DE10215464B9 - Method and apparatus for estimating a state variable - Google Patents

Abstract

...Method for determining an estimated value β 1 of a non-directly measurable slip angle β in vehicles, the slip angle β being describable at least by a non-linear differential equation comprising a solution β _{nl of} the non-linear differential equation by numerical integration,
a driving state described at least by the slip angle is modeled in a working point by a linear or linearized differential equation of 1st order,
wherein a value β _{lin is} determined by solving the linear or linear differential equation, and
for determining the floating angle estimated value β 1, the solution β _{nl is} linked to the determined value β _lin by a fusion,
wherein the fusion comprises a weighted addition of the values β _{i of} the slip angle:

...

Description

The invention relates to a method and an apparatus for estimating a state variable that can be described by a non-linear differential equation.

A large number of methods for improving the driving dynamics of a vehicle require the slip angle as the control and / or parameter value. However, the slip angle can be measured and / or determined directly only with great technical effort. Depending on the measured quantities, the slip angle can be described by a non-linear differential equation. It is known to observe the slip angle by a method of state quantity estimation. This example, from the DE 40 30 653 A1 known method is based on a Kalman-Bucy filter.

For the design of a Kalman-Bucy filter, a linearization of the nonlinear differential equation by one operating point is necessary. The lateral dynamics of a vehicle, however, has a strong non-linear behavior, which is dependent on external boundary conditions such as the road characteristics and / or the driving condition. Strong deviations from the operating point chosen for the design of the Kalman-Bucy filter can therefore lead to numerical instability in the observer equations obtained by linearization.

It is known to counter these numerical problems by a robust design and / or an adaptation of the observer term. The disadvantage, however, is that such a design reacts only slowly to changing properties. In particular, highly dynamic phenomena such as incipient vehicle instability, for example due to a change in the road surface, can not be sufficiently detected with such an observer.

From the post-published DE 102 12 582 A1 a method for controlling the driving dynamics is known in which a first calculation of a slip angle β _lin by solving a linear or linear differential equation of the first order and a second calculation of the slip angle β _nl by a direct integration, wherein a resulting slip angle by a suitable fusion method, preferably via a weighted addition. The weighting factors can be adapted for the specific vehicle type. In this case, the adaptation of the method to the vehicle type can take place via driving tests.

bestimmt, die mittels einer linearen Differentialgleichung erster Ordnung gegeben ist. Als zweite Schwimmwinkelgeschwindigkeit wird eine aus einem Beobachterfahrzeugmodell stammende Größe für die Schwimmwinkelgeschwindigkeit β ._Obs bestimmt. Das Beobachterfahrzeugmodell beruht hierbei ebenfalls auf linearen Differentialgleichungen erster Ordnung.From the DE 195 15 046 A1 A system for driving stability control is known wherein a slip angle is estimated by integrating an addition of two predetermined slip angle velocities. This is a so-called kinematic float angle velocity

determined by a first-order linear differential equation. As the second float angular velocity, a magnitude for the slip angle velocity β derived from an observer model of the vehicle becomes. _Obs definitely. The observer vehicle model is also based on first order linear differential equations.

From the DE 100 59 030 A1 An apparatus for estimating a vehicle side slip angle is known, wherein a first vehicle side slip angle estimator S1 for estimating a vehicle side slip angle and a second vehicle slip angle estimator S2 for estimating a vehicle side slip angle are provided based on a vehicle speed, vehicle lateral acceleration, yaw rate, and steering angle, and also a vehicle motion model. At this time, in accordance with a result of a determination of a tire load determining means TR, between the estimation of the vehicle side slip angle by the first estimator S1 and the second estimator S2 is changed.

From the EP 0 970 876 A2 It is known that a first slip angle is determined by integrating a slip angular velocity, the slip angular velocity being determined by a non-linear 4-wheel motion model of the vehicle. A second slip angle is determined based on a linear 2-wheel motion model of the vehicle. Further, it is disclosed that either the second slip angle or the first slip angle is selected by means of a selector, and the second slip angle is used when a running state is a state in which the vehicle is traveling straight at a low speed. The first float angle is selected when the vehicle is in other driving conditions.

From the EP 0 615 892 A2 It is known that an approximate value for a slip angle is determined based on front wheel control information and motion information. Further, based on a neural network, a correction value is determined by which the approximate value is corrected.

