The invention relates to systems and methods for determining the speed of a driven wheel. Specifically, the invention determines the speed of a driven wheel using the speed of a drive shaft and the speed of a second driven wheel, and compensates for timing factors.
Vehicle systems, such as electronic stability control systems, require knowledge of the speed of each of the wheels of the vehicle. The speed of the wheels needs to be accurately determined in near real time (e.g., every 5 milliseconds). To achieve this, many modern vehicles use wheel speed sensors on each wheel with the sensors hard-wired to the control system or linked via a communication bus.
In one embodiment, the invention provides a controller. The controller includes a processor and a non-transitory computer readable medium. The processor is configured to receive the speed of a first driven wheel from a wheel speed sensor and the speed of a drive shaft from a drive shaft sensor. The non-transistory computer readable medium includes program instructions executed by the processor for determining a speed of a second driven wheel based on a plurality of detected speeds of the first driven wheel and detected speeds of the drive shaft over time.
In another embodiment the invention provides a method of determining a speed of a first wheel of a vehicle. The vehicle includes a controller, a differential, a second driven wheel, and a drive shaft. The first and second wheels are driven by the drive shaft. The method includes detecting a speed of the second driven wheel, the second driven wheel driven by the differential, detecting a speed of the drive shaft, the drive shaft driving the differential, transmitting the speed of the second driven wheel to the controller, transmitting the speed of the drive shaft to the controller, compensating for delays in transmission of the speed of the second driven wheel and the drive shaft, compensating for differences in when the speed of the second driven wheel is detected and when the speed of the drive shaft is detected, and determining a speed of the first wheel, using the speed of the second driven wheel, the speed of the drive shaft, and the compensating acts, the first wheel driven by the differential.
Other aspects of the invention will become apparent by consideration of the detailed description and accompanying drawings.
Before any embodiments of the invention are explained in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways.
The wheel speed sensors 160, 165, and 170 detect the speed of their respective wheels and communicate that speed to the controller 175. The speed can be communicated via the communication network 180 or directly (e.g., an analog signal, a PWM signal, etc.). Similarly, the drive shaft speed sensor 140 detects the speed of the drive shaft 135 and communicates that speed to the controller 175. The differential 145 is driven by the drive shaft 135 and divides the torque between the left and right rear wheels 120 and 115 such that the wheels can turn at different rates. The sum of the speeds of the left and right rear wheels 120 and 115 is two times the speed of the drive shaft 135 (assuming a one to one gear ratio). The controller 175 estimates the speed of one of the driven wheels 115 and 120 as described below (for the description below, the controller 175 estimates the speed of the left rear wheel 120).
The speed of the left rear wheel 120 can be approximated using equation 1 below. Solving for L, the determined speed of the left rear wheel, provides equation 2 below:
T=(L+R)/2 (eq. 1)
L=2T−R (eq. 2)
Determining the speed of the left rear wheel 120 using these equations is generally accurate enough for use with anti-lock braking systems which update approximately every 50 msec. However, an ESC system updates approximately every 5 msec. If the measured speeds of the right rear wheel 115 and/or the drive shaft 135 are communicated to the controller 175 via a communications network 180, the controller 175 receives the measured speeds after a delay exceeding the ESC update time. For example,
The error between actual speed of a wheel and the calculated wheel speed (e.g., due to the delays above) can be further exacerbated by differences in the update speeds of the different sensors. For example,
To improve the performance of the system, more accurate determination of the wheel speed is needed. By taking into account past conditions (versus using only the latest readings), models can be developed to accurately estimate wheel speed.
For an open differential, the speed of a driven left wheel is defined by
L(k)=2T(k)−R(k)
where:
Considering errors along with delays in the inputs for T and R, L(k) becomes L(k)=F(T(k), T(k−1) . . . R(k), R(k−1) . . . L(k), L(k−1) . . . other vehicle states) where:
The invention uses models to estimate the function F. Three methods or models are used: acceleration, Taylor Series, and drivetrain modeling. The acceleration method uses the acceleration of the left driven wheel to estimate the speed of the left driven wheel at cycle k. The following equation is used to perform the estimation:
L(k)=L(k−1)+L′(k−1)(dt)
where:
The calculations can be smoothed using a weighted average of several past cycles or a filtered value. Empirical vehicle data can also be used to limit a change in the estimated speed of the wheel to an absolute change. Acceleration can also be modeled as discussed below in relation to a drivetrain model.
A Taylor Series is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. A Taylor Series for modeling the speed of a left driven wheel takes the form:
L(k)=L(k−1)+L′(k−1)(dt)/1!+L″(k−1)(dt)2/2!
where:
Again, the calculations can be smoothed using a weighted average of several past cycles or a filtered value. Empirical vehicle data can also be used to limit a change in the estimated speed of the wheel to an absolute change.
