DE102019105665A1 - Control device and method for controlling a drive system of a hybrid vehicle - Google Patents

Abstract

A method for regulating a drive system of a hybrid drive vehicle can have, for example: Determining default control variable data based on a model by means of an optimization method, the default control variable data representing a default course of control variables of the drive system for a section of a predefined route, wherein the second optimization method has dynamic programming using the Pontryagin maximum principle, and based on determined auxiliary optimization data, target values for one or more parameters of the second model for the section are determined to determine the default control variable data based on route Data, actual control variable data, taking into account parameters that represent the drive system of the hybrid drive vehicle.

Description

Various embodiments relate to a control device for controlling a drive system of a hybrid vehicle, e.g. a hybrid electric vehicle, and a method for controlling a drive system of a hybrid vehicle, e.g. of a hybrid electric vehicle.

In general, in the field of vehicle technology, cruise control systems can be used to support the driver of a vehicle with longitudinal guidance. Conventional cruise control systems regulate, for example, with or without taking other road users into account, the speed to a static speed setpoint, although the drive energy used and thus the operating costs are given little or no consideration.

To calculate an optimal speed, for example, a so-called optimal control problem can be solved, which is, however, particularly for drive systems of hybrid vehicles on comparatively long distances (e.g. on distances of more than 50 km, e.g. more than 100 km, or more than 200 km) with a high computational effort is connected to these calculations in a reasonable time, e.g. in less than 10 minutes, less than 1 minute or less than 10 seconds, in particular using the computing power currently available in hybrid vehicles. For example, a computer system with a computing power in a range from approximately 1 GFLOPS to approximately 100 TFLOPS can currently be used in a hybrid vehicle.

According to various embodiments, a control device and a method for controlling a drive system of a hybrid vehicle are provided. The control device and the method are based on the solution of an optimal control problem and are set up, for example, in such a way that the computational effort for solving the optimal control problem is kept so small that the optimal control problem can be calculated by means of a vehicle-internal computer system and is solved almost optimally. For this purpose, a model-based predictive control (abbreviated as MPC and referred to as model predictive control) with two optimization stages is implemented. A first (upper) MPC level is used, which takes into account the entire planned route, for example, in order to calculate partial route target values using a sequential quadratic program, with the partial route target values being used in a second (lower) MPC level for partial routes (ie with a shorter horizon than the first MPC stage) to determine the optimal control of the vehicle by means of the partial route target variables. The solution of the optimal control problem in the lower MPC level takes place by means of a combination of dynamic programming and the Pontryagin maximum principle. The low computational effort of the model predictive control described here with two optimization levels can achieve energy and cost savings of up to 38% in a hybrid vehicle (e.g. in a parallel hybrid electric vehicle) compared to a conventional cruise control system with essentially constant speed specifications.

According to various embodiments, a hybrid electric vehicle can have an internal combustion engine and an electric motor, which can optionally be used alternately or simultaneously to drive the hybrid electric vehicle. It goes without saying that the principles described herein can also be applied to similar vehicles with two different drives.

One aspect of various embodiments relates to a model predictive control (MPC) of a drive train of a vehicle with two different drive types, e.g. a hybrid electric vehicle (HEV). Due to the two different types of drive, the overall model used for the model predictive control or regulation is comparatively complex, i.e. the parameter space for describing the drive system is comparatively large (e.g. 5 to 20 parameters or more than 20 parameters are used) and in particular of a mixed-integer type. Due to the complexity, the computational effort can conventionally be a limiting variable for the use of such controls or regulators in a vehicle, provided that a computing system of the vehicle itself is to be used to perform the calculations of the model predictive control or regulation.

According to various embodiments, model predictive regulation takes place in two optimization stages (also referred to as MPC stages). The first optimization stage provides, for example, an approximation of lower quality than the second optimization stage and, on the other hand, has a larger horizon than the second optimization stage. Thus, in the first optimization stage (with a loss in quality), a large total route can be taken into account, e.g. more than 200 km, and in the second optimization stage the entire route can be used for different route sections (referred to as partial routes) a calculation with a higher quality is carried out (e.g. without loss of quality). In particular, the second optimization stage is set up in such a way that the optimal control problem is completely solved, ie that all model parameters used are also taken into account in the second optimization stage.

According to various embodiments, the first stage of the model predictive control is based on an approximation using SQP, i. on a sequential quadratic program. The second stage is based on a calculation using a combination of dynamic programming (DP) and Pontryagin's maximum principle (PMP). SQP is, for example, sufficiently well suited for approximating the relevant continuous quantities with non-linear behavior, e.g. the efficiency maps of various drives, the state of charge of an energy storage device (e.g. a battery), the level of a fuel tank, etc. The combination of PMP and DP allows, for example, a sufficiently good calculation of a mixed (integer / continuous) state space. Integer states are, for example, the gear of the vehicle transmission, the two states of a start-stop function, etc.

