Model-Based Predictive Regulation of an Electric Machine in a Drivetrain of a Motor Vehicle

Abstract

A processor unit (3) is configured for executing an MPC algorithm (13) for model predictive control of an electric machine (8) of a drive train (7) of a motor vehicle (1). The MPC algorithm (13) includes a longitudinal dynamic model (14) of the drive train (7) and a cost function (15) to be minimized. The cost function (15) includes a first term, a second term, and a third term. The processor unit (3) is configured for determining an input variable for the electric machine (8) by executing the MPC algorithm (13) as a function of the first, second, and third terms such that the cost function is minimized.

Claims

1-11: (canceled)

12. A system for model predictive control of an electric machine (8) of a drive train (7) of a motor vehicle (1), comprising: a processor unit (3) configured for executing an MPC algorithm (13) for model predictive control of an electric machine (8) of a drive train (7) of a motor vehicle (1), the MPC algorithm (13) comprising a longitudinal dynamic model (14) of the drive train (7) and a cost function (15) to be minimized, the cost function (15) comprising, as a first term, an electrical energy weighted with a first weighting factor and predicted according to the longitudinal dynamic model (14), which is provided within a prediction horizon by a battery (9) of the drive train (7) for driving the electric machine (8), as a second term, a driving time weighted with a second weighting factor and predicted according to the longitudinal dynamic model (14), which the motor vehicle (1) requires to cover an entire distance predicted within the prediction horizon, and as a third term with a third weighting factor, a value predicted according to the longitudinal dynamic model (4) of a torque that the electric machine (8) provides for driving the motor vehicle (1), wherein the processor unit (3) is configured for determining an input variable for the electric machine (8) by executing the MPC algorithm (13) as a function of the first term, as a function of the second term, and as a function of the third term such that the cost function (15) is minimized.

13. The processor unit (3) of claim 12, wherein the cost function (15) comprises: an energy consumption final value weighted with the first weighting factor, which the predicted electrical energy assumes at an end of the prediction horizon; and a driving time final value weighted with the second weighting factor, which the predicted driving time assumes at the end of the prediction horizon.

14. The processor unit (3) of claim 12, wherein: the third term comprises a first value, weighted with the third weighting factor, of a torque that the electric machine (8) provides for driving the motor vehicle (1) to a first waypoint within the prediction horizon, which is predicted according to the longitudinal dynamic model (14); the third term comprises a zeroth value, weighted with the third weighting value, of a torque that the electric machine (8) provides for driving the motor vehicle (1) to a zeroth waypoint, which is situated directly ahead of the first waypoint; and in the cost function (15), the zeroth value of the torque is subtracted from the first value of the torque.

15. The processor unit (3) of claim 12, wherein: the cost function (15) comprises a fourth term having a fourth weighting factor; the fourth term comprises a gradient of the torque predicted according to the longitudinal dynamic model (14); and the processor unit (3) is configured for determining the input variable for the electric machine (8) by executing the MPC algorithm (13) as a function of the first term, as a function of the second term, as a function of the third term, and as a function of the fourth term such that the cost function (15) is minimized.

16. The processor unit (3) of claim 15, wherein the fourth term comprises a quadratic deviation of the gradient of the torque, which has been multiplied by the fourth weighting factor and summed.

17. The processor unit (3) of claim 15, wherein: the cost function (15) comprises, as a fifth term, a slack variable weighted with a fifth weighting factor; and the processor unit (3) is configured for determining the input variable for the electric machine (8) by executing the MPC algorithm (13) as a function of the first term, as a function of the second term, as a function of the third term, as a function of the fourth term, and as a function of the fifth term such that the cost function (15) is minimized.

18. The processor unit (3) of claim 12, wherein a tractive force of the electric machine (8) is limited via a delimitation of a characteristic map of the electric machine (8).

19. A motor vehicle (3), comprising: a driver assistance system (16); and a drive train (7) with an electric machine (8), wherein the driver assistance system (16) is configured for accessing an input variable for the electric machine (8) via a communication interface, the input variable determined by the processor unit (3) of claim 12, and controlling, by way of an open-loop system, the electric machine (8) based on the input variable.