L(k) can also be estimated using various vehicle states including applied brake torque, friction co-efficient, and load on a wheel among others. The vehicle states can be calculated using a drivetrain model.
An example drivetrain model includes models of the (1) engine and torque converter pump assembly, (2) torque converter turbine and transmission input shaft, (3) transmission output shaft and drive shaft, (4) ring gear of the open differential, (5) torque transfer from the engine to the differential, (6) drive axle torque, and (7) total drive dynamics.
An engine and torque converter pump assembly model calculates the available torque converter pump output using engine combustion torque. Neglecting the elastic and friction term, the equation of motion can be simplified as:
T
p
=T
e
−J
eωe (eq. 1)
where:
Note: elastic, friction, and damping are neglected in the equations.
A torque converter turbine and transmission input shaft model calculates the available torque at transmission input shaft using:
T
I
=T
pƒ(1/v)−JIωI (eq. 2)
where:
A transmission output shaft and drive shaft model calculates the available torque at drive shaft from:
T
d
=T
I
G
tj
−J
dωd (eq. 3)
where:
The angular acceleration has the following relation:
ωd=ωI/Gtj (eq. 3a)
The ring gear of the open differential model calculates the available torque at open differential ring gear using:
T
rg
=T
d
G
A
−J
rgωrg (eq. 4)
where:
The speed relation among ring gear, drive shaft and wheel speed is:
ωrg=ωd/GA=(ωAR+ωAL)/2 (eq. 4a)
where:
A torque transfer from engine to differential model calculates the available torque at the ring gear. The available torque at the ring gear can be described by engine combustion torque, engine rotational acceleration, and wheel rotational acceleration (a known variable).
Substituting torque equations (1), (2) and (3) into equation (4), results in:
T
rg
={[T
e
−J
eωe)ƒ(1/v)−JIωI]Gtj−Jdωd}GA−Jrgωrg (eq. 5)
Substituting speed equation (3a) and (4a) into equation 5 and simplifying it results in:
T
rg=ƒ(1/v)GtjGATe−ƒ(1/v)GtjGAJeωe−Gtj2GA2JI(ωAR+ωAL)/2−GA2Jd(ωAR+ωAL)/2−Jrg(ωAR+ωAL)/2 (eq. 5a)
where:
A drive axle torque model calculates the drive axle torque for each drive axle. For an open differential, each drive axle torque is approximately half of the ring gear torque when neglecting torque lost at the spider or similar gear.
T
AR
˜T
rg/2˜TRRwhl+TbR+JAωAR (eq. 6)
T
AL
˜T
rg/2˜FTLRwhl+TbL+JAωAL (eq. 6a)
where:
A total drive dynamics model calculates the available torque at the differential ring gear (Kardan torque):
G(1/v)GtjGATe−G(11/v)FtjGAJeωe−Gtj2GA2JI(ωAR+ωAL)/2−GA2Jd(ωAR+ωAL)/2−Jrg(ωARωAL)/2
While the torque consumed at the axle is:
FTLRwhl+TbL+JAωAL+FTRRwhl+TbR+JAωAR
Simplifying the total drive dynamics model results in:
[ƒ(1/v)GtjGA]Te−[ƒ(1/v)GtjGA]Jeωe−JA(ωAR+ωAL)˜(FTL+FTR)Rwhl+TbL+TbR
where:
Another model of the drivetrain can be represented by a linear system of the form:
x
1
=Ax+Bu (eq. 6a)
y=Cx (eq. 6b)
where:
A closed loop observer (eqs. 7a and 7b below) can be constructed to estimate the states of x. The observer estimates the state of x faster than the system operates, allowing any errors to converge to zero. By feeding errors back into the observed and actual vehicle outputs, the system corrects, driving the error to zero. Thus:
x2=Ax3+BuL(y−y1) (eq. 7a)
y1=Cx3 (eq. 7b)
where:
Combining equations 6a and 6b with 7a and 7b results in:
x
1
−x
2
=A(x−x3)−L(y−y1)
y−y
1
=C(x−x3)
The resulting error between observed and actual vehicle states (including wheel speed) is:
e=(A−LC)e1
y−y
1
=Ce
1
Because these equations have no inputs, (A−LC) can be designed to be solved for any speed. Therefore, (A−LC) is designed to decay the error to zero for initial conditions. The vector L can be obtained and used in the observer (eq. 7a) to solve for the wheel speed.
The use of the above models enables a speed of a driven wheel to be predicted accurately. This allows a wheel speed sensor to be eliminated saving costs while improving the performance of systems that use the wheel speed.
Various features and advantages of the invention are set forth in the following claims.