- Email: [email protected]
Nonlinear distance and cruise control for passenger cars
Copyright © IFAC Advances in Automotive Control, Ascona, Switzerland, 1995
Nonlinear distance and cruise control for passenger cars St. Germann and R. Isermann Technical Ulliversity of Darmstatit, Institute of Automatic COlltrol, Laboratory for Control Engineering and Process Automation, Laruigraf·Georg.Strafte 4; D-64283 Damlstadt; Germany, Telephone :0049-6151-162 1 14,e·mail:[email protected]. TH ·DARMSTADT. DE: Telefax:0049-615J-293604
Abstract: A methodology for designing an automated vehicle longitudinal velocity and distance controller is presented and applied to an automobile. Typically a vehicle is described by velocity depended dynamics and specific nonlinearities. Therefore the controller consists of a three layer structure. In the first layer a linearization of the nonlinearities is done in order to achieve a simplified structure for controller design purposes. With respect to changes in the typical vehicle parameters . mass and aerodynamical drag . an adaptive controller structure is used and these parameters are estimated by a recursive least squares algorithm. Based on classical controlling techniques a linear acceleration controller is developed in the middle layer. Up to now no mathematical equations are available describing the subjective demands of the driver and passengers during longitudinal motion. Therefore a fuzzy controller is applied in the upper layer. This controller based on the linguistic description of comfort demands. The complete structure is used in two different series fabricated vehicles and experimental results are shown for highway traffic as well as for stop-go traffic on highway congestions. Key Words: vehicle dynamics, longitudinal motion, intelligent vehicle highway systems, fuzzy logic. intelligent cruise control
1. INTRODUCTION
adapt the speed of the controlled vehicle to that of a slower vehicle ahead in order to keep an adequate distance. It is an assisting system, so the driver is free to override by braking or accelerating and an autonomous system which does not require communication for its functions. Actually it only deals with longitudinal motion and does not feature any lateral control. The functions of the intelligent cruise control are
Although the present system of roads and highways with manually operated cars and trucks has provided an excellent means of transportation, a costly expansion of system capacity will probably be required in the future to satisfy the increasing demand for transportation. As traffic has increased so has congestion and the extension of existing transportation systems is becoming impractical and undesirable. Other approaches have included expanding mass transport facilities and promoting car-pooling. But these techniques are effective only in situations where there are substantial numbers of users who have common origins, destinations and travel times. An alternative approach is to apply automation techniques to vehicles and road ways to increase the capacity and efficiency of existing facilities while retaining the advantages of individualized mobility . This is the concept of intelligent vehicle highway systems (IVHS) and of intelligent cruise control (lee) which is a substantial part of this contribution. Like no other system before lee will improve safety, comfort and efficiency by adapting speed automatically to the demands of traffic flow and by increasing the road capacity as a result of speed harmonization. Smoother driving will also reduce fuel consumption and emissions. As an extension of existing cruise control systems, lee will not necessarily keep a fixed set speed but
• Maintaining a desired speed specified by the dri ver on open roads • Adapting speed and maintaining a safe distance from preceding vehicles • Warning the driver, if there is a risk of collision All these functions must be served on a wide range of operating points starting with a standing vehicle up to a maximum speed of about 200 km/h. With respect to stability and interaction with other vehicle systems as for example automatic transmission and engine control systems a model based approach for the controller development wa~ chosen .
2. MODEL OF LONGITUDINAL MOTION Dynamic vehicle behaviour is usually described by large non-linear differential equation systems consisting of various linear and non linear submodels.
209
representing the dynamics of the whole car during longitudinal and lateral motion. However. with regard to the implementation of on-line calculations. models have to be of low order. Therefore the model for controlling the longitudinal motion of a passenger car is divided into different subsystems. The basic longitudinal motion dynamics of a vehicle is described by models of the powertrain. the brake and a mass - damper system with damping from air drag and rolling resistance. The powertrain includes the engine, the transmission with gearbox and torque converter and the wheels with rubber tyre. A block diagram of the interactions among these components is shown in Fig. 1. commanded brake pressure
commanded throttle angle
The engine model constituted for the intelligent cruise control consists of two states: • the pressure of the intake manifold • the angle velocity of the crankshaft From the mass continuity equation we get the following expression for the time derivative of the air mass streaming through the intake manifold d dt m",
(1)
where the inlet air flow is
= Arh (l-cos(a)) ~ '£I
road I envlromenl
(2)
JRTo with
if P"'>0.53
'£1=
Po
, iif
0.685
Pm
<;;
(3)
0.53
Po
and the outlet mass of the manifold is
.... or V8hIde Fig. I
(4)
Model of longitudinal dynamic consisting of different submodels
With respect to the most essential time constants, the models for the engine and the vehicle are now shortly discussed.
