F2000I398
Seoul 2000 FISITA World Automotive Congress
June 12-15, 2000, Seoul, Korea
A Throttle/Brake Control Law for Vehicle Intelligent Cruise Control
Kyongsu Yi1) *, Youngjoo Cho1), Sejin Lee1), Joonwoong Lee2) and Namkyoo Ryoo2)
1)
School of Mechanical Engineering, Hanyang University, Seoul, 133-791, KOREA
2)
Hyundai Motor Company, Kyunggi-Do, 445-850, KOREA
A throttle/brake control law for the intelligent cruise control(ICC) systems has been proposed in this paper. The ICC
system consists of a vehicle detection sensor, a controller and throttle/brake actuators. For the control of a throttle/brake
system, we introduced a solenoid-valve-controlled electronic vacuum booster(EVB) and a step-motor controlled throttle
actuator. Nonlinear computer model for the electronic vacuum booster has been developed and the simulations were
performed using a complete nonlinear vehicle model. The proposed control law in this paper consists of an algorithm that
generates the desired acceleration/deceleration profile in an ICC situation, a throttle/brake switching logic and a throttle
and brake control algorithm based on vehicle dynamics. The control performance has been investigated through computer
simulations and experiments. The results indicate the proposed ICC throttle/brake control law can provide satisfactory
vehicle-to-vehicle distance and velocity control performance.
Keywords: Intelligent Cruise Control, Optimal Design, Electronic Vacuum Booster, Kalman Filter, Duty Ratio
1. INTRODUCTION
Sliding control has been used for vehicle longitudinal
control to deal with nonlinearities in vehicle dynamics
[3,8]. A neural net has been used to compute the desired
vehicle acceleration for an ICC [6]. It was indicated that a
linear PID-controller could not provide satisfactory
performance because the controller was not able to handle
the noisy sensor data, resulting in a jerky driving behavior
[2].
Compared to the ordinary cruise control, the goal of an
ICC is to prevent the vehicle-to-vehicle spacing from
dropping an unsafe level. The throttle and brakes should
be gently controlled so that the driver is aware that the ICC
controller has taken over, but is not surprised by this
action. In order to achieve high customer acceptance, an
ICC system has to perform similarly to an experienced
human driver.
This paper describes a throttle/brake control law for
vehicle intelligent cruise control. The ICC system
considered in this study consists of a vehicle-detectionsensor, a controller and throttle/brake actuators. For the
control of a throttle/brake system, a solenoid-valvecontrolled electronic vacuum booster (EVB) and a stepmotor controlled throttle actuator have been used. A
nonlinear computer model for the electronic vacuum
booster has been developed and the simulations were
performed using a complete nonlinear vehicle model. The
proposed control law in this paper consists of an algorithm
that generates the desired acceleration/ deceleration profile
in an ICC situation, a throttle/brake switching logic and a
throttle/brake control algorithm. The control performance
has been investigated through computer simulations and
vehicle tests. The results indicate the proposed ICC
throttle/brake control law can provide satisfactory
Active safety systems and driver assistant systems have
been active topics of research and development since
1990’s due to the potential for increased vehicle safety and
improved driving comfort. One of the driver assistant
systems currently under development by most automotive
manufacturers around the world and recently
commercialized by several companies is Intelligent Cruise
Control (ICC) system. Ordinary cruise control systems for
passenger cars are becoming less and less meaningful
because the increasing traffic density rarely makes it
possible to drive at a pre-selected speed. ICC systems
control both speed and distance to preceding vehicles and
can improve the driving comfort and reduce the danger of
rear-end-collision. Although there already exist product
ICC systems, the bandwidth of such systems is very low
and the headway distance (the safe vehicle-to-vehicle
distance to avoid collisions) is large. Therefore, these
systems are almost useless on the busy urban traffic
highway, and it is concluded that the bandwidth of the
longitudinal vehicle control system should be increased
significantly to reduce the headway distance and to be
meaningful in the busy urban traffic highway.