20. A method for model predictive control of an electric machine (8) of a drive train (7) of a motor vehicle (1), the method comprising: executing an MPC algorithm (13) for model predictive control of an electric machine (8) of a drive train (7) of a motor vehicle (1) by processor unit (3), wherein the MPC algorithm (13) comprises includes a longitudinal dynamic model (14) of the drive train (7) and a cost function (15) to be minimized, and wherein the cost function (15) comprises, as a first term, an electrical energy weighted with a first weighting factor and predicted according to the longitudinal dynamic model (14), which is provided within a prediction horizon by a battery (9) of the drive train (7) for driving the electric machine (8), as a second term, a driving time weighted with a second weighting factor and predicted according to the longitudinal dynamic model (14), which the motor vehicle (1) requires needs to cover an entire distance predicted within the prediction horizon, and as a third term with a third weighting factor, a value predicted according to the longitudinal dynamic model (14) of a torque that the electric machine (8) provides for driving the motor vehicle (1); and determining an input variable for the electric machine (8) as a function of the first term, as a function of the second term, and as a function of the third term by executing the MPC algorithm (13) by the processor unit (3) such that the cost function (15) is minimized.

21. A computer program product (11) for model predictive control of an electric machine (8) of a drive train (7) of a motor vehicle (1), the computer program product (11), when executed on a processor unit (3), instructs the processor unit (3) to: execute an MPC algorithm (13) for model predictive control of an electric machine (8) of a drive train (7) of a motor vehicle (1), wherein the MPC algorithm (13) comprises a longitudinal dynamic model (14) of the drive train (7) and a cost function (15) to be minimized, wherein the cost function (15) comprises, as a first term, an electrical energy weighted with a first weighting factor and predicted according to the longitudinal dynamic model (14), which is provided within a prediction horizon by a battery (9) of the drive train (7) for driving the electric machine (8), as a second term, a driving time weighted with a second weighting factor and predicted according to the longitudinal dynamic model (14), which the motor vehicle (1) requires to cover an entire distance predicted within the prediction horizon; and as a third term with a third weighting factor, a value predicted according to the longitudinal dynamic model (14) of a torque that the electric machine (8) provides for driving the motor vehicle (1); and determine an input variable for the electric machine (8) by executing the MPC algorithm (13) as a function of the first term, as a function of the second term, and as a function of the third term such that the cost function (15) is minimized.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Exemplary embodiments of the invention are explained in greater detail in the following with reference to the diagrammatic drawings, wherein identical or similar elements are labeled with the same reference characters, wherein

[0031] FIG. 1 shows a side view of a vehicle including a drive train, which includes an electric machine and a battery,

[0032] FIG. 2 shows a characteristic map of an electric machine for the vehicle according to FIG. 1,

[0033] FIG. 3 shows a diagram, which shows the torque of the electric machine for the vehicle according to FIG. 1 with respect to the kinetic energy, and

[0034] FIG. 4 shows a diagram, which shows an acceleration of the vehicle according to FIG. 1 with respect to the speed.

DETAILED DESCRIPTION

[0035] Reference will now be made to embodiments of the invention, one or more examples of which are shown in the drawings. Each embodiment is provided by way of explanation of the invention, and not as a limitation of the invention. For example, features illustrated or described as part of one embodiment can be combined with another embodiment to yield still another embodiment. It is intended that the present invention include these and other modifications and variations to the embodiments described herein.

[0036] FIG. 1 shows a motor vehicle 1, for example, a passenger car. The motor vehicle 1 includes a system 2 for the model predictive control of an electric machine of a drive train of the motor vehicle 1. The system 2 in the exemplary embodiment shown includes a processor unit 3, a memory unit 4, a communication interface 5, and a detection unit 6 for detecting state data related to the motor vehicle 1. The motor vehicle 1 also includes a drive train 7, which can include, for example, an electric machine 8, which can be operated as a motor and as a generator, a battery 9, and a transmission 10. The electric machine 8, in the motor mode, can drive wheels of the motor vehicle 1 via the transmission 10, which can have, for example, a constant ratio. The battery 9 can provide the electrical energy necessary therefor. The battery 9 can be charged by the electric machine 8 when the electric machine 8 is operated in the generator mode (recuperation). Optionally, the battery 9 can also be charged at an external charging station. Likewise the drive train of the motor vehicle 1 can optionally include an internal combustion engine 21, which, alternatively or in addition to the electric machine 8, can drive the motor vehicle 1. The internal combustion engine 21 can also drive the electric machine 8 in order to charge the battery 9.