Differentiating the thermodynamic state equation for manifold volume and neglecting changes of temperatures leads to d - m dt m
(5)
=
With respect to equations (2) - (S) the following differential equation for the intake manifold pressure dynamics is formulated.
d
RT
Po
1
V w.,o
_ P =_m A (l-cos(a))--,¥ _ 5 mj dt m V rh fliT 4 RT m
Fig. 2
Model of the engine
VRTo
1t
m
(6) Additional process dynamics come from the fuelling rate of the engine and the mass flow rate
Models for the longitudinal vehicle dynamics with different types of engines were developed several times, see e.g. [I] - [3]. 210
of the exhaust gas . They are neglected because the complete engine system works in a lower bandwidth relative to these processes.
• Most classical control design methods are aimedat linear systems. In case of slight nonlinearities. a linear approximation can be made and linear control and analysis may be subsequently applied But with respect to the highly nonlinear vehicle dynamics and the wide range of operating points, however. simple linear methods are inadequate.
The other important subsystem is the vehicle. The longitudinal tyre force F. is equivalent to the sum of four forces acting upon the vehicle. Fig.3.
• Parameter scheduling or gain scheduling may be used in cases of moderate nonlinearities. This method is based on a linearization around many operating points and the controller is designed by fulfilling certain design requirements in each operating point. Therefore this technique is suitable for every single operating point but not for dynamical change of operating points as for example during the change of the desired velocity in cruise control.
• aerodynamical drag • rolling resistance • uphill resistance • inertia of the vehicle (including rotational parts of the poweruain ) This leads to eq. (7). where A. denotes the ratio of the inertia of the poweruain part rotating with wheel rate to the complete mass of the vehicle .
-i.
••rodynamiclll drag
FL • 112 • cw • P • A • (i.i..).
~~~ ~eo~-=: ():I
• Feedback and/or feedforward linearization can be used for a linearization of the model. But with respect to the drivers requests a linear controlled vehicle might not operate with desired comfort in all operating points.
Fill • k.- • • F•• m • i rotting r....tlne. inertia of vehde
uph" r.&iatance
F• • ",. g • oIn(.)
Fig. 3
• The most essential parameters. the complete mass of the vehicle and the aerodynamical drag ma~ change with different load situations (Fig . -i ) Therefore an adaptive structure, submitting these parameters to an estimation process, is necessarily proposed.
Longitudinal vehicle model Fig. 4
Normally A. depends on the selected gear. but tolerating small errors it can be set to a mean value .
Different payload situations for passenger cars
• The acceptance of intelligent cruise control by the driver is an essential aspect for controller design . Up to now no mathematical formulation of comfort for longitudinal motion exists . Using measured data to train artificial neural networks might be a suitable access to this problem, but this approach requires a lot of measurement data containing all different driving situations and involves a higher computation effort than other techniques .
Our complete vehicle model for the longitudinal dynamics consists of four states. the pressure of the intake manifold. the angle speed of the engine. the brake pressure and the velocity of the vehicle. Additionally. a fifth state is used in order to obtain the position of the vehicle. e.g. for distance controlling.
• A linguistic formulation for the comfon requests by the driver using fuzzy logic means a good access with less effort to nonlinear controller design . But typically the states of the vehicle are not necessarily the same variables in a linguistic formulation. This technique has also the disadvantage that the generated controller is only valid for one specific driver - vehicle - load combination .
3. CONTROLLER SELECTION Regarding to the controller design. a wide range of candidates can be chosen for this application .
211
Fuzzy dislance conlroller
It is obvious that one single controller technique can not fulfil all specifications to an intelligent cruise control. Therefore as an optimal solution a combination of feedback linearization technique with a linear acceleration controller and an additional fuzzy system is proposed, see Fig. 5.