There has been a lot of research conducted on the vehicle
longitudinal control including the ICC [1-7]. There have
been many attempts to apply PID-type control laws [4] in
the development of an ICC. Gain Scheduling and Adaptive
Scheme have been used in ICC development to meet the
various situations encountered by the controlled vehicle
[5,6]. Linear Quadratic (LQ) and Linear Quadratic
Gaussian (LQG) optimal control theories have been used
to develop a car following algorithm [7].
* kyongsu@email.hanyang.ac.kr
1
performances in vehicle-to-vehicle distance control and
velocity control.
Intake Manifold
Throttle
2. ICC VEHICLE
Fig. 1 shows a vehicle longitudinal control system. The
system consists of a radar sensor, a controller (ECU), a
brake actuator (active booster) and a throttle actuator. An
ICC vehicle considered in this study, a radar sensor,
throttle and brake actuators are shown in Figure 2. The
vehicle is equipped with a MMW radar distance sensor, a
controller, a solenoid-valve-controlled ElectronicVacuum-Booster (EVB) and a step-motor controlled
throttle actuator.
Electronic
Vacuum
Booster
air
Engine
solenoid
Master
Cylinder
ICC ECU
Active Booster
Vacuum
Booster
Throttle Actuator
Brake
Pedal
Radar
Wheel
Fig. 1 Vehicle longitudinal control system
Fig. 3 A schematic diagram of the EVB brake actuator
system
Brake Actuator
3. THROTTLE/BRAKE CONTROL ALGORITHM
Throttle Actuator
The throttle and brakes should be gently controlled so that
the driver is aware that the ICC controller has taken over
and is not surprised by the control action. It has been
reported that automotive decelerations up to 2.5 m / sec 2
were comfortable to human passengers [10]. The
throttle/brake control algorithm has been designed such
that the vehicle deceleration should not exceed this limit.
The maximum of the vehicle acceleration has been limited
to 1 m / sec 2 in order to prevent the kick-down of the
automatic transmission.
MMW Radar
Fig. 2 An ICC vehicle and equipments
3.1 ICC ALGORITHM
A schematic diagram of the EVB brake actuator system is
shown in Figure 3. Vacuum booster differential pressure is
controlled by a PWM solenoid-valve. Modeling of the
EVB, simulation and experiment results on the dynamic
characteristics and control performance of the EVB have
been described in detail in [9]. It is indicated that steady
state value of the differential pressure is proportional to
the duty ratio. It should be noted that time constant varies
significantly depending on the duty inputs and the steady
state values of the EVB differential pressure have
significant nonlinear characteristics. The nonlinear
characteristics are due to friction in the valve and air flow
characteristics.
A stepper motor has been used as the throttle actuator. The
stepping time of this motor is 4 milliseconds and the step
angle is 0.75 degree.
A block diagram of the vehicle and ICC algorithm is
shown in Figure 4. The distance to a preceding vehicle and
the relative velocity are measured using a MMW radar
sensor. The distance and relative speed to the preceding
vehicle and the pre-selected speed are fed to a ICC
controller. Comparison of the headway distance and the
distance to the preceding vehicle is used to determine
control mode between the speed control and the distance
control. In the case of the speed control, the controller
works like a conventional cruise control. The controller
controls the throttle and brakes such that the vehicle
acceleration tracks the desired acceleration, which is
designed so that the vehicle-to-vehicle distance converges
smoothly to the headway distance.
2
In this study, ρ = 4 and r = 5 have been used.
In the case that the ICC senses a cut-in vehicle, the control
law, u = − k ⋅ x , demands large, uncomfortable
accelerations. In order to avoid large accelerations, which
deteriorate ride comfort, the desired acceleration, a des ,
has been obtained using a saturation function and a second
order filter as follows:
a des
ω2
= 2
(5)
u sat s + 2ς ⋅ ω ⋅ s + ω 2
Set : ( Headwaytime, Speed )
ICC controller
Target detected?
: Yes
Target detected?
: No
Speed
Control
Optimal Design
Desired
Accel. / Decel.