According to various embodiments, a combination of SQP and PMP-DP is clearly used in a two-stage optimization principle for the energy-optimized control of the longitudinal guidance and the drive train of a hybrid vehicle. This results in the advantage, for example, that a complete optimization of all relevant parameters in the second stage (PMP-DP) is made possible and can also take place in such a way that the calculation can be carried out in a corresponding vehicle in such a way that the calculation is efficient. The result of the two-stage optimization is, for example, of high quality compared to an optimal calculation based on DP.

According to various embodiments, a control / regulating device can be set up to control / regulate a drive system of a hybrid vehicle and have at least one processor. The at least one processor can be set up, for example: (I) to receive route data, the route data associated with a predefined route and representing a predefined gradient profile and a predefined speed limit profile, for example; (II) receive actual control variable data, the actual control variable data representing an actual state of at least one continuous control variable and at least one discrete control variable of the drive system; (III) to determine auxiliary optimization data based on a first model by means of a first optimization method, the first model having: a first state parameter which represents a charge / discharge state of an energy store of the drive system, a second state parameter which represents a driving time, and at least one continuous control parameter, which represents the at least one continuous control variable of the drive system, and wherein the auxiliary optimization data represent a course of the first state parameter (ie the charge / discharge state of the energy store) and the second state parameter (ie the travel time), wherein the first optimization method comprises sequential quadratic programming (optimization, SQP); (IV) based on a second model by means of a second optimization method to determine default control variable data, the second model having: a first state parameter which represents the charge / discharge state of the energy store, a second state parameter which represents the travel time, at least one continuous control parameter, which represents the at least one continuous control variable of the drive system, and at least one integer control parameter, which represents the at least one discrete control variable of the drive system, the default control variable data a default course of the at least one continuous control variable and the at least represent a discrete control variable of the drive system for a respective section of the predefined route, the second optimization method being dynamic programming (optimization, DP) using the Pontryagin maximum principle ps (PMP), and wherein target values for the first state parameter and the second state parameter of the second model for the respective partial route are determined by means of the determined auxiliary optimization data; and (V) output the default control variable data for operating the drive system based on the output default control variable data.

Furthermore, another aspect of various embodiments can clearly be seen in providing a control / regulating device which is set up: (I) to receive route data, the route data representing at least one predefined gradient profile and a predefined speed limit profile assigned to a predefined driving route; (II) receiving actual control variable data, the actual control variable data representing a respective actual state of a control variable set, the control variable set having continuous control variables and discrete control variables of the drive system; (III) to determine auxiliary optimization data based on a first model by means of a first optimization method, the first model having: a first continuous state parameter, which indicates a charge / discharge state of an energy store Drive system represents, a second continuous state parameter which represents a driving time, a first control parameter set which represents the continuous control variables of the drive system, and wherein the auxiliary optimization data represent a course of the first state parameter and the second state parameter assigned to the predefined route, the first The optimization method has sequential quadratic programming (optimization, SQP) for determining the auxiliary optimization data on the basis of the received route data and actual control variable data, taking into account the first and second continuous state parameters and the first control parameter set; (IV) based on a second model by means of a second optimization method to determine default control variable data, the second model having: a first state parameter which represents the charge / discharge state of the energy store, a second state parameter which represents the travel time, a first control parameter set, which represents the continuous control variables of the drive system, and a second control parameter set, which represents discrete control variables of the drive system, wherein the default control variable data is a default curve of the at least one continuous control variable and the at least one discrete control variable of the drive system for a Represent part of the predefined route, the second optimization method having dynamic programming (optimization, DP) using the Pontryagin maximum principle (PMP), and using the determined auxiliary optimization data Z Target values for the first state parameter and the second state parameter of the second model for the section are determined to determine the default control variable data on the basis of the received route data, the actual control variable data and the determined auxiliary optimization data, taking into account the first and second continuous state parameter and the first and second control parameter sets; and (V) output the default control variable data for operating the drive system based on the output default control variable data.