---
Fuzzy velocity controll..r
Fig. 6
-- -l
~
~ --
layvr 11/
Fig. 5
layer 11
I
Fuzzy-logic controller
The decision which desired acceleration to use for the acceleration controller is obtained by simply comparing both (eq 8). J
Gdtm =MIN(Gdem(ve[ocity),adtm(distance)
(8)
layer I
The minimum of both accelerations is used as the demanded acceleration for the vehicle in the actual driving situation . Figure 7 shows the 3-dimensional look - up - table representation of the fuzzy velocity controller for the two input values 'actual velocity' and 'desired velocity' and the output v alue 'desired acceleration' .
Controller structure for ICC
Using the feedback linearization in the first layer we get a transfer function (acceleration of the vehicle to gas or brake) of third order for using the gaspedal as actuator and a transfer function of second order if the brake is used. A split range controller is used to decide which actuator ( the gas or the brake) has to be triggered. Additionally the gear can also be selected by this controller in order to achieve a sufficient gear behaviour and to avoid swinging of the gear shifts. Optimal load adaption is achieved by means of recursive parameter estimation. For estimation purposes a recursive least squares estimator is used ( see [4],[5] ). Based on classical controller design techniques an acceleration controller is developed in the middle layer. An additional fuzzy controller is used for the accommodation to different operating points in the upper layer. For the output value of the fuzzy controller 'demanded acceleration' was defined as a typically linguistic variable. For some driving manoeuvres the maximal tolerated jerk ( change of the acceleration ) can also be used as a linguistic variable for the acceleration controller.
fuzzy velocity amlroll"r
50
o
Fig. 7
0
Look-up-table representation tor luzzy velo(;il) controller ( no obstacle)
The fuzzy distance controller uses as input values the 'deviation between actual distance and security distance ', the 'relative velocity' and the 'air speed' The output value is the same as for the velocit) controller. In Fig. 8 the look-up-table representation of this controller for one specific true air speed is shown . If a slower vehicle ahead appears another advantage should be mentioned. Due to the controller structure this caused a change in the operation mode from velocity to distance control In classical controller techniques a crisp decision is needed if the desired velocity or the distance should be controlled .
4. FUZZY-LOGIC CONTROLLER Based on the different linguistic input variables as there are 'air speed of the vehicle', 'relative velocity between the controlled vehicle and the preceding vehicle' , 'distance' and 'velocity deviation', two fuzzy controllers - one for distance and one for cruise control - are developed . The output value of both controllers is the 'demanded acceleration'. The structure of this fuzzy controller is shown in Fig 6.
212
desired acceleration by the distance controller is still lower than the acceleration by the velocity controller. Summarizing. there is a smooth change in the demanded acceleration and the controller mode is chosen automatically by the fuzzy controller.
1-_· . . . .)
fuzzy di&tancB ccntro/ler
5. EXPERIMENTAL RESULTS The next figure shows the experimental results of the acceleration controller for a test vehicle"
Fig" 8
Look-up-table representation of fuzzy distance controller for one specific air speed
Based on the fuzzy formulation of distance and velocity a smooth change in the desired acceleration occurs if a slower vehicle ahead is detected"
~L-
__-L____L-__-L____
~
__~__________
41 _ i ~ 3c..
~
-;
iI
-:l ,:·~-·_·.: uP.~ 71: ,o:-do_wn_h ,": f;~o;-
! :1-""-""-'"-iLO-"-'-"
'-'1:1:.:-"""-""'--"-"""
---:;3;;;00:-----:;'350
tune (seC)
Fig" 10 .:-
I
1
0 - "- - , - - _. "--"-
c
desired aoc."rallOn
~
.!!
" -"~"" "
...... - . . .. -_._ ... ,- --
~-
The advantages of the described strategy for the acceleration controller with linearization and parameter adaptation are:
....
:lSMi'ed KCeleraoon
IvekXlIy cont~r)
Q
. :.I.~~~. ~~l.
-1
~
~
.20
Fig. 9
10
20
Results of acceleration controller
30
40
60 50 lime (sec)
• The technique of feedback linearization guarantees best response for the commanded acceleration.