Switching Logic
if u ≥ u max
u max

u sat = sat (u ) =  u
if u min < u < u max
(6)
u
if u ≤ u min
 min
where u = −k ⋅ x = −(k1 ⋅ x1 + k 2 ⋅ x 2 + k 3 ⋅ x3 ) . The filter
damping ratio, ς , of 1 and the cutoff frequency, ω , of 5
Throttle/Brake
Control Algorithm
Sensors
- Relative distance
- Relative velocity
Duty-ratio
Throttle
Throttle
Actuator
Brake
Actuator
rad / sec have been used. u min of –2.5 m / sec 2 and
u max of 1 m / sec 2 have been used to provide comfortable
ride quality and to avoid the kick-down of the automatic
transmission during the speed control mode. This approach
can saturate the vehicle jerk and acceleration at some
maximum value.
Vehicle
Fig. 4 ICC algorithm
3.2 DESIRED ACCELERATION PROFILE
3.3 THROTTLE/BRAKE SWITCHING LOGIC
Linear optimal control theory has been used to design a
desired acceleration. Using integrators to model the
vehicles, a state space model for the ICC and preceding
vehicles can be written as follows:
0 1 0  0  0
x = Ax + Bu + Γw = 0 0 0 x + − 1u + 1 w
(1)
0 0 0  1  0
The states are x T = [ x1 x2 x3 ] = [ x p − xcc v p − vcc
Depending on the desired acceleration that the ICC vehicle
must follow, the ICC controller applies throttle or brake
control. Fig. 5 shows a switching line with hysteresis. The
switching line indicates the vehicle acceleration (the
minimum acceleration, a min ) when the throttle is closed
( α = 0 ) for a given vehicle velocity. The minimum
acceleration line has been used as a switching line in the
throttle/brake controls. The ICC controller applies throttle
control when a des ≥ a min + h or brake control when
vcc ] ,
the input, u , is the ICC vehicle acceleration and the
disturbance, w , is the preceding vehicle acceleration. x
and v indicate position and velocity, respectively.
Subscripts, p and cc , indicate the preceding and ICC
vehicles, respectively. The gains for the state feedback
law, u = − k ⋅ x , are chosen to minimize the cost function:
∞
(
)
∞
(
a des ≤ a min − h for a given vehicle speed. Switching logic
with hysteresis is necessary to avoid frequent switching
between throttle and brake controls.
0.0
)
2
2
2
Acceleration [m/sec ]
J = E[∫ ed + ρ ⋅ ev + r ⋅ u2 dt] =E[∫ xT Q x + uT R u dt] (2)
0
0
ed and ev are the distance and velocity errors,
respectively, and defined as follows:
ed = d h − ( x p − xcc ) = x3 ⋅ t h − x1 , ev =v p −vcc = x2
(3)
where d h and t h (=1.2 seconds) are the headway time
distance and headway time, respectively. The weighting
factors, ρ and r , are chosen to give a tradeoff between
performance and ride comfort. The matrices, Q and R ,
are defined as follows:
0 − th 
 1

ρ
0 , R = [r ].
Q= 0
(4)
− t h 0 t h 2 
-0.2
Throttle Control
-0.4
h
h
α=0
-0.6
Brake Control
-0.8
0
20
40
60
80
100
120
140
Velocity [km/hr]
Fig. 5 Throttle/brake switching
3.4 THROTTLE CONTROL
3
160
180
At the low level of acceleration, wheel slip is quite small.
The no-slop assumption has been incorporated in previous
throttle/brake control designs for vehicle longitudinal
control in Intelligent Cruise Control or in Automated
Highways [3,8]. A throttle control law has been derived
under a no-slip condition of the driving wheels. A block
diagram of the throttle control algorithm is shown in Fig.6.
