Patent Application
20170225688
The present description relates to techniques for designing virtual sensors of at least a variable affecting the vehicle dynamics, able to give in real time reliable estimates of the variables of interest using data measured from Electronic Stability Control systems or other devices typically available in production cars and heavy vehicles.
These techniques are in particular directed to estimate the side slip angle of the vehicle and/or the lateral and longitudinal velocity and/or the tire-road friction coefficient. Obtaining in real-time on production vehicles reliable estimates of these variables may allow the design of stability, traction and braking control systems achieving significant performance improvements over the present one.
Many methods have been proposed in past years on the technical problem object of the present invention, i.e. the estimation of variables affecting the vehicle dynamics (e.g. the sideslip angle), whose direct measurement requires the use of sensors which are too complex and/or expensive for their use in production vehicles. All these methods are based on a two-step procedure: first, a suitable model of the vehicle (the model including for instance dynamic or kinematic equations with given degree of freedom) is derived; then, a suitable estimation algorithms (which can be based, among others, on the Kalman Filter, or the Sliding Mode Observer, or the Moving Horizon Estimator, or the Particle Filters), is designed on the base of the derived model and implemented on an electronic board for estimating in real-time the variable of interest (e.g. sideslip angle), using the data available from the ESC system or other vehicle devices (e.g. signals pertaining steering angle, wheel velocities, yaw rate, lateral acceleration, . . . ).
These two-step methods suffer from severe drawbacks, which are synthetically described as follows. The estimation algorithms operate on identified models which are only approximate description of the real vehicle dynamic behaviour. Even if a very accurate model could be obtained, finding optimal estimates (e.g. minimal variance) is computationally intractable when the identified model is nonlinear, and computationally tractable but necessarily approximate methods are then used. Due to the approximations in the modelling and estimation steps, no methods exist for evaluating how accurate the two-step methods may be. Even the boundedness of estimation error is not easily achieved for complex systems. Even more relevant, the vehicle models are depending on parameters that may change according to different operational conditions (dry or wet road, tyre wear status, car load . . . ) whose real-time values are not detected in normal production vehicles. Due to these problems (model and estimation approximations, variable operational conditions), none of the above discussed methods appears to have reached the capability of designing estimation algorithms for sideslip angle, longitudinal and lateral velocities, tire-road friction coefficient, achieving acceptable estimation accuracies. This is also evidenced by the fact that no estimator of these variables, designed with these methods, has been made available on commercial vehicles.
An object of one or more embodiments is to overcome the limitations inherent in the solutions achievable from the prior art.
According to one or more embodiments, that object is achieved thanks to a method for estimating a variable affecting the vehicle dynamics having the characteristics specified in claim 1. One or more embodiments may refer to a corresponding system, to a virtual sensor module, to a vehicle equipped with such a system or virtual sensor module, as well as to a computer-program product that can be loaded into the memory of at least one computer and comprises parts of software code that are able to execute the steps of the method when the product is run on at least one computer. As used herein, reference to such a computer program product is understood as being equivalent to reference to a computer-readable means containing instructions for controlling the processing system in order to co-ordinate implementation of the method according to the embodiments. Reference to “at least one computer” is evidently intended to highlight the possibility of the present embodiments being implemented in modular and/or distributed form. The at least one computer can be for example, at the level of a electronic control board of the vehicle or a so-called Electronic Control Unit (ECU) comprising portions of software code for implementing the aforesaid method.
The claims form an integral part of the technical teaching provided herein in relation to the various embodiments.
According to the solution described herein, the method includes
calculating the estimate of the at least a variable by an estimation procedure comprising
the optimal non linear regression function being obtained by an offline optimal calculation procedure including:
In various embodiments, the measured variables acquired from a testing vehicle and/or from a vehicle simulator include steering angle, lateral acceleration, four wheel speeds, yaw rate, longitudinal acceleration and the operation of acquiring a set of reference data includes acquiring data relating to said measured variables and to lateral and longitudinal velocities, the latter being obtained from specific sensors operating on a test vehicle and/or from a vehicle simulator.
In various embodiments the set of reference data is acquired by testing on a test vehicle and/or by a simulator of the vehicle.