100
Desired acceleration during merging manoeuvre
At the beginning there is no velocity deviation. Therefore the desired acceleration by the velocity controller is zero. Because no obstacle is detected the distance controller allows a acceleration of about 0 .75 m/sec 2 . The minimum of both accelerations is zero; the vehicle is in cruise control mode . At 17 sec a preceding vehicle is detected. but the distance is much greater than the air speed accompanying security distance. The demanded acceleration by the velocity controller is still lower and the vehicle is still in cruise control mode. At 30 sec. the controlled vehicle reaches the security distance. The distance controller demands a deceleration. The demanded acceleration of the velocity controller is still zero. The vehicle is now in distance controlling mode. As a result a deviation between the demanded and the actual velocity occurs. Therefore the velocity controller wants to accelerate the vehicle. But as long as there is still a vehicle ahead. the
• Concerning uphill and downhill gradients no significant difference between the commanded acceleration and the real velocity acceleration occurs . In Fig. II the results for the yelocity controller are shown" '1:\
!,
-,
!
3r- 1,
~ ~
2ct
I i
;eanrroa jl~:r-I :...:!
'..;.::J
.-
. -'
.......... - , deSired
time (seC t
Fig. II
Results of velocity controller
• The desired velocity is reached without an~ overshoot. • No difference is detected between dri \'ing on an even road and up- and downhill dri\'ing "
213
force gravitational constant rolling resistance kr mass m pressure (manifold. ambient) Pm'PO specific gas constant of air R T m,Tu temperature (manifold. ambient) vehicle speed v intake manifold volume Vm engine displacement Vs angle velocity of engine w, throttle angle ex isentropic exponent of air X uphill gradient ~
F g
• The velocity trajectories are the comfort demands of the driver. Concerning distance control, the results are shown in Fig. 12.
......... ... lime
Fig. 12
IMC'
Results of distance controller
Indices: engine: e: 0: ambient
-
m:
[N] [m/sec 2] [kg/sec] [kg] [N/m2] [- ) [K] [m/s] [m 3 ] [m 3 ] [rad/sec] [rad] [ -] [rad]
manifold:
8. REFERENCES • The actual velocity is nearly the same as the velocity of the vehicle ahead. • There is no significant difference between the demanded and the measured distance detectable. • The velocity profile matches exactly with the trajectories of a comfortable driving style.
[I] D. Cho and J.K. Hedrick, 'Automotive powertrain modelling for control. Transactions ASME Journal of Dynamic Systems'. Measurement and Control. Vol. Ill. 1989 [2] M . Mitschke; 'Fahrzeugtechnik Band A+C. Springer Verlag 1988 [3] Bosch; 'Automotive Handbook. 2. edition'. Robert Bosch GmbH 1986 [4] M. Wiirtenberger, St. Germann; 'Parameter estimation for nonlinear vehicle models', ASME Winter Annual Meeting Anaheim 1991 [5] St. Gennann, R. Isennann; 'Simulation and parameter estimation for nonlinear vehicle dynamics with MATLAB·. MATLAB Conference 1993 [6] R. Isennann, K. H. Lachmann. D . Matko; 'Adaptive Control Systems', Prentice Hall, 1992 [7] J. K . He d r i c k. D. M c M a h 0 n. et. a I . : 'Longitudinal Vehicle Colltrol/er Design jar IVHS Systems', American Control Conference . Baltimore 1994 [8] E. Bakker. L. Nyborg, H. B. Pacejka: 'Tyre modelling for use in vehicle dynamics studies' . SAE 870421, 1987 [9] R. Mayr; 'Intelligent Cruise Control for Vehicles based on Feedback Linearization' American Control Conference. Baltimore 1994 [10] B.M. Pfeiffer, R. Isermann; 'Criteri(/ tll r successful applications of Fuzzy Control' . EUFIT 1993 [11] E.H . Mamdani; 'Application of fu::::y algorithms for control of simple dynamic Plant', Proc. IEEE vol 121 1974
6. CONCLUSION A method for designing an automated vehicle longitudinal velocity and distance controller is presented and applied to an automobile. The controller consists of a three layer structure. In the first layer the typical nonlinearities as the described engine dynamics are linearized by feedback and feedforward linearization. Based on classical controlling techniques a linear acceleration controller is developed in the middle layer. A fuzzy controller was designed based on linguistic fonnulation for the desired vehicle acceleration as a function of distance, relati ve velocity, desired velocity and air speed. Experimental results are shown for highway traffic as well as for stop-go traffic on highway congestions. The implementation of this technique guarantees on the one hand side the best subjective comfort for the driver and on the other hand the possibility of adaptation to different load situations or to different types of engines with a minimum of effort.