The dynamic equation for a vehicle model of a typical
passenger car encountering a grade with angle θ is[1]
dv
Mv
= Ft − Fa − M v g sin θ = Ft − FL
(7)
dt
where M v is the vehicle mass, v the vehicle speed, Ft the
throttle opening angles as a function of the engine speed
and torque. The throttle angle command, α des , has been
computed from the computed throttle angle and the vehicle
acceleration feedback using the Proportional-plusIntegration control as follows:
∫
α des = α f + K p × ( ades − a ) + K i × (ades − a )dt (14)
where a is the vehicle acceleration and K p , K I gains. It
has been recognized that the control law with large gains
results in a very jerky driving behavior due to the torque
production delay of the engine. Small gains have been
used in this study. The actual throttle angle is controlled by
the stepper motor to minimize the error between the actual
and the desired throttle angles.
tire longitudinal force at the wheel, Fa the aerodynamic
drag force, g the gravitational constant, θ the road grade
and FL the driving resistance load. Since the inertia of the
Desired
Acceleration
wheel and axle, J w , is relatively small compared to the
vehicle mass, i.e.:
J
(8)
M v >> w2
r
where r is the effective tire radius, the tire longitudinal
force (the tire tractive force), Ft , can be written as
follows:
1
1
Ft ≈ Ts − Tb
(9)
r
r
where Ts is the driving axle shaft torque and Tb the total
brake torque.
For a given desired acceleration, the required tire tractive
force is computed as follows:
Ft = M v a des + FL
(10)
When the desired acceleration for a given vehicle velocity
is greater than the switching line, i.e., the throttle control
region, the desired shaft torque, Ts , is computed from the
equations (9) and (10) as follows:
Ts = r ( M v a des + FL )
(11)
Desired Tractive
Force
ades
Ftr
r
Desired
Shaft Torque
Rd Rgi
Desired
Turbine Torque
Torque-Converter
Model
Tt
Tp
Ts
Engine Map
αf
PI control
K p × (ades − a) + Ki × ∫ (ades − a)dt
+
+
αdes
Actual
Acceleration
a
Fig. 6 Throttle control algorithm
3.5 BRAKE CONTROL
The brake torque is applied only when the engine braking
is not sufficient to follow the desired acceleration profile.
A block diagram of the brake control algorithm is shown
in Fig.7. When the desired acceleration for a given vehicle
velocity is smaller than the switching line, i.e., the brake
control region, the desired brake torque, Tb ,des , is
computed from the equations (9) and (10) as follows:
Tb ,des = −r ( M v a des + FL ) + Ts
(15)
The shaft torque, Ts , is computed using the engine map as
follows:
1
Ts =
Tnet (ω e ,0)
(16)
Rg
The driving resistance load, FL , changes relatively slowly
and the estimated value of the load can be used for the
computation of the desired shaft torque, Ts . It has been
presented in recent researches that the estimated value of
the driving resistance load can be obtained from the
vehicle longitudinal acceleration, engine speed and wheel
speed measurements.
The desired engine net torque, Tnet , can be computed from
the desired shaft torque as follows:
Tnet = R g Ts
(12)
Since the total brake torque is proportional to the brake
pressure, the desired brake pressure, p w,des , can be
obtained by the equation:
1
p w,des =
Tb,des
Kb
(17)
where K b is the lumped gain for the entire brake system.
where R g is the gear ratio from the engine to the wheels.