In various embodiments, the operation of obtaining a non linear regression function includes, given the functions belonging to a class of functions with given fading memory, finding the function in such class which minimizes the maximum over a measuring time interval of the module of the difference of said function, calculated over a vector of data of the measured variables at previous instants of time, with the arc tangent of the ratio of lateral to longitudinal velocity, assigning said found function as non linear regression function to obtain said estimation.
In various embodiments the sideslip angle is calculated as a function of the estimates of the lateral velocity and of the longitudinal velocity, in particular the arc tangent of their ratio, the estimate of longitudinal velocity being obtained as an optimal non linear regression function calculated on the basis of subset of said set of measured variables pertaining to the longitudinal velocity, said subset including data relating to steering angle, four wheel speeds and longitudinal acceleration, the estimate of lateral velocity being obtained as a optimal non linear regression function calculated on a basis of a further subset of the set of measured variables including lateral acceleration and yaw rate, and the estimate of longitudinal velocity previously obtained.
In various embodiments, a sensor for the estimation of at least a variable affecting a vehicle dynamics is implemented on a processing module and configured to calculate the estimate of the at least a variable describing the motion dynamic of a vehicle taking in account said set of dynamic variables measured during the motion of the vehicle and applying to said set of measured dynamic variables at least an optimal non linear regression function to obtain said estimate, said optimal non linear regression function being obtained according to the method of any of the previous embodiments.
In various embodiments, the sensor has a processing module comprised in the Electronic Control Unit or in a electronic control board of the vehicle.
In various embodiments, the sensor receives the set of dynamic variables measured during the motion of the vehicle from a module configured to measure dynamic variables of the vehicle which comprises an ESC (Electronic Stability Control) system.
In various embodiments, the sensor is integrated in a system for the estimation of at least a variable affecting a vehicle dynamics, including said module configured to measure dynamic variables of the vehicle during its motion
and said processing module configured to calculate in real time an estimate of the at least a variable affecting a vehicle dynamics on the basis of such measured dynamic variables.
The embodiments will now be described purely by way of a non-limiting example with reference to the annexed drawings, in which:
The ensuing description illustrates various specific details aimed at an in-depth understanding of the embodiments. The embodiments may be implemented without one or more of the specific details, or with other methods, components, materials, etc. In other cases, known structures, materials, or operations are not illustrated or described in detail so that various aspects of the embodiments will not be obscured.
Reference to “an embodiment” or “one embodiment” in the framework of the present description is meant to indicate that a particular configuration, structure, or characteristic described in relation to the embodiment is comprised in at least one embodiment. Likewise, phrases such as “in an embodiment” or “in one embodiment”, that may be present in various points of the present description, do not necessarily refer to the one and the same embodiment. Furthermore, particular conformations, structures, or characteristics can be combined appropriately in one or more embodiments.
The references used herein are intended merely for convenience and hence do not define the sphere of protection or the scope of the embodiments.
In
With the numerical reference 10 is indicated a block representing a vehicle to which is associated a sideslip angle β to be measured. An ESC system 12, or another system of the vehicle controlling the stability of the vehicle 10 on the basis of the measurement of the value of variables of the vehicle 10 during its motion, measures, in way known per se, the following measured variables MQ of the vehicle 10, during its motion: steering angle α, lateral acceleration ay, four wheel speeds ws, yaw rate {dot over (ψ)}, longitudinal acceleration ax. As mentioned, these are the variables basically measured by an ESC system and the method here described operates on real time preferably on the basis of only such variables measured by the ESC 12. Such variables MQ are fed to a sideslip angle virtual sensor module 11, which, on the basis of such variables supplies in real time an estimate {circumflex over (β)} of the sideslip angle β of the vehicle 10.
The virtual sensor 11 implements a procedure DVSβ for the estimation of a variable affecting the motion of a vehicle, in particular in this case the sideslip angle, which is designed by the method sketched in
The reference data set Dd is then passed to a operation 220 of design of the virtual sensor DVSβ which in step 230 is then implemented in a software module 11. This module, embedded in an ECU available on vehicle 10, receiving in real time only the signal, pertaining to measured variables MQ, i.e. [ay, ws, {dot over (ψ)}, α], measured by the vehicle Electronic Stability Control 12, supplies in real-time an estimate {circumflex over (β)} of the sideslip angle β.