[0037] A computer program product 11 can be stored on the memory unit 4. The computer program product 11 can be run on the processor unit 3, for the purpose of which the processor unit 3 and the memory unit 4 are connected to each other by the communication interface 5. When the computer program product 11 is run on the processor unit 3, the computer program product 11 instructs the processor unit 3 to perform the functions described in conjunction with the drawing and/or to carry out method steps.

[0038] The computer program product 11 includes an MPC algorithm 13. The MPC algorithm 13 includes a longitudinal dynamic model 14 of the drive train 7 of the motor vehicle 1 and a cost function 15 to be minimized. The processor unit 3 executes the MPC algorithm 13 and thereby predicts a behavior of the motor vehicle 1 based on the longitudinal dynamic model 14, wherein the cost function 15 is minimized. An optimal rotational speed and an optimal torque of the electric machine 8 for calculated points in the prediction horizon result as the output of the optimization by the MPC algorithm 13. For this purpose, the processor unit 3 can determine an input variable for the electric machine 8, enabling the optimal rotational speed and the optimal torque to set in. The processor unit 3 can control, by way of an open-loop system, the electric machine 8 based on the determined input variable. In addition, this can also be carried out by a driver assistance system 16, however.

[0039] The detection unit 6 can measure current state variables of the motor vehicle 1, record appropriate data, and supply the current state variables and data to the MPC algorithm 13. In this way, route data from an electronic map can be updated, in particular cyclically, for a prediction horizon (for example, 400 m) ahead of the motor vehicle 1. The route data can include, for example, uphill grade information, curve information, and information about speed limits. Moreover, a curve curvature can be converted, via a maximum permissible lateral acceleration, into a speed limit for the motor vehicle 1. In addition, a position finding of the motor vehicle can be carried out by the detection unit 6, in particular via a GPS signal generated by a GNSS sensor 12 for the precise localization on the electronic map. The processor unit 3 can access this information, for example, via the communication interface 5.

[0040] The longitudinal dynamic model 14 of the motor vehicle 1 can be expressed mathematically as follows:

[00001]$\frac{\mathrm{dv}\left(t\right)}{\mathrm{dt}}=\left(F_{\mathrm{trac}}\left(t\right)-F_r\left(\alpha \left(t\right)\right)-F_{\mathrm{gr}}\left(\alpha \left(t\right)\right)-F_d\left(v\left(t\right)\right)\right)/m_{\mathrm{eq}}$

Wherein:

[0041] v is the speed of the motor vehicle; [0042] F.sub.trac is the tractive force that is exerted by the prime mover or the brakes upon the wheels of the motor vehicle; [0043] F.sub.r is the rolling resistance, which is an effect of the deformation of the tires during rolling and depends on the load of the wheels (on the normal force between the wheel and the road) and, thus, on the inclination angle of the road; [0044] F.sub.gr is the gradient resistance, which describes the longitudinal component of gravity, which acts upon the motor vehicle during operation uphill or downhill, depending on the gradient of the roadway; [0045] F.sub.d is the drag force of the motor vehicle; and [0046] m.sub.eq is the equivalent mass of the motor vehicle; the equivalent mass includes, in particular, the inertia of the turned parts of the drive train, which are subjected to the acceleration of the motor vehicle (prime mover, transmission input shafts, wheels).

[0047] By converting time dependence into distance dependence

[00002]$\frac{d}{\mathrm{ds}}=\frac{d}{\mathrm{dt}}*\frac{\mathrm{dt}}{\mathrm{ds}}=\frac{d}{\mathrm{dt}}*\frac{1}{v}$

and coordinate transformation in order to eliminate the quadratic speed term in the aerodynamic drag with the

[00003]$e_{\mathrm{kin}}=\frac{1}{2}*m_{\mathrm{eq}}*{v\left(t\right)}^2,$

result is

[00004]$\frac{{\mathrm{de}}_{\mathrm{kin}}}{\mathrm{ds}}=F_{\mathrm{trac}}\left(s\right)-F_r\left(\alpha \left(s\right)\right)-F_{\mathrm{gr}}\left(\alpha \left(s\right)\right)-F_d\left(e_{\mathrm{kin}}\left(s\right)\right).$

[0048] In order to ensure that the problem is quickly and easily solvable by the MPC algorithm 13, the dynamic equation of the longitudinal dynamic model 14 is linearized, in that the speed is expressed, via coordinate transformation, by kinetic energy de.sub.kin. As a result, the quadratic term for calculating the aerodynamic drag F.sub.d is replaced by a linear term and, simultaneously, the longitudinal dynamic model 14 of the motor vehicle 1 is no longer described as a function of time, as usual, but rather as a function of distance. This fits well with the optimization problem, since the predictive information of the electrical horizon is based on distance.