7. NOMENCLATURA a Ath c,
vehicle acceleration throttle area aerodynamic drag coefficient
[m/sec 2] [m2 ] [kg/m]
214
Nonlinear distance and cruise control for passenger cars St. Germann and R. Isermann Technical Ulliversity of Darmstatit, Institute of Automatic COlltrol, Laboratory for Control Engineering and Process Automation, Laruigraf·Georg.Strafte 4; D-64283 Damlstadt; Germany, Telephone :0049-6151-162 1 14,e·mail:[email protected]. TH ·DARMSTADT. DE: Telefax:0049-615J-293604
Abstract: A methodology for designing an automated vehicle longitudinal velocity and distance controller is presented and applied to an automobile. Typically a vehicle is described by velocity depended dynamics and specific nonlinearities. Therefore the controller consists of a three layer structure. In the first layer a linearization of the nonlinearities is done in order to achieve a simplified structure for controller design purposes. With respect to changes in the typical vehicle parameters . mass and aerodynamical drag . an adaptive controller structure is used and these parameters are estimated by a recursive least squares algorithm. Based on classical controlling techniques a linear acceleration controller is developed in the middle layer. Up to now no mathematical equations are available describing the subjective demands of the driver and passengers during longitudinal motion. Therefore a fuzzy controller is applied in the upper layer. This controller based on the linguistic description of comfort demands. The complete structure is used in two different series fabricated vehicles and experimental results are shown for highway traffic as well as for stop-go traffic on highway congestions. Key Words: vehicle dynamics, longitudinal motion, intelligent vehicle highway systems, fuzzy logic. intelligent cruise control
1. INTRODUCTION
adapt the speed of the controlled vehicle to that of a slower vehicle ahead in order to keep an adequate distance. It is an assisting system, so the driver is free to override by braking or accelerating and an autonomous system which does not require communication for its functions. Actually it only deals with longitudinal motion and does not feature any lateral control. The functions of the intelligent cruise control are
Although the present system of roads and highways with manually operated cars and trucks has provided an excellent means of transportation, a costly expansion of system capacity will probably be required in the future to satisfy the increasing demand for transportation. As traffic has increased so has congestion and the extension of existing transportation systems is becoming impractical and undesirable. Other approaches have included expanding mass transport facilities and promoting car-pooling. But these techniques are effective only in situations where there are substantial numbers of users who have common origins, destinations and travel times. An alternative approach is to apply automation techniques to vehicles and road ways to increase the capacity and efficiency of existing facilities while retaining the advantages of individualized mobility . This is the concept of intelligent vehicle highway systems (IVHS) and of intelligent cruise control (lee) which is a substantial part of this contribution. Like no other system before lee will improve safety, comfort and efficiency by adapting speed automatically to the demands of traffic flow and by increasing the road capacity as a result of speed harmonization. Smoother driving will also reduce fuel consumption and emissions. As an extension of existing cruise control systems, lee will not necessarily keep a fixed set speed but
• Maintaining a desired speed specified by the dri ver on open roads • Adapting speed and maintaining a safe distance from preceding vehicles • Warning the driver, if there is a risk of collision All these functions must be served on a wide range of operating points starting with a standing vehicle up to a maximum speed of about 200 km/h. With respect to stability and interaction with other vehicle systems as for example automatic transmission and engine control systems a model based approach for the controller development wa~ chosen .
2. MODEL OF LONGITUDINAL MOTION Dynamic vehicle behaviour is usually described by large non-linear differential equation systems consisting of various linear and non linear submodels.
209
representing the dynamics of the whole car during longitudinal and lateral motion. However. with regard to the implementation of on-line calculations. models have to be of low order. Therefore the model for controlling the longitudinal motion of a passenger car is divided into different subsystems. The basic longitudinal motion dynamics of a vehicle is described by models of the powertrain. the brake and a mass - damper system with damping from air drag and rolling resistance. The powertrain includes the engine, the transmission with gearbox and torque converter and the wheels with rubber tyre. A block diagram of the interactions among these components is shown in Fig. 1. commanded brake pressure
commanded throttle angle
The engine model constituted for the intelligent cruise control consists of two states: • the pressure of the intake manifold • the angle velocity of the crankshaft From the mass continuity equation we get the following expression for the time derivative of the air mass streaming through the intake manifold d dt m",
(1)
where the inlet air flow is
= Arh (l-cos(a)) ~ '£I
road I envlromenl
(2)
JRTo with
if P"'>0.53
'£1=
Po
, iif
0.685
Pm
<;;
(3)
0.53
Po
and the outlet mass of the manifold is
.... or V8hIde Fig. I
(4)
Model of longitudinal dynamic consisting of different submodels
With respect to the most essential time constants, the models for the engine and the vehicle are now shortly discussed.