In the embodiment here described the set of reference sampled data Dd is the following:
D
d
={a
y(t),ws(t),{dot over (ψ)}(t),ax(t),α(t),νx(t),νy(t)t=Δt, . . . ,N*Δt} (1)
With t is indicated the time instant of the acquisition, varying from Δt to N*Δt, where Δt is the sampling time and N is the number of acquired samples. For the sake of notational simplicity in the following a sampling time Δt=1 is considered. This reference data set Dd may include experimental data typically measured on a testing vehicle, in particular a car or a heavy vehicle, for evaluating the dynamic performances of the vehicle under consideration, in particular data of the variables used by the known two-step methods for building and testing the vehicle model. Such reference data, or part of this reference data, can be however also acquired not by direct measurement, but by simulation: if a reliable simulator of the vehicle is available, the data of the reference data set Dd of equation (1) can be generated by such simulator. In both cases, such data of the reference data set Dd have to be related to driving tests, either executed or simulated, which are performed within given ranges for speed, braking, road-tire friction condition, car load, driving style and other parameters, defining different operational conditions OC of the vehicle 10, which are in particular the operational conditions of interest.
As per equation (1), the reference data set Dd includes acquired reference data [ay, ws, {dot over (ψ)}, ax, α] corresponding to the variables MQ measured on the vehicle 10 during the vehicle motion, supplied by the ESC system 12 to the virtual sensor 11, i.e. steering angle α, lateral acceleration ay, four wheel speeds ws, yaw rate {dot over (ψ)}, longitudinal acceleration ax. However, the reference data set Dd includes also further acquired reference data pertaining to longitudinal and lateral velocity vx and vy. These longitudinal and lateral velocity vx and vy data can be preferably provided by the vehicle simulator, in order to keep the measuring equipment necessary for the off-line design of virtual sensor 11 to a minimum. However, in case that the reference data set Dd is obtained from measurements on a testing vehicle, these data can be provided by laboratory optical or inertial plus GPS sensors, in a way known per se. The longitudinal and lateral velocity vx and vy data are used only in the definition, or design, of the estimation procedure DVSβ implemented by the virtual sensor 11 and are not needed for the real time estimation.
It is here described in general a solution for the estimation of a variable affecting the vehicle dynamics. Although the embodiments described in the following are directed mainly to obtain an estimate of sideslip angle, in some of these embodiments the method here described can be exploited to estimate other variables of interest in describing the motion of a vehicle, without necessarily obtaining also the sideslip angle.
The embodiments of the solution here described are in general based on the realization of a virtual sensor DVSβ as a discrete-time nonlinear regression equation of the form:
β(t+1)=ƒβ(rβ(t)) (2)
r
β(t)=ay(t), . . . ,ay(t−ny),ws(t), . . . ,ws(t−nw),{dot over (ψ)}(t), . . . ,{dot over (ψ)}(t−nψ),ax(t), . . . ,ax(t−nx),α(t), . . . ,α(t−nα)
i.e. given a time t at which the variables MQ are measured, the estimated sideslip angle {circumflex over (β)} at subsequent time instant t+1 is obtained by the value of a nonlinear regression function ƒβ evaluated at the argument vector rβ(t) which is a vector of variables acquired from the ESC system 12 of vehicle 10, measured over respective intervals of time ny, nw, nψ, nx and nα which are given integers. Such intervals of time ny, nw, nψ, nx and nα define the memory of the virtual sensor DVSp and can be set as different one with respect to the other.
The operation 220 of designing the virtual sensor DVSβ is obtained by finding a function ƒβ which is solution of the following E-Robust Design Problem: making use of the data contained in the set of reference data Dd and of information on their measurement accuracy, i.e. each measured value is considered with its measurement accuracy or error, find, for a desired accuracy level ε, a regression function ƒp giving an estimation error bounded as |β(t)−{circumflex over (β)}(t)|≦ε, i.e. the module of the difference between the sideslip angle β and its estimate {circumflex over (β)} is lower or equal than a desired accuracy level E for any time t, for the whole ranges of operational conditions OC of interest (the operation conditions OC can include, among others, road-tire friction, car load, tire status), the test vehicle or simulator undergoing such operational conditions OC to obtain the data set 0, at step 210.
Three embodiment examples are here presented.