Furthermore, another aspect of various embodiments can clearly be seen in providing a method for regulating a drive system of a hybrid vehicle, wherein the method can have, for example: (I) determining auxiliary optimization data based on a first model by means of a first optimization method, the first Model has: a first continuous state parameter which represents a charge / discharge state of an energy store of the drive system, a second continuous state parameter which represents a travel time, a first control parameter set which represents continuous control variables of the drive system, and the auxiliary optimization data having a course represent the first state parameter and the second state parameter assigned to a predefined route, the first optimization method having sequential quadratic programming for Determining the auxiliary optimization data based on route data and actual control variable data, taking into account the first and second continuous state parameters and the first control parameter set; (II) Finding Specification control variable data based on a second model by means of a second optimization method, the second model having: a first state parameter which represents the charge / discharge state of the energy store, a second state parameter which represents the driving time, a first control parameter set which represents the continuous control variables of the drive system, and a second set of control parameters which represents discrete control variables of the drive system, the default control variable data representing a default course of the continuous control variables and the discrete control variables of the drive system for part of the predefined route, the second Optimization method has dynamic programming using the Pontryagin maximum principle, and using the determined auxiliary optimization data, target values for the first state parameter and the second state parameter r of the second model for the part of the predefined route can be determined to determine the default control variable data based on the route data, the actual control variable data and the determined auxiliary optimization data taking into account the first and second continuous state parameters and the first and second set of control parameters; and (III) outputting the default control variable data for operating the drive system based on the output default control variable data.

Furthermore, another aspect of various embodiments can clearly be seen in providing a method for regulating a drive system of a hybrid vehicle, wherein the method can have, for example: (I) determining auxiliary optimization data based on a first model by means of a first optimization method, the first Optimization method has sequential quadratic programming to determine the auxiliary optimization data based on route data and actual control variable data taking into account parameters which represent the drive system of the hybrid drive vehicle, and wherein the auxiliary optimization data is assigned to a course of a subset of the parameters represent predefined driving route; (II) Determination of default control variable data based on a second model by means of a second optimization method, the default control variable data representing a default course of control variables of the drive system for a section of the predefined route, the second optimization method being dynamic programming using the Pontryagin maximum principle, and based on the determined auxiliary optimization data, target values for one or more parameters of the second model for the section are determined to determine the default control variable data based on the route data, the actual Control variable data taking into account parameters which represent the drive system of the hybrid drive vehicle; and (III) outputting the default control variable data for operating the drive system based on the output default control variable data.

Exemplary embodiments are shown in the figures and are explained in more detail below.

• 1 eine Regelvorrichtung in einer schematischen Darstellung, gemäß verschiedenen Ausführungsformen;
• 2 ein Hybridfahrzeug mit einer Regelvorrichtung in einer schematischen Darstellung, gemäß verschiedenen Ausführungsformen;
• 3A beispielhaft ein Wirkungsgradkennfeld eines Verbrennungsmotors, welches bei der Regelung mittels der Regelvorrichtung berücksichtigt werden kann, gemäß verschiedenen Ausführungsformen;
• 3B beispielhaft ein Wirkungsgradkennfeld eines Elektromotors, welches bei der Regelung mittels der Regelvorrichtung berücksichtigt werden kann, gemäß verschiedenen Ausführungsformen;
• 4 das Prinzip eines Optimalsteuerungsproblems, welches mittels zweier Optimierungsstufen basierend auf SQP und PMP-DP gelöst werden kann, gemäß verschiedenen Ausführungsformen;
• 5 und 6 jeweils ein Lösungsprinzip eines Optimalsteuerungsproblems mittels PMP-DP, gemäß verschiedenen Ausführungsformen;
• 7 beispielhaft Fahrstrecken-Daten, welche der Regelvorrichtung zugeführt werden können, gemäß verschiedenen Ausführungsformen;
• 8 einen Zusammenhang zwischen der Lösungsgüte einer PMP-DP Berechnung eines Optimalsteuerungsproblems und dem zeitlichen Berechnungsaufwand, gemäß verschiedenen Ausführungsformen;
• 9 beispielhaft ein Kraftstoffverbrauchskennfeld für eine Verbrennungsmotor-Getriebe-Einheit unter einer kraftstoffoptimalen Gangwahl, gemäß verschiedenen Ausführungsformen;
• 10 eine zweistufig modellbasierte prädikative Regelvorrichtung in einer schematischen Darstellung, gemäß verschiedenen Ausführungsformen;
• 11 eine schematische Darstellung einer zweiten Stufe einer zweistufigen modellbasierten prädikativen Regelvorrichtung, gemäß verschiedenen Ausführungsformen; und
• 12 eine beispielhafte Tangensfunktion, welche in einem Regler verwendet werden kann, um Verletzungen von Energiespeichergrenzen zu vermeiden, gemäß verschiedenen Ausführungsformen.