[0049] In addition to the kinetic energy, there are two further state variables, which, within the scope of a simple optimization problem, must also be described in a linear and distance-dependent manner. On the one hand, the electrical energy consumption of the drive train 7 is usually described in the form of a characteristic map as a function of torque and prime mover speed. In the exemplary embodiment shown, the motor vehicle 1 has a fixed ratio between the electric machine 8 and the road on which the motor vehicle 1 moves. As a result, the rotational speed of the electric machine 8 can be directly converted into a speed of the motor vehicle 1 or even into a kinetic energy of the motor vehicle 1. In addition, the electrical power of the electric machine 8 can be converted into energy consumption per meter via division by the appropriate speed. As a result, the characteristic map of the electric machine 8 obtains the form shown in FIG. 2. In order to be able to utilize this characteristic map for the optimization, the energy consumption per meter is linearly approximated: Energy.sub.perMeter≥a.sub.i*e.sub.kin+b.sub.i*F.sub.trac for all i.

[0050] The cost function 15 to be minimized can be expressed mathematically as follows:

[00005]$\min \left(-w_{\mathrm{Bat}}.Math.E_{\mathrm{Bat}}\left(s_E\right)+w_{\mathrm{Time}}.Math.T\left(s_E\right)+w_{\mathrm{Tem}}.Math.\underset{s=1}{\overset{s_E-1}{.Math.}}{\left(\frac{F_A\left(s\right)-F_A\left(s-1\right)}{\Delta s}\right)}^2+w_{\mathrm{TemStart}}.Math.{\left(F_A\left(s_1\right)-F_A\left(s_0\right)\right)}^2+\underset{s=1}{\overset{s_E-1}{.Math.}}{w}_{\mathrm{Slack}}.Math.{\mathrm{Var}}_{\mathrm{Slack}}\right)$

Wherein:

[0051] w.sub.Bat is the weighting factor for the energy consumption of the battery [0052] E.sub.Bat is the energy consumption of the battery [0053] S is the distance [0054] S.sub.E-1 is the distance one time step before the end of the prediction horizon [0055] F.sub.A is the drive force that is provided by the electric machine, transmitted by a transmission at a constant ratio, and applied at a wheel of the motor vehicle [0056] W.sub.Tem is the weighting factor for torque gradients [0057] W.sub.TemStart is the weighting factor for torque surges [0058] T is the time that the vehicle needs in order to cover the entire distance predicted within the prediction horizon [0059] w.sub.Time is the weighting factor for the time T [0060] S.sub.E is the distance to the end of the horizon [0061] w.sub.Slack is the weighting factor for the slack variable [0062] Var.sub.Slack is the slack variable

[0063] The cost function 15 has exclusively linear and quadratic terms. As a result, the overall problem has the form of a quadratic optimization with linear constraints and a convex problem results, which can be solved well and quickly.

[0064] The cost function 15 includes, as a first term, an electrical energy E.sub.Bat weighted with a first weighting factor w.sub.Bat and predicted according to the longitudinal dynamic model, which is provided within a prediction horizon by the battery 9 of the drive train 7 for driving the electric machine 8.

[0065] The cost function 15 includes, as a second term, a driving time T weighted with a second weighting factor W.sub.Time and predicted according to the longitudinal dynamic model 14, which the motor vehicle 1 needs in order to cover the predicted distance. As a result, depending on the selection of the weighting factors, a low speed cannot always be evaluated as optimal and, thus, the problem no longer exists that the resultant speed is always at the lower edge of the permitted speed.

[0066] The energy consumption and the driving time can both be evaluated and weighted at the end of the horizon. These terms are therefore active only for the last point of the horizon.