In the first embodiment, leading to a virtual sensor indicated as DVS0, the offline operation 220 is related to finding a regression function ƒβ* solution of the following optimization problem:
ƒβ*=arg mimaxt=m, . . . ,T|arctan(νy(t)/νx(t))−ƒ(rβ(t−1)| (3)
where the data contained in the reference data set Dd are used for computing the right end side of (3).
is a class of functions with given fading memory defined as:
i.e. the functions ƒ of class respect the Lipschitz condition for each time t. The constant of the Lipschitz condition is a product of parameters γ, ρ to the k-th power, where 0≦y<∞, 0≦ρ<∞, and k varies from 1 to m, where m=max[ny, nw, nψ, nx, nα], i.e. the maximum interval among the different interval of measurement of the variables MQ.
Recalling that by definition the sideslip angle is β(t)=arctan(νy(t)/νx(t) and {circumflex over (β)}(t)=ƒβ(rβ(t−1)), see equation (2), it follows that the regression function ƒβ* solution of (3) is found as the function ƒ in said class of fading memory functions which minimizes the maximum estimation error |β(t)−{circumflex over (β)}(t)| for any time instant t and for the whole ranges of operational conditions OC of interest (dry/wet road or road-tire friction coefficient, vehicle load, tyre status, etc.) accounted for in the experimental conditions used to acquire the reference data set Dd.
The values of ρ and m in equations (3) and (4) are design parameter of the estimation procedure DVSβ: the larger are selected, the lower is the estimation error ε that can be achieved, but the larger is the transient response time of the estimate {circumflex over (β)}.
The value of parameter γ can be selected operating on the reference data Dd according to step 5b of the procedure described in section D of the paper C. Novara, F. Ruiz, M. Milanese, “Direct Filtering: A New Approach to Optimal Filter Design for Nonlinear Systems”, IEEE Trans. on Automatic Control, 58, pp. 89-99, 2013.
In section II.D of the same paper, a method for solving the optimization problem (3) is described.
Finally, let ε* be computed as:
ε=maxt=m, . . . ,T|arctan(νy(t)/νx(t))−ƒβ*(rβ(t−1)| (5)
where the data contained in the reference data set Dd are used for computing the right end side of (5).
The errors of the estimation procedure DVSβ described by the function ƒβ* are bounded as |β(t)−{circumflex over (β)}*(t)|≦ε* for all times t and the whole ranges of operational conditions OC included in the data set Dd. Then, if ε*≦ε, the derived virtual sensor DVSβ is a solution to the E-Robust Design Problem.
All the computation from (3) to (5) are performed by offline operation 220, using the data contained in the reference data set Dd.
The virtual sensor implementing this embodiment in real-time on the vehicle, represented by 11 in
where the values of ay, ws, ax, {dot over (ψ)}, α at the required times are acquired from the ESC module 12 and ƒβ* is the regression function computed offline as solution of (3).
Thus, the first embodiment regards a method for the estimation of at least a variable, which is in the embodiment the sideslip angle β, affecting the vehicle 10 dynamics, including measuring variables MQ, of the vehicle 10 during its motion, calculating in real time an estimate β* of said variable represented by the sideslip angle β on the basis of such measured variables MQ, performing the step 230 of calculating the estimate of the sideslip angle β by an estimation procedure, DVSβ, comprising taking in account a set of variables MQ, i.e. the vector rβ(t) of variables acquired from the ESC system 12, measured during the motion of the vehicle 10 over respective time intervals ny, nw, nψ, nx, nα and applying on such set of measured variables an optimal non linear regression function ƒβ* calculated with respect to such sideslip angle β to obtain such estimation, said optimal non linear regression function ƒβ* being obtained by an offline optimal calculation procedure, i.e. operation 220, including: on the basis of an acquired set of reference data Dd, finding, for a desired accuracy level ε, a regression function ƒβ giving an estimation error lower or equal than said desired accuracy level ε in a given set of operative conditions OC, the acquired set of reference data Dd being obtained by an operation 210 of acquiring in said given set of operative conditions OC a set of reference data Dd of variables including variables corresponding to said measured variables MQ of the vehicle 10 and a lateral velocity vy and a longitudinal velocity vx of the vehicle 10.
A second embodiment, leading to a virtual sensor of the vehicle sideslip angle, indicated as DVSβν, is based on the design of two virtual sensors of the longitudinal velocity νx and lateral velocity νy, indicated as DVSvx and DVSvy, respectively.