Show it

• 1 a control device in a schematic representation, according to various embodiments;
• 2 a hybrid vehicle with a control device in a schematic representation, according to various embodiments;
• 3A an example of an efficiency map of an internal combustion engine, which can be taken into account in the control by means of the control device, according to various embodiments;
• 3B an example of an efficiency map of an electric motor, which can be taken into account in the control by means of the control device, according to various embodiments;
• 4th the principle of an optimal control problem, which can be solved by means of two optimization stages based on SQP and PMP-DP, according to various embodiments;
• 5 and 6th each a solution principle of an optimal control problem by means of PMP-DP, according to various embodiments;
• 7th exemplary route data that can be fed to the control device, according to various embodiments;
• 8th a relationship between the solution quality of a PMP-DP calculation of an optimal control problem and the time required for calculation, according to various embodiments;
• 9 exemplary a fuel consumption map for an internal combustion engine-transmission unit under a fuel-optimal gear selection, according to various embodiments;
• 10 a two-stage model-based predictive control device in a schematic representation, according to various embodiments;
• 11 a schematic representation of a second stage of a two-stage model-based predictive control device, according to various embodiments; and
• 12 an exemplary tangent function that can be used in a controller in order to avoid violations of energy storage limits, according to various embodiments.

In the following detailed description, reference is made to the accompanying drawings, which form a part hereof, and in which there is shown, for purposes of illustration, specific embodiments in which the invention may be practiced. It goes without saying that other embodiments can be used and structural or logical changes can be made without departing from the scope of protection of the present invention. It goes without saying that the features of the various exemplary embodiments described herein can be combined with one another, unless specifically stated otherwise. Therefore, the following description is not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims.

In at least partially autonomous vehicles, the driver can no longer freely choose the speed, for example. This allows, for example, the speed to be automatically adjusted in such a way that the energy costs required for a trip are as minimal as possible or another destination can be optimized. The method described here or the control device described here determines, for example, this optimized speed (or the control variables required to set the optimized speed) for every possible drive train configuration (electric vehicle, conventional vehicle, hybrid electric vehicle).

According to various embodiments, a method for generating an optimized energy management and driving strategy is described. The method for generating an energy management and driving strategy relates to route data. The route data can represent, for example, a predetermined gradient as well as a predetermined permissible speed band along the route ahead. The predefined permissible speed band can for example have respective maximum and minimum speeds along the route ahead. The travel time can also be specified as a parameter. According to various embodiments, the cost-optimized values of the control variables (for example gear selection, engine start / stop control, brake, internal combustion engine and / or electric motor torque) are determined as a function of a vehicle model. In a control loop, for example, the actual control variables are determined (represented by means of corresponding actual control variable data) and the control variables are adjusted accordingly according to default control variables (represented by means of corresponding default control variable data), the default control variables being based on a two-stage Optimization procedures are determined. A deviation of the actual control variables from the default control variables can be clearly reduced.

Based on a corresponding modeling of a drive system of a hybrid vehicle, a complex mixed-integer optimal control problem can result, which cannot be solved with conventional solution methods with the appropriate quality with at the same time low computational effort. For example, simplifications are made in conventional solution methods, e.g. the travel time is not considered as a state in order to make the simplified problem calculable with the help of dynamic programming. Overall, the conventional solution methods are not suitable for solving the complete optimization problem with such a low computational effort that it can be calculated while the vehicle is in motion.

The control device described herein and the method described herein relate to an optimal control in a two-stage, model-based, predictive control (MPC). In the first stage of the MPC, the problem approximated as a sequential quadratic program (SQP) is solved for the entire driving course ahead. The state curves determined for the journey time and the energy storage energy are used by the second stage to solve the complete optimal control problem for short sections of the route ahead. This second stage uses a combination of dynamic programming (DP) and Pontryagin's maximum principle (PMP), called PMP-DP. The combination of the SQP in the first stage of the MPC and the PMP-DP in the second stage of the MPC solves the complete optimal control problem in the second stage (e.g. in contrast to conventional bilevel MPC). By means of the described combination of the algorithms SQP and PMP-DP, the computational effort for the completely optimal solution can be reduced for the first time to such an extent that the method can be calculated on a control unit for vehicle use, e.g. on a control unit with a computing power of 1 GLOPS to 100 TFLOPS.

1 illustrates a control device 100 in a schematic view, according to various embodiments. The control device 100 can be used, for example, to control a drive system of a hybrid electric vehicle, for example as described herein with a combustion engine and an electric drive set up in parallel therewith. It is understood that the control device 100 can also be used in the same or a similar way to regulate another drive system, for example a drive system of a hybrid fuel cell vehicle, or generally a vehicle with more than two different types of drive. It is also understood that the control device described herein 100 can also be set up as a control device, that is to say that the actual control variables are not readjusted while the vehicle is in motion, but rather are determined only once in advance, for example. Such a control can be helpful in that, for example, routes traveled several times can be optimized in advance.