Differentiating the thermodynamic state equation for manifold volume and neglecting changes of temperatures leads to d - m dt m
(5)
=
With respect to equations (2) - (S) the following differential equation for the intake manifold pressure dynamics is formulated.
d
RT
Po
1
V w.,o
_ P =_m A (l-cos(a))--,¥ _ 5 mj dt m V rh fliT 4 RT m
Fig. 2
Model of the engine
VRTo
1t
m
(6) Additional process dynamics come from the fuelling rate of the engine and the mass flow rate
Models for the longitudinal vehicle dynamics with different types of engines were developed several times, see e.g. [I] - [3]. 210
of the exhaust gas . They are neglected because the complete engine system works in a lower bandwidth relative to these processes.
• Most classical control design methods are aimedat linear systems. In case of slight nonlinearities. a linear approximation can be made and linear control and analysis may be subsequently applied But with respect to the highly nonlinear vehicle dynamics and the wide range of operating points, however. simple linear methods are inadequate.
The other important subsystem is the vehicle. The longitudinal tyre force F. is equivalent to the sum of four forces acting upon the vehicle. Fig.3.
• Parameter scheduling or gain scheduling may be used in cases of moderate nonlinearities. This method is based on a linearization around many operating points and the controller is designed by fulfilling certain design requirements in each operating point. Therefore this technique is suitable for every single operating point but not for dynamical change of operating points as for example during the change of the desired velocity in cruise control.
• aerodynamical drag • rolling resistance • uphill resistance • inertia of the vehicle (including rotational parts of the poweruain ) This leads to eq. (7). where A. denotes the ratio of the inertia of the poweruain part rotating with wheel rate to the complete mass of the vehicle .
-i.
••rodynamiclll drag
FL • 112 • cw • P • A • (i.i..).
~~~ ~eo~-=: ():I
• Feedback and/or feedforward linearization can be used for a linearization of the model. But with respect to the drivers requests a linear controlled vehicle might not operate with desired comfort in all operating points.
Fill • k.- • • F•• m • i rotting r....tlne. inertia of vehde
uph" r.&iatance
F• • ",. g • oIn(.)
Fig. 3
• The most essential parameters. the complete mass of the vehicle and the aerodynamical drag ma~ change with different load situations (Fig . -i ) Therefore an adaptive structure, submitting these parameters to an estimation process, is necessarily proposed.
Longitudinal vehicle model Fig. 4
Normally A. depends on the selected gear. but tolerating small errors it can be set to a mean value .
Different payload situations for passenger cars
• The acceptance of intelligent cruise control by the driver is an essential aspect for controller design . Up to now no mathematical formulation of comfort for longitudinal motion exists . Using measured data to train artificial neural networks might be a suitable access to this problem, but this approach requires a lot of measurement data containing all different driving situations and involves a higher computation effort than other techniques .
Our complete vehicle model for the longitudinal dynamics consists of four states. the pressure of the intake manifold. the angle speed of the engine. the brake pressure and the velocity of the vehicle. Additionally. a fifth state is used in order to obtain the position of the vehicle. e.g. for distance controlling.
• A linguistic formulation for the comfon requests by the driver using fuzzy logic means a good access with less effort to nonlinear controller design . But typically the states of the vehicle are not necessarily the same variables in a linguistic formulation. This technique has also the disadvantage that the generated controller is only valid for one specific driver - vehicle - load combination .
3. CONTROLLER SELECTION Regarding to the controller design. a wide range of candidates can be chosen for this application .
211
Fuzzy dislance conlroller
It is obvious that one single controller technique can not fulfil all specifications to an intelligent cruise control. Therefore as an optimal solution a combination of feedback linearization technique with a linear acceleration controller and an additional fuzzy system is proposed, see Fig. 5.