These two virtual sensors are designed by the offline operation 220, making use of reference data Dd, as follows:
νx*(t)=ƒx*(rx(t−1)) (7)
r
x(t−1)=ws(t−1), . . . ,ws(t−nw−1),ax(t−1), . . . ,ax(t−nx−1),α(t−1), . . . ,α(t−nα−1)
rx is a vector composed by a subset of the measured variables MQ, i.e. the four wheels speed w, longitudinal acceleration ax, and steering angle α. In various embodiments other choices for the subset composing vector rx are possible.
ƒx*: is the solution of the optimization problem:
ƒx*=arg mimaxt=m, . . . ,T|νx(t)−ƒ(rx(t−1)| (8)
where the data contained in the reference data set Dd are used for computing the right end side of (8).
The ƒx* solution of the above optimization problem gives estimates νx*(t) of longitudinal velocity νx(t) which minimize the maximum estimation error |νx(t)−νx*(t)| for any t and for the whole ranges of operational conditions OC of interest (dry/wet road, vehicle load, tyre status, etc.) accounted for in the experimental conditions used to acquire the reference data set Dd.
νy*(t)=ƒy*(ry(t−1)) (9)
r
y(t−1)=ay(t−1), . . . ,ay(t−ny−1),{dot over (ψ)}(t−1), . . . ,{dot over (ψ)}(t−nψ−1),νx*(t−1), . . . ,νx*(t−nx−1)
ry is a vector composed by a subset of the measured variables MQ, i.e. the lateral acceleration ay, yaw rate {dot over (ψ)}, with the addition of the estimate of the longitudinal velocity νx* obtained from (7) and (8). In various embodiments other choices for the subset composing vector ry are possible.
ƒy* is the solution of the optimization problem:
ƒy*=arg mimaxt=m, . . . ,T|νy(t)−ƒ(ry(t−1)| (10)
where the data contained in the reference data set Dd are used for computing the right end side of (10).
The ƒy* solution of the above optimization problem gives estimates νy*(t) of longitudinal velocity νy(t) which minimize the maximum estimation error |νy(t)−νt*(t)| for any t and for the whole ranges of operational conditions OC of interest (dry/wet road, tyre status, etc.) accounted for in the experimental conditions used to acquire the reference data set Dd
βν*(t)=arctan(νy*(t)/νx*(t))
i.e. as the arc tangent of the ratio of the optimal estimate νy* for the lateral velocity vy over the optimal estimate νx* of the longitudinal velocity vx.
ε2*=maxt=m, . . . ,T|arctan(νy(t)/νx(t))−arctan(νy*(t)/νx*(t))
where the data contained in the reference data set Dd are used for computing the right end side of (11).
This quantity provides a bound on the estimation errors of the virtual sensor DVSβν designed according this second embodiment, i.e. |β(t)−{circumflex over (β)}ν*(t)|≦ε* for all times t and the whole ranges of operational conditions OC included in the data set Dd. Then, if ε*≦ε, the derived estimation procedure DVSs, is a solution to the ε-Robust Design Problem. The ƒx* and ƒx* solutions of the optimization problems (8) and (10) can be obtained by using the algorithm described in the previously cited Novara-Ruiz-Milanese paper.
All computations from (7) to (11) are performed by offline operation 220, using the data contained in the reference data set Dd as described above.
The virtual sensor DVSβν implementing this embodiment in real-time on the vehicle, represented by 11 in
νx*(t)=ƒx*(ws(t−1), . . . ,ws(t−nw−1), . . . ,ax(t−1), . . . ,ax(t−nx−1),α(t−1), . . . ,α(t−nα−1)) (12)
where the values of ws, ax, α at the required times are acquired online from the ESC module 12 and ƒx* is the regression function computed offline as solution of (8).
νy*(t)=ƒy*(ay(t−1), . . . ,ay(t−ny−1),{dot over (ψ)}(t−1), . . . ,{dot over (ψ)}(t−nψ−1),νx*(t−1), . . . ,νx*(t−nx−1)) (13)
where the values of ay, {dot over (ψ)} at the required times are acquired online from the ESC module 12, the values of νx* at the required times are the optimal estimates of the longitudinal velocities computed online from (12), and ƒy* is the regression function computed offline as solution of (10).