According to various embodiments, the control device 100 at least one processor 102 exhibit. The at least one processor 102 or the control device 100 can be set up, for example, route data 103 to recieve. The route data 103 can represent, for example, a predefined gradient curve and / or a predefined speed limit curve assigned to a predefined route (see for example 7th ). It goes without saying that the route data 103 can also represent other conditions regarding the route. The predefined speed limit profile can be at least a profile of a maximum The speed to be driven is based on the predefined route, for example in relation to different sections of the predefined route. The predefined speed limit profile can also be a profile of a minimum speed to be driven in relation to the predefined route, for example in relation to different sections of the predefined route.

According to various embodiments, the at least one processor 102 the control device 100 be set up in such a way that it (instead of the predefined speed limit profile or in addition to it) receives route properties (eg curve radii and / or traffic sign information) and uses the route properties to determine or adapt the predefined speed limit profile.

Furthermore, the at least one processor 102 or the control device 100 be set up, for example, default control variable data 105s (also referred to as target control variable data) and actual control variable data 105i to recieve. According to various embodiments, the drive system of a hybrid vehicle can be operated based on control variables, with the actual control variable data 105i the respective actual values (which represent the currently available values) of the control variables and the target control variable data 105s the respective target values of the control variables (clearly adapted to the route). The control variables can have continuous variables (referred to as continuous control variables), such as the drive torque of the respective drive, the braking torque of the brake system, etc. Furthermore, the control variables can be discrete control variables, such as the state of a transmission (e.g. the gear of a gear shift), the state of a start / stop system for starting and stopping an internal combustion engine, etc.

According to various embodiments, the received actual control variable data 105i represent an actual state of at least one continuous control variable and at least one discrete control variable of the drive system. The at least one processor can 102 or the control device 100 be set up based on a first model (M1) by means of a first optimization method (OPT1) auxiliary optimization data 105h to investigate.

According to various embodiments, the first model can have the following: a first state parameter which represents, for example, a charge / discharge state of an energy store of the drive system, a second state parameter which represents a travel time, and at least one continuous control parameter which represents the at least one continuous control variable of the The drive system. According to various embodiments, the first state parameter can assume a comparatively large number (e.g. more than 100, more than 500, or more than 1000) of mutually different values. According to various embodiments, the continuous control parameter can assume a comparatively large number (e.g. more than 100, more than 500, more than 1000) of mutually different values. The fact that, according to various embodiments, the travel time is contained as a state parameter in the first model (M1) can make it possible, for example, to take corresponding boundary conditions for the travel time into account in the optimization.

According to various embodiments, the auxiliary optimization data 105h represent a course of the first state parameter (ie clearly a course of the charge / discharge state of an energy store) and the second state parameter (ie clearly the driving time). The course can be determined, for example, for the entire predefined route, for example for a route of more than 50 km, more than 100 km, or more than 200 km. It goes without saying that the course can also be determined for a distance of less than 50 km. As part of a regulation, the course can be determined, for example, for the entire predefined route at predefined times.

According to various embodiments, the first optimization method can have or be sequential quadratic programming (optimization, SQP). Using sequential quadratic programming, in particular models with continuous (for example non-integer, for example fractional-rational) parameters can be optimized efficiently. According to various embodiments, the first model (M1) cannot optimize integral control parameters and / or integral state parameters. According to various embodiments, an integer parameter (eg state parameter, control parameter, etc.) can have a comparatively small number (eg less than 50 , less than 25th , or less than 10 ) assume mutually different values. The term program, as used herein with reference to a sequential quadratic program or a dynamic program, can also be referred to as a program, for example a sequential quadratic program or a dynamic program.

Furthermore, the at least one processor 102 or the control device 100 be set up to determine default control variable data based on a second model (M2) using a second optimization method (OPT2).

According to various embodiments, the second model (M2) can have the following, for example: a first state parameter that represents the charge / discharge state of the energy store, a second state parameter that represents the travel time, at least one continuous control parameter that represents the at least one continuous control variable of the Drive system represents, and at least one integer control parameter which represents the at least one discrete control variable of the drive system.

According to various embodiments, the default control variable data can represent a default course of the at least one continuous control variable and the at least one discrete control variable of the drive system for part of the predefined route. The second optimization method (OPT2) can have or be dynamic programming (optimization, DP) using the Pontryagin maximum principle (PMP). Using the determined auxiliary optimization data 105h For example, target values for the first state parameter and the second state parameter of the second model (M2) can be determined for the part of the predefined route. The second optimization method (OPT2) can thus clearly be used efficiently in order to completely solve the problem, in which case, for example, integer and non-integer parameters (eg control parameters and / or status parameters) can be optimized at the same time. The integer parameters can be used, for example, to model discrete quantities, and the non-integer parameters can be used, for example, to model continuous quantities.