---
Fuzzy velocity controll..r
Fig. 6
-- -l
~
~ --
layvr 11/
Fig. 5
layer 11
I
Fuzzy-logic controller
The decision which desired acceleration to use for the acceleration controller is obtained by simply comparing both (eq 8). J
Gdtm =MIN(Gdem(ve[ocity),adtm(distance)
(8)
layer I
The minimum of both accelerations is used as the demanded acceleration for the vehicle in the actual driving situation . Figure 7 shows the 3-dimensional look - up - table representation of the fuzzy velocity controller for the two input values 'actual velocity' and 'desired velocity' and the output v alue 'desired acceleration' .
Controller structure for ICC
Using the feedback linearization in the first layer we get a transfer function (acceleration of the vehicle to gas or brake) of third order for using the gaspedal as actuator and a transfer function of second order if the brake is used. A split range controller is used to decide which actuator ( the gas or the brake) has to be triggered. Additionally the gear can also be selected by this controller in order to achieve a sufficient gear behaviour and to avoid swinging of the gear shifts. Optimal load adaption is achieved by means of recursive parameter estimation. For estimation purposes a recursive least squares estimator is used ( see [4],[5] ). Based on classical controller design techniques an acceleration controller is developed in the middle layer. An additional fuzzy controller is used for the accommodation to different operating points in the upper layer. For the output value of the fuzzy controller 'demanded acceleration' was defined as a typically linguistic variable. For some driving manoeuvres the maximal tolerated jerk ( change of the acceleration ) can also be used as a linguistic variable for the acceleration controller.
fuzzy velocity amlroll"r
50
o
Fig. 7
0
Look-up-table representation tor luzzy velo(;il) controller ( no obstacle)
The fuzzy distance controller uses as input values the 'deviation between actual distance and security distance ', the 'relative velocity' and the 'air speed' The output value is the same as for the velocit) controller. In Fig. 8 the look-up-table representation of this controller for one specific true air speed is shown . If a slower vehicle ahead appears another advantage should be mentioned. Due to the controller structure this caused a change in the operation mode from velocity to distance control In classical controller techniques a crisp decision is needed if the desired velocity or the distance should be controlled .
4. FUZZY-LOGIC CONTROLLER Based on the different linguistic input variables as there are 'air speed of the vehicle', 'relative velocity between the controlled vehicle and the preceding vehicle' , 'distance' and 'velocity deviation', two fuzzy controllers - one for distance and one for cruise control - are developed . The output value of both controllers is the 'demanded acceleration'. The structure of this fuzzy controller is shown in Fig 6.
212
desired acceleration by the distance controller is still lower than the acceleration by the velocity controller. Summarizing. there is a smooth change in the demanded acceleration and the controller mode is chosen automatically by the fuzzy controller.
1-_· . . . .)
fuzzy di&tancB ccntro/ler
5. EXPERIMENTAL RESULTS The next figure shows the experimental results of the acceleration controller for a test vehicle"
Fig" 8
Look-up-table representation of fuzzy distance controller for one specific air speed
Based on the fuzzy formulation of distance and velocity a smooth change in the desired acceleration occurs if a slower vehicle ahead is detected"
~L-
__-L____L-__-L____
~
__~__________
41 _ i ~ 3c..
~
-;
iI
-:l ,:·~-·_·.: uP.~ 71: ,o:-do_wn_h ,": f;~o;-
! :1-""-""-'"-iLO-"-'-"
'-'1:1:.:-"""-""'--"-"""
---:;3;;;00:-----:;'350
tune (seC)
Fig" 10 .:-
I
1
0 - "- - , - - _. "--"-
c
desired aoc."rallOn
~
.!!
" -"~"" "
...... - . . .. -_._ ... ,- --
~-
The advantages of the described strategy for the acceleration controller with linearization and parameter adaptation are:
....
:lSMi'ed KCeleraoon
IvekXlIy cont~r)
Q
. :.I.~~~. ~~l.
-1
~
~
.20
Fig. 9
10
20
Results of acceleration controller
30
40
60 50 lime (sec)
• The technique of feedback linearization guarantees best response for the commanded acceleration.