βν*(t)=arctan(νy*(t)/νx*(t)) (14)
where νy*(t) and νx*(t) are the optimal estimates previously computed via (12) and (13).
This second embodiment, in addition to give a virtual sensor DVSβν of sideslip angle β that may be more accurate than given by the first embodiment virtual sensor DVSβ, provides also the virtual sensors DVSvx and DVSvy, giving estimates of vehicle longitudinal and lateral velocities, respectively. Note that obtaining reliable estimates of these variables represents a relevant technical aspect per se, being the knowledge of νx(t) and νy(t) of great value for optimizing traction and braking control systems, collision avoidance systems, etc.
Since the computation of (12) and (13) giving the estimates of lateral velocity νy*(t) and longitudinal velocity νx*(t) occur before the calculation of equation (14) estimating the sideslip angle {circumflex over (β)}ν*, it is possible by the second embodiment here described to design virtual sensors DVSvx and DVSvy estimating only lateral velocity and/or longitudinal velocity, without necessarily estimating also the sideslip angle.
A third embodiment of the method, leading to the design of a virtual sensor of sideslip angle indicated as DVSβμ, envisage, at step 210, to operate a partition of the reference data set Dd in a number L of reference subsets Dd1, Dd2, . . . , DdL. Each one of said subsets identified by a determined operational condition of interest in said given set of operation conditions OC, contains data acquired for a same value (or values range) of such operational condition of interest. In the embodiment here described it is considered that the partition is performed according to the road-tire friction coefficients μ1, μ2, . . . , μL, which can be considered as the most relevant operational condition OC affecting vehicle dynamics. For the sake of exposition simplicity, partition in L=2 subsets is considered, but the method can be easily extended to larger values of L, as shown below. Assuming that in the reference data set Dd the data for t=1, . . . , M are acquired with friction coefficient μ≅μ1, and for t=M+1, . . . , N are acquired with μ≅μ2, the two reference subsets are:
D
d1
={a
y(t),ws(t),{dot over (ψ)}(t),ax(t),α(t),νx(t),νy(t)t=1, . . . ,M}
D
d2
={a
y(t),ws(t),{dot over (ψ)}(t),ax(t),α(t),νx(t),νy(t)t=M+1, . . . ,N} (15)
After such partition step, in the offline operation 220 the following estimators are evaluated, by finding functions which are solution of a E-Robust Design Problem, i.e.:
β1*(t+1)=ƒβ1*(rβ(t))
where rβ(t) is given in equation (2) and ƒβ1* is the solution of the following optimization problem:
ƒβ1*=arg mimaxt=m, . . . ,T|arctan(νy(t)/νx(t))−ƒ(rβ(t−1)| (16)
where the data contained in the first reference data set Dd1 are used for computing the right end side of (16).
β2*(t+1)=ƒβ2*(rβ(t))
where ƒβ2* is the solution of the following optimization problem:
ƒβ2=arg mimaxm−M+1+m, . . . ,N|arctan(νy(t)/νx(t))−ƒ(t−1)| (17)
where the data contained in the second reference data set Dd2 are used for computing the right end side of (17).
{dot over (ψ)}1*(t+1)=ƒ{dot over (ψ)}1*(r{dot over (ψ)}(t))
where r{dot over (ψ)}(t)=ws(t), . . . , ws(t−nw), ay(t), . . . , ay(t−ny),α(t), . . . , α(t−nα), is a vector composed by a subset of the measured variables MQ, i.e. the four wheels speed ws, lateral acceleration ay, and steering angle α and ƒ{dot over (ψ)}1* is the solution of the optimization problem:
ƒ{dot over (ψ)}1*=arg mimaxt=m, . . . ,M|{dot over (ψ)}(t)−ƒ(rψ(t−1)| (18)
where the data contained in the first reference data set Dd1 are used for computing the right end side of (18).
{dot over (ψ)}2*(t+1)=ƒ{dot over (ψ)}2*(r{dot over (ψ)}(t))
where ƒ{dot over (ψ)}2* is the solution of the following optimization problem:
ƒ{dot over (ψ)}2*=arg mimaxt=M+1+m, . . . ,N|{dot over (ψ)}(t)−ƒ(rψ(t−1)| (19)
where the data contained in the second reference data set Dd2 are used for computing the right end side of (19).