The invention is therefore the technical problem of providing a method and an apparatus for the reliable determination of the slip angle in vehicles without restrictions on the permissible range, wherein the slip angle is given in dependence on measured variables by a non-linear differential equation.

The solution to the problem results from the objects with the features of claims 1 and 9. Further advantageous embodiments emerge from the subclaims.

A determination of an estimated value β 1 of the non-directly measurable slip angle β in vehicles, wherein the slip angle β is describable at least by a nonlinear differential equation, comprises a solution β _{nl of} the nonlinear differential equation by numerical integration, a modeling of the driving state described at least by the slip angle in one Operating point by a linear or linearized differential equation 1st order, a calculation of a value β _lin by solving the linear or linearized differential equation and a fusion of the solution β _nl at least with the determined value β _lin for determining the Schwimmwinkelschätzwertes β ^.

A linear or linearized differential equation can be solved analytically by known methods. Within the framework of the modeling accuracy of the linearization, the state quantity can thus be determined exactly. In contrast, a nonlinear differential equation can only be solved by numerical integration. The usual numerical integration methods solve the equation of motion by a piecewise approximation of the solution with polynomials of higher order. Due to inaccuracies, for example from modeling, measurement noise and / or numerical boundary conditions, such as computer accuracies, the value of the state variable obtained by a numerical integration of the differential equation deviates from an exact solution. When integrated over a longer period of time, these deviations add up. For a numerical integration numerical problems like drift and / or numerical instabilities have to be considered. The choice of the integrator decisively determines the numerical stability and / or necessary calculation times. Preferably, an integrator according to the Runge-Kutta method 3./2. Used order.

A fusion of the resulting values of the state variable to an estimated value makes it possible to make targeted use of the advantages of the respective investigation paths. The validity is not limited to an operating point defined by the linearization, but depending on the vehicle condition and / or the boundary conditions, the respectively suitable method is selected. If possible, the determination of the state quantity is done by using the linear model. The use of the linear model is advantageous over direct integration, for example, in terms of numerical stability.

In this case, the validity of the linear or linearized model is evaluated by an error e, wherein at least one weighting w _{i is determined} for an addition of the values of the state variables β _i as a function of the error e. In the area of validity of the model, the values of the state variable z _lin calculated using the linear differential equation are to be preferred to the values from the numerical integration. In the case of strong deviations of the framework conditions underlying a modeling, however, a validity of the linear or linearized differential equation is no longer given. In this case, the state variables are to be determined via direct integration.

In a preferred embodiment, the linear one-track model is used for the formulation of the linear differential equation. For a variety of vehicle dynamics problems, the linear one-track model is suitable for determining the yaw rate ψ. and the float angle β determined vehicle state z _lin = (β _lin ψ. _lin ) ^T as a function of manipulated variables u such as a steering intervention u = δ to determine. The complexity of the linear Einspurmodells is arbitrary selectable, so for example, depending on the application, non-linear tire effects are negligible or to consider.

In another embodiment, vehicle speed v, lateral and longitudinal acceleration a _x , a _y and the yaw rate ψ. directly accessible measured quantities.

The fusion of the ascertained values of the state variable into an estimated value preferably takes place via a weighted addition. However, other fusion methods, for example using statistical methods or by means of or fuzzy logic are conceivable.

In another embodiment, the error e is defined by the deviation of a directly measurable measured variable y from its calculated value y _lin : e = y - y _lin where y _{lin is} a measurement equation y _lin = Cz _lin is calculable.

In order to minimize the influence of measurement inaccuracies and / or measurement noise, it is advantageous to filter the detected error e.

In a preferred embodiment, the non-linear differential equation is extended by a state-dependent feedback. As a result of the feedback, the value β _nl obtained by numerical integration is "filtered" by the value β _lin calculated using the linear or linearized differential equation and thus counteracts the numerical problems of the integration: β. _nl = f (β _nl , t) + H (β _lin - β _nl )

The choice of the feedback gain H has a significant influence on the quality of the direct integration. In a preferred embodiment, the gain depends on the validity of the linear or linear differential equation: H = H (e).

In the range of validity of the linear or linearized model, a good match of the values y _lin obtained by solving the linear differential equation and the associated measured values y is given. Confidence in the quantities β _lin obtained on the basis of the linear model is therefore also correspondingly high. Any deviations of the value β _nl obtained by integration from this value β _lin are therefore evaluated errors in the direct integration, for example due to numerical problems, and a corresponding "filtering" of the values is carried out. Outside the scope of the linear model, there are large deviations e. Confidence in the quantities β _lin obtained from the linear model is correspondingly low. Β variations of the integral _nl from the calculated by the linear model value β _lin therefore have only an infinitesimal impact on the numerical integration.