According to various embodiments, the default control variable data 105s from the at least one processor 102 or the control device 100 are output (for example to a control system) for operating the drive system of a hybrid vehicle based on the output specification control variable data 105s .

According to various embodiments, for example by means of the at least one processor 102 the control device 100 or by means of another computer system 112 , based on the actual control variable data 105i and the default control variable data 105s each setting data 107 can be calculated, with corresponding adjusting devices 114 the setting data 107 in such a way that there is a discrepancy between the actual control variable data 105i from the default control variable data 105s reduced. Adjusting devices 114 can for example have at least one actuator for braking the hybrid vehicle, at least one actuator for changing the speed of the internal combustion engine of the hybrid vehicle, at least one actuator for changing the speed of the electric motor of the hybrid vehicle, at least one controller for changing a state of a start / stop system of the hybrid vehicle , at least one actuator for changing the state of the transmission of the hybrid vehicle.

2 illustrates components of a drive system 202 of a hybrid electric vehicle 200 which can be taken into account in the first model (M1) and / or second model (M2), according to various embodiments.

The drive system 202 of the hybrid electric vehicle 200 has an internal combustion engine, for example 204 and an associated fuel tank 214 on. By means of the internal combustion engine 204 a drive torque (a torque) can be generated, the efficiency being dependent on the speed, as for example in 3A based on an exemplary family of characteristics 300v is illustrated.

The internal combustion engine 204 can by means of a start / stop system 224 started and stopped. Especially if the hybrid electric vehicle 200 no torque required by means of the internal combustion engine 204 is provided, the start / stop system 224 and the internal combustion engine 204 be set up so that the internal combustion engine 204 is turned off. A control of a clutch 208 of the drive system 202 can be linked to the start / stop system 224 so that, for example, the internal combustion engine 204 disengages when stopped.

The drive system 202 of the hybrid electric vehicle 200 also has, for example, at least one electric motor 206 and at least one associated energy store 216 on. By means of the electric motor 206 a drive torque (a torque) can be generated, with the efficiency likewise is speed-dependent, as it is for example in 3B based on an exemplary family of characteristics 300e is illustrated.

Optionally, the hybrid electric vehicle 200 a converter 226 have, for example an alternating current (AC) / direct current (DC) converter for operating the electric motor 206 by means of the corresponding energy from the energy store 216 .

The motor shafts of the electric motor 206 and the internal combustion engine 204 can by means of the coupling 208 can either be coupled with one another or uncoupled from one another.

The drive system 202 of the hybrid electric vehicle 200 also has, for example, a braking system 210 on, by means of which a braking torque can be applied to the front and / or rear wheels (for the sake of clarity, the braking system 210 only shown schematically for the front wheels).

According to various embodiments, the drive system 202 of the hybrid electric vehicle 200 a gear 230 (e.g. an automatic transmission). The gear 230 can for example be operated in several (eg 5, 6, 7, 9 or more than 9) gear steps. On the input side, the transmission can receive a torque from the electric motor 206 and / or the internal combustion engine 204 to be provided.

The hybrid electric vehicle 200 can for example the control device described herein 100 have for controlling / regulating the operation of the components of the drive system 202 . Thus, the hybrid electric vehicle can 200 be driven at least partially autonomously or drive fully autonomously.

According to various embodiments, the gear selection of the transmission 230 , the start / stop control, the torque of the internal combustion engine 204 , the torque of the electric motor 206 , and the torque of the braking system 210 Control variables of the control device 100 be. In the second model (M2), for example, the gear selection of the transmission 230 and the start / stop control can each be described by means of integer parameters and the torques, for example, by means of continuous (eg fractional-rational) parameters. In the first model, for example, the gear selection of the transmission 230 and the start / stop control are not taken into account.

System states can be, for example, the energy storage energy, the kinetic energy (or the speed) and the time. With both models (M1, M2), the energy storage energy, the kinetic energy (or the speed) and the time can be described by means of continuous (e.g. fractional-rational) state parameters.

4th illustrates a calculation of a profile of the charge / discharge state of the energy store 216 (eg the first state parameter of the first model M1) based on the first model (M1) and SQP, according to various embodiments. The course of the charge / discharge state of the energy store determined by means of the first model (M1) and SQP 216 can be used to set a target energy for respective sections and to optimize these sections using the second model (M2) and PMP-DP.

The target amount can be a target state (e.g. the target energy) based on a section of the route for travel time (the second state parameter) and the charge / discharge state of the energy store (the first state parameter).