K b lumps all the uncertainties in the brake model from the
The engine net torque is represented as a function of
engine speed, ω e , and throttle angle, α , as follows:
brake pressure to the brake torque. The parameter, K b ,
has been obtained from experimental data. A value of
K b = 850 Nm / Pa was used and it provides a good fit to
one set of the experimental results. Since the brake line
pressure is equal to the brake master cylinder pressure at
low frequency actuation, the desired master cylinder
pressure, p mc,des , is set to be the brake pressure, i.e.:
Tnet = Tnet (ω e ,α )
(13)
Typically the engine map is provided by the engine
manufacturer as a look up table. The throttle angle, α f ,
for the desired net engine torque for a given engine speed
can be computed from the engine map that shows the
4
u = g −1 ( pd ,des ) + P ⋅ ( pd ,des − pd ) + I ⋅ ∫ ( pd ,des − pd )dt
1
Tb,des
(18)
Kb
Since the master cylinder pressure is directly connected to
the vacuum booster, the desired vacuum booster pressure,
is given by:
A
p d ,des = mc p mc,des
(19)
Ad
pmc,des = p w,des =
+ D ⋅ ( p d ,des − p d )
where u means the applied duty input to the EVB
solenoid valve, p d the measured EVB differential
pressure, P, I , D the gains and g (⋅) the function
representing the relationship between the duty input to the
EVB solenoid valve and the steady state values of the
EVB differential pressure, i.e.:
p d = g (u )
(21)
where Amc is the area of the master cylinder and Ad the
area of the diaphragm of the vacuum booster. Since the
vehicle acceleration is limited in a range [-2, 1] m / s 2 in
an ICC, the proportioning valve is not activated so both
the rear and the front brakes experience the same brake
pressure. In addition, since the brake pressure is controlled
at a low frequency range in an ICC, the inertial effect of
the connecting rod between the master cylinder and the
vacuum booster is not significant. Therefore the simplified
equations (16), (17) and (18) represent accurately the
brake system in case of an ICC.
4. VEHICLE TESTS
Numerical simulations and vehicle tests have been done to
evaluate the performance of the proposed control
algorithms. Vehicle tests have been conducted using a test
vehicle, a 2000cc passenger car equipped with a MMW
radar distance sensor, a controller, an EVB brake actuator
and a step motor controlled throttle actuator. The
differential pressure, p d , of the vacuum booster was
controlled by a PWM solenoid valve. The pressure was
proportional to the duty ratio input to the solenoid valve. A
pressure sensor was installed on the EVB to measure the
differential pressure and the measured pressure was used
as the feedback in the brake control. The already
existing wheel speed sensors, engine RPM sensor, and a
Throttle Position Sensor (TPS) have used to estimate the
vehicle accelerations and to implement the control laws.
Optimal Design : Desired Deceleration
udes = −k1 ⋅ ( x p − xcc ) − k2 ⋅ (v p − vcc ) − k3 ⋅ vcc
Saturation
udes
Filter
ωn
2
2
s + 2ζωn s + ωn
2
ades
4.1 VEHICLE SPEED CONTROL
In the case of the speed control, the controller controls the
throttle angle such that the vehicle acceleration tracks the
desired acceleration profile, which is designed so that the
vehicle speed converges to the set-speed. The desired
acceleration, a des , has been obtained using the equations
(5) and (6) with
u = k 2 ⋅ (v set − vcc )
Desired Wheel Pressure
Pw,des =
1
[−rM v ades + Ts − rFL ]
Kb
Desired Differential Pressure
Pd ,des
(20)
where v set is the set-speed determined by the driver.
Fig. 8 shows a comparison of vehicle test and simulation
results. Vehicle speeds and throttle angles measured by the
TPS are compared. The ICC vehicle’s initial speed has
been set to be 80 km / h and the set-speed has been
increased to 100 km / h at 2 seconds. As soon as the setspeed is increased, the stepper motor is controlled based
on the throttle control algorithm. The maximum vehicle
accelerations have been limited to 1 m / s 2 in the
simulations and vehicle tests. As indicated in the Fig.8, the
simulation results predict the vehicle test results very
closely.
A
= mc Pw,des
Ad
Duty-ratio : Feedforward + PID control
u = g −1 ( Pd , des ) + P × ( Pd , des − Pd )
+ I × ∫ ( Pd ,des − Pd )dt + D × ( Pd ,des − Pd )
Fig. 7 Brake control algorithm
As indicated in section 2, the EVB brake actuator system
dynamics is not negligible and the EVB shows nonlinear
characteristics. Therefore, a feed forward plus
proportional-integral-derivative (PID) control law is used
to control the EVB pressure:
5
A throttle/brake control law for vehicle ICC has been
presented. The control law was developed considering the
throttle and brake actuators characteristics. The
performance of the proposed control laws was investigated
via simulations and vehicle tests. The control laws were
implemented on a test vehicle. An ICC system used in the
tests consists of a MMW radar sensor, a stepper-motorthrottle actuator, an EVB brake actuator, and a controller.