In a further embodiment, the function values for the filter H = H (e) are adapted by tests on the vehicle under different Fahrzustands- and / or different boundary conditions. Influence on the functional values, in addition to the driving state, has specific characteristics typical of the vehicle and / or the characteristics of the road, for example due to a wet or icy road condition and / or due to a special road surface. The values are stored in the form of tables and thus accessible to the status observer during vehicle operation.

For adaptation of the filter values, besides other such tuning by road tests, other methods are also conceivable, for example the use of learning algorithms or an optimization by simulation calculation and / or combinations.

Preferably, first the filter values H are determined by driving tests. In a further step, the weighting factors w for the specific vehicle type are adapted by driving tests. Instead of adaptation by driving test other methods, such as the use of learning algorithms or adaptation methods are conceivable.

The invention is described below with reference to a preferred embodiment. The pictures show:

1 : schematic representation of a linear one-track model

2 : Block diagram of a swimming angle observer

1 shows a linear Einspurmodell a vehicle with front axle steering, with wheels of the front axle to a wheel 1 and wheels of the rear axle on a wheel 2 are reduced. The center of gravity S of the vehicle is the origin of an xyz coordinate system. x ₁ , x ₂ are the distances of the wheels 1 . 2 from the center of gravity S. Actuating action variable for a front-axle steering is a steering angle δ ₁ to Rad 1 , The angle between the vehicle's longitudinal axis 3 and the direction of the vehicle speed v is the slip angle β. The movement about the vertical vehicle axis z is due to the yaw rate ψ. described. The slip angles at the wheels 1 . 2 are thus

For the slip angle between the wheel position and the direction of travel applies at steering intervention on the front axle: α ₁ = β - δ ₁ , α ₂ = β ₂

In vehicle transverse direction y, the lateral forces F ₁ and F ₂ engage the wheels. The forces F ₁ and F ₂ are determined via a skew stiffness c _{α, i} and the slip angle α _i : F _i = c _{α, i} α _i

dabei ist J_z das Massenträgheitsmoment um die z-Achse und m die Masse des Fahrzeugs.The linear differential equation for the in 1 illustrated linear one-track model without consideration of non-linear tire effects and / or effects of a non-linear steering ratio is:

where J _{z is} the mass moment of inertia about the z axis and m is the mass of the vehicle.

2 shows the block diagram of a Schwimmwinkelbeobachter. Comprehensive one arithmetic unit 5 for a calculation of a float angle value β _nl by a numerical integration, a computing unit 6 , for the determination of a floating angle value β _lin by solving a linear differential equation, and a computing unit 7 , for a fusion of the float angle value β _nl with the calculated float angle value β _lin to an estimated value β ^. The computing units can be executed either as separate modules or as a single module.

The determination of the linear float angle value β _lin is carried out using the in 1 shown single track model using the equation (1). If further effects are to be considered in the determination, then the equation should be extended accordingly. Conceivable, for example, extensions to non-linear tire models and / or a non-linear steering ratio. The equation (1) is analytically solvable by known methods. The arithmetic unit 6 be at least the measured and / or determined values of the vehicle speed v, the yaw rate ψ as input data. and the steering engagement δ supplied. Output variables are the linear floating angle value β _lin and an error e. The error e is the deviation of the in the arithmetic unit 5 calculated value ψ. _lin from a reading ψ.: e = ψ. - ψ. _lin

The arithmetic unit 6 At least the measured and / or determined values of the vehicle speed v, the transverse and longitudinal acceleration a _y , a _x and the yaw rate ψ. fed. The nonlinear relationship between the slip angle β and these measurands is given by the following nonlinear differential equation:

The arithmetic unit 5 In addition, the calculated float angle value β _lin and the error e are supplied. The determination is made by numerical integration of the equation

The driving state-dependent feedback depends on the validity of the linear model. Where: | E | → ∞ ⇒ H (e) = 0, e → 0 ⇒ H (e) → H _max

In a computing unit 7 the separately determined values of the slip angle β _lin , β _{nl are combined} to form a common estimated value β 1. The fusion of the determined slip angle values to a float angle estimate is done by a weighted addition: β 1 = wβ _lin + (1-w) β _nl

The weight depends on the validity of the linear model and is therefore chosen such that: e → 0 ⇒ w = 1, | E | → ∞ ⇒ w = 0

By the method and / or the device, a reliable determination of the float angle and the float angle velocity is given. There is no restriction on a permissible range. The estimation method thus serves as the basis for arbitrary control algorithms for improving the driving dynamics.