• minimiere $${\displaystyle {\int }_{S_o}^{S_e}\left(F_{Kraftstoffkosten}\left(\overrightarrow{u},\overrightarrow{x},s\right)+F_{Batterieenergiekosten}\left(\overrightarrow{u},\overrightarrow{x},s\right)\right)ds},$$
  
  wobei s die Fahrstrecke repräsentiert mit So als Startpunkt und S_e als Endpunkt, wobei $\overrightarrow{u}$
  
  die Steuergrößen repräsentiert, und wobei $\overrightarrow{x}$
  
  die Systemzustände repräsentiert. Anstelle der Kraftstoffkosten und Energiespeicher-Energiekosten können auch andere Größen minimiert werden, z.B. Kraftstoffverbrauch und Energieverbrauch. In den hierin beschriebenen mathematischen Formeln können die Vektoren $\overrightarrow{u}\text{ und }\overrightarrow{\text{x}}$
  
  auch notiert sein als u und x.

According to various embodiments, the optimal control problem can be formulated mathematically as follows:

• minimize $${\displaystyle {\int }_{{\mathrm{S.}}_O}^{{\mathrm{S.}}_e}\left({\mathrm{F.}}_{KraftstOffkOsten}\left(\overrightarrow{u},\overrightarrow{x},s\right)+{\mathrm{F.}}_{\mathrm{B.}atterieenerGiekOsten}\left(\overrightarrow{u},\overrightarrow{x},s\right)\right)ds},$$
  
  where s represents the route with So as the starting point and S _e as the end point, where $\overrightarrow{u}$
  
  represents the control variables, and where $\overrightarrow{x}$
  
  represents the system states. Instead of the fuel costs and energy storage costs, other variables can also be minimized, for example fuel consumption and energy consumption. In the mathematical formulas described herein, the vectors $\overrightarrow{u}\text{and}\overrightarrow{\text{x}}$
  
  also be noted as u and x.

The following are details of the modeling of the drive system 202 of the hybrid electric vehicle 200 and the control aspects of the control device 100 or corresponding control procedures are described by way of example.

According to various embodiments, the state of the internal combustion engine or the start / stop system, σ, can be a discrete system state, for example either on or off. The corresponding control variable u _σ controls σ and at the same time the state of the clutch 208 . The condition of the clutch 208 is thus also discreet, the clutch is accordingly 208 considered either closed or open. The drive wheels of the hybrid electric vehicle can move when the transmission is in neutral 200 independent of the gear 230 and the drive units 204 , 206 move. This property is used in so-called sailing. Is the clutch 208 closed, own the internal combustion engine 204 and the electric motor 206 for example the same speed or angular speed or at least a fixed ratio of the respective speeds or angular speeds ω (v, g).

The angular speed ω (v, g) depends on the longitudinal vehicle speed v, the dynamic wheel radius r and the gear ratio (g). The gear ratio (g) is defined, for example, by the respective gear, which represents a further discrete system state. The corresponding control variable u _g controls g.

zusammengefasst sein und die zugehörigen Zustände g und σ im Vektor $\overrightarrow{x_d}.$

Both discrete control variables u _g and u _σ can for example be in the vector $\overrightarrow{u_d}$

be combined and the associated states g and σ in the vector $\overrightarrow{x_d}.$

zusammengefasst sein können. Es ergibt sich entsprechend der resultierende Steuergrößenvektor $\overrightarrow{u}=\left(\overrightarrow{u_c},\overrightarrow{u_d}\right).$

For the torques, M _E , of the internal combustion engine 204 and, M _M , of the electric motor 206 For example, corresponding forces F _E = M _E / r and F _M = M _M / r can be defined which, together with the force of the conventional brake F _{B, represent} continuous control variables and in the vector $\overrightarrow{u_c}$

can be summarized. The resulting control variable vector results accordingly $\overrightarrow{u}=\left(\overrightarrow{u_c},\overrightarrow{u_d}\right).$

Furthermore, according to various embodiments, the efficiency of the transmission 230 (η _g ) must be taken into account, as well as the driving resistances (e.g. caused by mass inertia, air resistance, rolling resistance, road gradient, and braking force).

$$F_{\text{w}}\left(v\right)=\text{m}v\frac{dv}{ds}+{\text{c}}_{\text{a}}{v}^2+c_{\alpha }+F_{\text{B}},$$

wobei F_T,d(u) die dissipative Kraft des Getriebes beschreibt. Ferner ist m die Fahrzeugmasse, c_a ein konstanter Beiwert für den Luftwiderstand und c_α ein Faktor, der von der Steigung des Fahrwegs abhängt.Overall, the equilibrium of forces on the wheel, F _w (v), can be described as follows: $${\mathrm{F.}}_{\text{W.}}\left(v\right)=\left({\mathrm{F.}}_{\text{M.}}+{\mathrm{F.}}_{\text{E.}}\sigma -{\mathrm{F.}}_{\text{T}\text{, d}}\left(\mathbf{u}\right)\right)\mathrm{\gamma }\left(G\right)\forall \in s\left[{\text{s}}_0,{\text{s}}_{\text{f}}\right],$$