[0067] Excessively high torque gradients within the horizon are disadvantageous. Therefore, torque gradients are already penalized in the cost function 15, namely by the term

[00006]$w_{\mathrm{Tem}}.Math.{.Math.}_{s=1}^{s_E-1}{\left(\frac{F_A\left(s\right)-F_A\left(s-1\right)}{\Delta s}\right)}^2.$

The quadratic deviation of the drive force per meter is weighted with a weighting factor W.sub.Tem and minimized in the cost function. Alternatively to the drive force F.sub.A per meter, the torque M.sub.EM provided by the electric machine 8 can also be utilized and weighted with the weighting factor W.sub.Tem, and so the alternative term

[00007]$w_{\mathrm{Tem}}.Math.{.Math.}_{s=1}^{s_E-1}{\left(\frac{M_{\mathrm{EM}}\left(s\right)-M_{\mathrm{EM}}\left(s-1\right)}{\Delta s}\right)}^2$

results. Due to the constant ratio of the transmission 10, the drive force and the torque are directly proportional to each other.

[0068] In order to ensure comfortable driving, one further term is introduced in the cost function 15 for penalizing torque surges, namely w.sub.TemStart.Math.(F.sub.A(s.sub.1)−F.sub.A(s.sub.0)).sup.2. Alternatively to the drive force F.sub.A, the torque M.sub.EM provided by the electric machine 8 can also be utilized here, and so the alternative term w.sub.TemStart.Math.(M.sub.EM(s.sub.1)−M.sub.EM(s.sub.0)).sup.2 results. For the first point in the prediction horizon, the deviation from the most recently set torque can be evaluated as negative and weighted with a weighting factor W.sub.TemStart in order to ensure that there is a seamless and smooth transition during the change-over between an old trajectory and a new trajectory.

[0069] Speed limits are hard limits for the optimization that are not permitted to be exceeded. A slight exceedance of the speed limits is always permissible in reality and tends to be the normal case primarily during transitions from one speed zone into a second zone. In dynamic surroundings, where speed limits shift from one computing cycle to the next computing cycle, it can happen, in the case of very hard limits, that a valid solution for a speed profile can no longer be found. In order to increase the stability of the computational algorithm, a soft constraint is introduced into the cost function 15. A slack variable Var.sub.Slack weighted with a weighting factor W.sub.Slack becomes active in a predefined narrow range before the hard speed limit is reached. Solutions that are situated very close to this speed limit are evaluated as poorer, i.e., solutions, the speed trajectory of which maintains a certain distance to the hard limit.

[0070] In order to respect the physical limits of the drive train components, the tractive force is limited by delimiting the characteristic map of the electric machine 8. The battery 9 is the limiting element for the maximum recuperation. In order not to damage the battery 9, in the exemplary embodiment shown, −50 kW should not be fallen below. For the linear constraint, this means that the minimum permissible torque of the electric machine 8 is limited in a linear manner with respect to the kinetic energy (or rotational speed). The torque limit is selected such that the maximum permissible power is not exceeded at any point and that the torque is zero (0) at the maximum permissible rotational speed. Permissible torques of the electric machine are therefore between the two delimiting lines 17 and 18, which are plotted in FIG. 3.

[0071] FIG. 4 illustrates the significance of the limitation of the acceleration. A first graph 19 shows the power limitation by the minimal −50 kW. A second graph 20 shows the limitation by the linear torque limit. At very low speeds, regenerative braking can still be carried out at up to −2.5 m/s.sup.2. As the speed increases, the maximum possible negative acceleration decreases considerably.

[0072] Modifications and variations can be made to the embodiments illustrated or described herein without departing from the scope and spirit of the invention as set forth in the appended claims. In the claims, reference characters corresponding to elements recited in the detailed description and the drawings may be recited. Such reference characters are enclosed within parentheses and are provided as an aid for reference to example embodiments described in the detailed description and the drawings. Such reference characters are provided for convenience only and have no effect on the scope of the claims. In particular, such reference characters are not intended to limit the claims to the particular example embodiments described in the detailed description and the drawings.

REFERENCE CHARACTERS

[0073] 1 vehicle [0074] 2 system [0075] 3 processor unit [0076] 4 memory unit [0077] 5 communication interface [0078] 6 detection unit [0079] 7 drive train [0080] 8 electric machine [0081] 9 battery [0082] 10 transmission [0083] 11 computer program product [0084] 12 GPS sensor [0085] 13 MPC algorithm [0086] 14 longitudinal dynamic model [0087] 15 cost function [0088] 16 driver assistance system [0089] 17 first delimiting line [0090] 18 second delimiting line [0091] 19 first graph [0092] 20 second graph [0093] 21 internal combustion engine