynamics for controlling the car after the tire burst. The feed-forward term was approximated by the output of a second-order filter. The approximation also provided a way to characterize the feed-forward term for different road curvatures and different tires (front/rear, left/right). Two different tire-blow-out detection algorithms were discussed. This was followed by the experimental phase. Open-loop experiments were conducted to verify the tire-burst model. Closed-loop tests were then carried out to validate the automatic lane-following performance after a tire burst. The results have shown that the burst-controller enables the car to follow the lane, even after a front tire has blown out. ACKNOWLEDGMENT This work was performed as part of the Partners for Advanced Transit and Highway (PATH) program, prepared under the sponsorship of the State of California; Business, Transportation and Housing Agency; Department of Transportation (Caltrans).
Patwardhan, S. and M. Tomizuka (1994). Feedforward controller design using nonlinear model inversion for automobile tire burst, Proc. of ASME Winter Annual Meeting, Chicago. Patwardhan, S., M. Tomizuka, W. Zhang and P. Devlin (1994). Theory and experiments of tire blow-out effects and hazard reduction control for automated vehicle lateral control system, Proc. of American Control Conference, Baltimore. Peng, H. and M. Tomizuka (1990). Vehicle Lateral Control for Highway Automation, Proc. American Control Conference, San Diego, pp 788-794. Uemura, Y., et al. (1985). Tire Pressure Warning System, Tenth Int. Technical Conf on Experimental Safety Vehicles, Oxford, England, July 1-4, pp. 288-294. Zhang, W., R. Parson and T. West (1990). An intelligent roadway reference system for vehicle lateral guidance/control, Proc. of American Control Conference, San Diego. APPENDIX
REFERENCES Patwardhan, S. (1994). Fault detection and tolerant control for lateral guidance of vehicles in automated highways, University of Calif. Berkeley, PATH Publication, UCB-ITS-PRR-9417.
Definition of variables for Eqs (3) and (4): x,y,z, Displacement and rotations about the three body fixed coordinate axes. O,O,c Road gradient and superelevation A,y angles Wind drag coefficient in x direction gwx Wind drag coefficient in y direction Kwy