By means of the estimation method, arbitrary state variables can be determined which, depending on directly determinable quantities, can be described at least by a non-linear differential equation. By linearization in one operating point, an associated linearized differential equation can be determined.

Claims (16)

Method for determining an estimated value β 1 of a non-directly measurable slip angle β in vehicles, wherein the slip angle β is describable at least by a non-linear differential equation comprising a solution β _{nl of} the non-linear differential equation by numerical integration, a driving state described at least by the slip angle at an operating point is modeled by a linear or linear differential equation of the first order, wherein a value β _{lin is} determined by solving the linear or linear differential equation, and to determine the Schwimmwinkelschätzwertes β ^ the solution β _{nl is} at least linked to the determined value β _lin by a merger wherein the fusion comprises a weighted addition of the values β _{i of} the slip angle:

characterized in that the validity of the linear or linearized differential equation is evaluated by an error e and at least one weight w _i for an addition of the values of the state variables β _{i is determined} as a function of the error e. A method according to claim 1, characterized in that a linear single-track model is used for the formulation of the linear differential equation. A method according to claim 2, characterized in that at least the vehicle speed v, the transverse and longitudinal acceleration a _y , a _x and the yaw rate ψ. directly accessible measurands are. Method according to one of Claims 1 to 3, characterized in that the error e is determined on the basis of the deviation between a directly measurable variable y and a quantity y _lin calculated using the linear or linearized differential equation: e = y-y _lin . Method according to one of the preceding claims, characterized in that the value of the error e is filtered. Method according to one of the preceding claims, characterized in that the nonlinear differential equation for the numerical integration is expanded by a state-dependent feedback: β. _nl = f (β _nl , t) + H (β _lin - β _nl ) A method according to claim 6, characterized in that the gain for the state-dependent feedback H is dependent on the error e. A method according to claim 6 or 7, characterized in that the values of the weight w _i and the gain H are determined by driving tests. Device for determining an estimated value β 1 of a non-directly measurable slip angle β in vehicles, the slip angle β being describable at least by a non-linear differential equation comprising a computing unit ( 5 ) to the solution β _{nl of} the non-linear differential equation by numerical integration, wherein a driving state described at least by the slip angle can be modeled in an operating point by a linear or linearized differential equation of 1st order, in a computing unit ( 6 ) a value β _{lin can be} determined by solving the linear or linearized differential equation, and in a computing unit ( 7 ) of the Schwimmwinkelschätzwertes β ^ can be determined by a fusion of the solution β _nl with at least the determined value β _lin , wherein the arithmetic unit ( 7 ) comprises a weighted addition of the determined values β _i :

characterized in that in the arithmetic unit ( 6 ) the validity of the linear or linearized differential equation can be evaluated by an error e and in the arithmetic unit ( 7 ) at least one weight w _i for an addition of the values β _i as a function of the error e can be determined. Apparatus according to claim 9, characterized in that a linear single-track model is used for the formulation of the linear differential equation. Apparatus according to claim 10, characterized in that at least the vehicle speed v, the transverse and longitudinal acceleration a _y , a _x and the yaw rate ψ by sensor and / or computing units. can be determined directly. Device according to one of claims 9 to 11, characterized in that in the arithmetic unit ( 6 ) the error e can be determined on the basis of the deviation between a directly measurable quantity y and a quantity y _lin calculated using the linear or linearized differential equation: e = y - y _lin . Device according to one of claims 9 to 12, characterized in that the arithmetic unit ( 6 ) includes a filter of error e. Device according to one of claims 9 to 13, characterized in that the non-linear differential equation for the numerical integration in the arithmetic unit ( 5 ) is expandable by a state-dependent feedback: β. _nl = f (β _nl , t) + H (β _lin - β _nl ) Apparatus according to claim 14, characterized in that the gain for the state-dependent feedback H is dependent on the error e. Apparatus according to claim 14 or 15, characterized in that the values of the weight w _i and the gain H can be determined by driving tests.

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