The ICC system was implemented on the test vehicle. The
vehicle test results show that vehicle speed and distance
control performances are satisfactory. The throttle and
brakes were gently controlled and the driver is not
surprised by the control action. The vehicle accelerations
were limited to [1~ -2.5] m / sec 2 in order not to deteriorate
ride comfort. The simulation and vehicle test results have
shown that the proposed throttle/brake control laws can
provide the ICC vehicle with an optimized compromise
between safety and comfort.
Experiment
Simulation
Experiment
Simulation
Fig. 8 Vehicle speed control: Simulations and vehicle tests
4.2 VEHICLE DISTANCE CONTROL
Vehicle distance control tests were done using two
vehicles: the ICC vehicle and a cut-in-vehicle. Fig. 9
shows the test results. The ICC vehicle’s set-speed was
100 km / h and a vehicle of 80 km / h had appeared in the
front of the ICC vehicle at 5.5 seconds. The initial relative
distance was approximately 133 m and the headway time
of 1.5 seconds has been used in this test. Since the speed
of the preceding vehicle is smaller than that of the ICC
vehicle, the ICC controller activates the brake control such
that the relative distance converges to the headway time
distance and the ICC vehicle speed converges to the
preceding vehicle’s speed. As illustrated in the Fig. 9, the
ICC vehicle speed converges smoothly to the preceding
vehicle speed and the relative distance converges to the
headway time distance. In this test, the headway time
distance was computed using the preceding vehicle speed
estimated using the ICC vehicle speed and the measured
relative speed.
REFERENCES
[1] Winner, H., Witte, S., Uhler, W., and Litchtenberg, B.,
“Adaptive Cruise Control System Aspects and
Development Trends,” SAE paper No. 961010, 1996.
[2] Muller, R. and Nocker, G., “Intelligent Cruise Control
with Fuzzy Logic,” In Intelligent Vehicles ’92 Symposium,
pp. 173-178, Detroit, 1992, IEEE Industrial Electronics
Society.
[3] Choi, S. and Devlin, P., “Throttle and Brake Combined
control for Intelligent Vehicle Highway Systems,” SAE
paper No. 951897, 1995.
[4] Chien, C.C., Ioannou, P., and Lai, M.C., “Entrainment
and Vehicle Following Controllers Design for Autonomous
Intelligent Vehicles,” Proceedings of the 1994 American
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1994.
[5] Ioannou, P., Xu, Z., Eckert, S., Clemons, D., and Sieja,
T., “Intelligent Cruiss Control: Theory and Experiment,”
Proceedings of the 32nd Conference on Decision and
Control, volume 2, pp.1885-1890, San Antonio, Texas,
December 1993.
[6] Germann, St. and Isermann, R., “Nonlinear Distance
and Cruise Control for Passenger Cars,” Proceedings of
the 1995 American Control Conference, pp. 3081-3085,
Seattle, Washington, June 1995.
[7] Elliasson, A., “A Controller for Autonomous
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International Conference on Vehicle Navigation and
Information Systems, pp. 170-175, IEEE, 1992.
[8] Hedrick, J.K., “Longitudinal Control and Platooning,”
In TOPTEC:Collision Avoidance Systems for Intelligent
Vehicles, Washington, D.C., April 1993, SAE.
[9] Yi, K., Lee, S.J., Lee, C., and Kong, Y., “Modeling and
Control of an Electronic-Vacuum Booster for Vehicle
Longitudinal Control,” paper in progress.
[10] Goldman, D.E., and von Gierke, H.E. Chapter 44 in
Shock and Vibration Handbook, Cyril M. Harris(ed),
McGraw-Hill Book Company, 3rd edition, 1988.
ICC vehicle speed
Preceding vehicle speed
Relative distance
Headwaytime distance
Fig. 9 Vehicle tests results
5. CONCLUSIONS
6