All computations from (16) to (19) are performed by offline operation 220, using the data contained in the reference data sets Dd1 and Dd2 as described above. The ƒ* solutions of the optimization problems (16), (17), (18), (19) can be obtained by using the algorithm described in the previously cited Novara-Ruiz-Milanese paper.
The virtual sensor implementing this embodiment in real-time on the vehicle, represented by 11 in
where the values of ws, ay, α at the required times are acquired from the ESC module 12 and ƒ{dot over (ψ)}1* and ƒ{dot over (ψ)}2* are the regression functions computed offline in (18) and (19), corresponding to consider that the actual operating condition is μ=μ1 or μ=μ2, respectively.
λ*(t)=arg min0≦λ≦1|{dot over (ψ)}(t)−λ{dot over (ψ)}1*(t)−(1−λ{dot over (ψ)}2*(t)| (22)
i.e. given the absolute value of the difference between the yaw rate {dot over (ψ)}(t) at current time t, measured in real-time at the ESC module 12, and a linear combination of the first yaw rate estimate {dot over (ψ)}1*(t) and second yaw rate estimate {dot over (ψ)}2*(t) having coefficients function of a parameter λ, finding the value of the parameter λ, comprised among 0 and 1, minimizing such difference. This optimization problem can be efficiently solved online using known linear search methods.
where the values of ay, ws, ax, {dot over (ψ)}, α at the required times are acquired from the ESC module 12 and ƒβ1*, and ƒβ2* are the regression functions computed offline in (16) and (17), corresponding to consider that the actual operating condition is μ=μ1 or μ=μ2, respectively.
βμ*(t)=λ*(t)β1*(t)−(1−λ*(t))β2*(t) (25)
i.e. as a linear combination of the first and second estimate of the sideslip angle having as coefficient functions of the optimal parameter λ*, namely the optimal parameter λ* and the negative value of its complement to one.
Thus the third embodiment just described obtains the estimate βμ* of the sideslip angle β, through the estimation of the yaw rate. The rationale of this embodiment is as follows.
Equations (20) and (21) define two virtual sensors which give estimates in real-time of the yaw rate.
However, the yaw rate needs not to be estimated, since it is actually measured in real-time by the ESC system 12. The yaw rate estimates are indeed exploited to detect in real-time the value of the tire-road friction coefficient μ, making use of the optimal parameter λ*, obtained as solution of the optimization problem (22) by comparing the two yaw rate estimates with the value actually measured by the ESC system 12.
If the vehicle 10 is operating, for example, on a road with actual friction coefficient μ1, then the first yaw rate estimate {dot over (ψ)}1*(t), being ƒ{dot over (ψ)}1* designed from data measured in conditions of same friction coefficient μ1, see (18), gives more accurate estimates than the second yaw rate estimate {dot over (ψ)}2*(t), being ƒ{dot over (ψ)}2* designed for a friction coefficient μ2, see (19), different from the actual one. Consequently, the solution of optimization problem (22) leads to λ*=1, thus detecting that actually the vehicle 10 is operating with friction coefficient μ1. Then, from equation (25), the sideslip estimate βμ*(t)=β1*(t) is provided. As can be seen from equations (16) and (25), the estimate β1*(t) of the sideslip angle is obtained by the virtual sensor described by regression function ƒβ1* that minimizes the estimation error for the operational condition μ1. Thus, this estimate, which exploits the partition of the reference data according to the μ values, achieves better (or at most equal) accuracy than achievable from the virtual sensor DVSβ of the first embodiment and the virtual sensor DVSβν of the second embodiment which, not detecting in real-time the value of the tire-road friction coefficient, need to balance their estimation performances for the range of p values the data set Dd account for.
Besides the above discussed estimation accuracy improvement over virtual sensors DVSβ and DVSβν, a further interesting feature of this third virtual sensor DVSβμ is that this third embodiment allows to obtain a virtual sensor, indicated as DVSμ, providing in real-time an estimate μ*(t) of the tire-road friction coefficient μ(t) at current time t, computed as follows:
μ*(t)=λ*(t)μ1(t)−(1−λ*(t))μ2(t) (26)
The estimation in real-time of the tire-road friction coefficient represents a relevant technical aspect per se. This information is indeed of relevant value for many vehicle dynamics problems, e.g. traction and braking control, vehicle dynamic control, collision avoidance, etc., but at present it is not made available on normal production vehicles. The design of the virtual sensor DVSμ for estimating only the tire-road friction coefficient requires the offline solutions only of optimization problems (18) and (19) and the online execution only of operations (20), (21), (22) and (26)).