100
Desired acceleration during merging manoeuvre
At the beginning there is no velocity deviation. Therefore the desired acceleration by the velocity controller is zero. Because no obstacle is detected the distance controller allows a acceleration of about 0 .75 m/sec 2 . The minimum of both accelerations is zero; the vehicle is in cruise control mode . At 17 sec a preceding vehicle is detected. but the distance is much greater than the air speed accompanying security distance. The demanded acceleration by the velocity controller is still lower and the vehicle is still in cruise control mode. At 30 sec. the controlled vehicle reaches the security distance. The distance controller demands a deceleration. The demanded acceleration of the velocity controller is still zero. The vehicle is now in distance controlling mode. As a result a deviation between the demanded and the actual velocity occurs. Therefore the velocity controller wants to accelerate the vehicle. But as long as there is still a vehicle ahead. the
• Concerning uphill and downhill gradients no significant difference between the commanded acceleration and the real velocity acceleration occurs . In Fig. II the results for the yelocity controller are shown" '1:\
!,
-,
!
3r- 1,
~ ~
2ct
I i
;eanrroa jl~:r-I :...:!
'..;.::J
.-
. -'
.......... - , deSired
time (seC t
Fig. II
Results of velocity controller
• The desired velocity is reached without an~ overshoot. • No difference is detected between dri \'ing on an even road and up- and downhill dri\'ing "
213
force gravitational constant rolling resistance kr mass m pressure (manifold. ambient) Pm'PO specific gas constant of air R T m,Tu temperature (manifold. ambient) vehicle speed v intake manifold volume Vm engine displacement Vs angle velocity of engine w, throttle angle ex isentropic exponent of air X uphill gradient ~
F g
• The velocity trajectories are the comfort demands of the driver. Concerning distance control, the results are shown in Fig. 12.
......... ... lime
Fig. 12
IMC'
Results of distance controller
Indices: engine: e: 0: ambient
-
m:
[N] [m/sec 2] [kg/sec] [kg] [N/m2] [- ) [K] [m/s] [m 3 ] [m 3 ] [rad/sec] [rad] [ -] [rad]
manifold:
8. REFERENCES • The actual velocity is nearly the same as the velocity of the vehicle ahead. • There is no significant difference between the demanded and the measured distance detectable. • The velocity profile matches exactly with the trajectories of a comfortable driving style.
[I] D. Cho and J.K. Hedrick, 'Automotive powertrain modelling for control. Transactions ASME Journal of Dynamic Systems'. Measurement and Control. Vol. Ill. 1989 [2] M . Mitschke; 'Fahrzeugtechnik Band A+C. Springer Verlag 1988 [3] Bosch; 'Automotive Handbook. 2. edition'. Robert Bosch GmbH 1986 [4] M. Wiirtenberger, St. Germann; 'Parameter estimation for nonlinear vehicle models', ASME Winter Annual Meeting Anaheim 1991 [5] St. Gennann, R. Isennann; 'Simulation and parameter estimation for nonlinear vehicle dynamics with MATLAB·. MATLAB Conference 1993 [6] R. Isennann, K. H. Lachmann. D . Matko; 'Adaptive Control Systems', Prentice Hall, 1992 [7] J. K . He d r i c k. D. M c M a h 0 n. et. a I . : 'Longitudinal Vehicle Colltrol/er Design jar IVHS Systems', American Control Conference . Baltimore 1994 [8] E. Bakker. L. Nyborg, H. B. Pacejka: 'Tyre modelling for use in vehicle dynamics studies' . SAE 870421, 1987 [9] R. Mayr; 'Intelligent Cruise Control for Vehicles based on Feedback Linearization' American Control Conference. Baltimore 1994 [10] B.M. Pfeiffer, R. Isermann; 'Criteri(/ tll r successful applications of Fuzzy Control' . EUFIT 1993 [11] E.H . Mamdani; 'Application of fu::::y algorithms for control of simple dynamic Plant', Proc. IEEE vol 121 1974
6. CONCLUSION A method for designing an automated vehicle longitudinal velocity and distance controller is presented and applied to an automobile. The controller consists of a three layer structure. In the first layer the typical nonlinearities as the described engine dynamics are linearized by feedback and feedforward linearization. Based on classical controlling techniques a linear acceleration controller is developed in the middle layer. A fuzzy controller was designed based on linguistic fonnulation for the desired vehicle acceleration as a function of distance, relati ve velocity, desired velocity and air speed. Experimental results are shown for highway traffic as well as for stop-go traffic on highway congestions. The implementation of this technique guarantees on the one hand side the best subjective comfort for the driver and on the other hand the possibility of adaptation to different load situations or to different types of engines with a minimum of effort.
7. NOMENCLATURA a Ath c,
vehicle acceleration throttle area aerodynamic drag coefficient
[m/sec 2] [m2 ] [kg/m]
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