As mentioned, the operations just described for partition in L=2 subsets, can be easily extended to larger values of the number L of reference subsets. In the offline operation 220 L functions ηβ1*, . . . , ƒβL* and L ƒ{dot over (ψ)}1*, . . . , ƒ{dot over (ψ)}L* are computed from L equations similar to equations (16), (17) and (18), (19), each one based on the corresponding reference subsets Dd1, Dd2, . . . , DdL. The virtual sensor 11 operating in real-time on the vehicle, at the current time t, computes L estimates {dot over (ψ)}1*(t), . . . , {dot over (ψ)}L*(t) of the yaw rate {dot over (ψ)}(t), obtained by L equations similar to equations (20), (21) and L estimates β1*(t), . . . , βL*(t) of the sideslip angle β(t), obtained by L equations similar to equations (23), (24). The yaw rate estimates are used in a vectorial version of equation (22) to determine the value of a vector Λ* of positive coefficients having sum one, minimizing the difference between the yaw rate {dot over (ψ)}(t), and a linear combination of such estimates {dot over (ψ)}1*(t), . . . , {dot over (ψ)}L*(t), having as coefficients the components of said vector Λ*. Finally the sideslip angle is obtained using a vectorial version of equation (25), i.e. a linear combination of sideslip estimates β1*(t), . . . , βL*(t), having as coefficients the components of said vector Λ*
The current embodiment has been illustrated with reference to the yaw rate as specific example of a variable {dot over (ψ)}) whose value is measured in real time on the vehicle (10) and depends on a condition of interest, e.g the road-friction coefficient μ, to be estimated.
It is clear however that the operations described with reference to the third embodiments can more in general used for detecting the real time value of an operational condition of interest OC on the basis of said vector Λ* of coefficients,
partitioning the reference data set Dd in a plurality L of reference subsets Dd1, Dd2, . . . , DdL according to the value of an operational condition of interest in the given set of operation conditions OC,
obtaining a plurality of estimate, corresponding to said reference subsets (Dd1, Dd2, . . . , DdL), of a variable affecting the vehicle dynamics, whose value is measured in real-time on the vehicle 10 and depends on said condition of interest OC, by said operation 220 of obtaining an optimal non linear regression function;
obtaining the vector Λ* of coefficients solution of an optimization problem minimizing the difference between the measured variable and a linear combination of such estimates of the variable affecting the vehicle dynamics having the coefficients determined by said vector of coefficients.
The solution according to the various embodiments here described allows to obtain the following advantages.
The method and virtual sensors according to the various embodiments here described allows to obtain the real-time estimation of the variables of interest which, at difference from the methods of prior art, allows implementation in normal production vehicles. In particular, the method is computationally tractable, and it allows to guarantee the estimation accuracy that can be achieved in different operational conditions a production vehicle has to operate (e.g. road-tire friction coefficient, load, tyre status), whose real-time values are not detected in production vehicles.
Of course, without prejudice to the principle of the embodiments, the details of construction and the embodiments may vary widely with respect to what has been described and illustrated herein purely by way of example, without thereby departing from the scope of the present embodiments, as defined the ensuing claims.
Although the solution is described with reference to variables measured by an ESC system, the solution can be implemented using also other measurements available in real time on the vehicle.
The solution described and claimed here are developed with particular attention to the estimation of vehicle sideslip angle, longitudinal and lateral velocities, tire-road friction coefficients, which are relevant variables for automotive safety systems related to monitoring and control of vehicle stability, steering, traction and braking. Reference to these particular variables is not, however, to be understood as in any way limiting the embodiments, which are in themselves applicable also to other vehicle dynamic variables, e.g. vertical and roll variables, relevant for suspension control systems; variables relevant in fields different from the automotive one, e.g. attitude estimation in aerospace and marine vehicles.
| Number | Date | Country | Kind |
|---|---|---|---|
| TO2014A000631 | Aug 2014 | IT | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/IB2015/055895 | 8/3/2015 | WO | 00 |