$${\mathrm{F.}}_{\text{w}}\left(v\right)=\text{m}v\frac{dv}{ds}+{\text{c}}_{\text{a}}{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="DE102019105665A1\_0090.png,DE102019105665A1\_0091.png"\; state="\{\{state\}\}">v</figure-callout>}}^2+c_{\alpha }+{\mathrm{F.}}_{\text{B.}},$$

where F _{T, d} (u) describes the dissipative force of the transmission. Furthermore, m is the vehicle mass, c _{a is} a constant coefficient for the air resistance and c _{α is} a factor that depends on the gradient of the route.

Die Änderung der kinetischen Energie kann durch eine minimale Beschleunigung amin und eine maximale Beschleunigung amax begrenzt sein.By introducing the kinetic energy E _V , nonlinearities can be eliminated and the state differential equation of the kinetic energy, f _V , results as follows: $$\begin{array}{c}{\mathrm{E.}}_{\text{V}}^{\text{'}}\left(u,{\mathrm{E.}}_{\text{V}},G\right)=f_{\text{V}}\left(u,{\mathrm{E.}}_{\text{V}},\sigma ,G\right)\\ =\left({\mathrm{F.}}_{\text{M.}}+{\mathrm{F.}}_{\text{E.}}\sigma -{\mathrm{F.}}_{\text{T}\text{, d}}u\right))\mathrm{\gamma }\left(G\right)-{\mathrm{F.}}_{\text{B.}}-2{\text{c}}_{\text{a}}{\mathrm{E.}}_{\text{V}}/m-c_{\alpha }\in \text{m}\left[{\text{a}}_{\text{min}},{\text{a}}_{\text{Max}}\right],\end{array}$$

The change in the kinetic energy can be limited by a minimum acceleration amin and a maximum acceleration amax.

Die Energiespeicher-Energie Es kann ebenfalls ein Systemzustand sein und mit den anderen kontinuierlichen Systemzuständen einem Vektor $\overrightarrow{x_c}$

zusammengefasst sein zu $\overrightarrow{x_c}=\left({\text{E}}_{\text{s}},{\text{ E}}_{\text{V}},\text{ t}\right)$

$\left({\text{E}}_{\text{S}},{\text{ E}}_{\text{V}},\text{ t}\right).$

Dieser Vektor kann zusammen mit dem Vektor der diskreten Systemzustände $\overrightarrow{x_d}$

in einem Zustandsvektor $\overrightarrow{x}=\left(\overrightarrow{x_c},\overrightarrow{x_d}\right)$

$\left(\overrightarrow{x_c},\overrightarrow{x_d}\right)$

zusammengefasst sein.Due to the formulation in the distance range, the travel time t results as a further system state, the state differential equation of which can be formulated as follows: $$f_{\text{t}}\left({\mathrm{E.}}_{\text{V}}\right)=t\text{'}\left({\mathrm{E.}}_{\text{V}}\right)=1/v=\sqrt{\frac{\text{<figure-callout id="2" label="m" filenames="DE102019105665A1\_0090.png,DE102019105665A1\_0091.png" state="{{state}}">m</figure-callout>}}{2{\mathrm{R.}}_{\text{V}}}.}$$

The energy storage energy It can also be a system state and a vector with the other continuous system states $\overrightarrow{x_c}$

be summarized to $\overrightarrow{x_c}=\left({\text{E.}}_{\text{s}},{\text{E.}}_{\text{V}},\text{t}\right)$

$\left({\text{E.}}_{\text{S.}},{\text{E.}}_{\text{V}},\text{t}\right).$

This vector can be used together with the vector of the discrete system states $\overrightarrow{x_d}$

in a state vector $\overrightarrow{x}=\left(\overrightarrow{x_c},\overrightarrow{x_d}\right)$

$\left(\overrightarrow{x_c},\overrightarrow{x_d}\right)$

be summarized.

kann in der Zustandsdifferentialgleichung der Energiespeicher-Energie verwendet werden wie folgt: $$f_{\text{S}}\left(F_{\text{M}},x\right)=E_{\text{S}}^{\text{'}}\left(F_{\text{M}},x\right)=-P_{\text{S}}\left(F_{\text{M}},x\right)/\sqrt{2E_{\text{V}}/m},$$

wobei die chemische (d.h. interne) Energiespeicher-Leistung P_S als negativ definiert ist, wenn der Energiespeicher geladen wird. Für Akkumulatoren kann die Energiespeicher-Leistung auch als Batterie-Leistung bezeichnet sein.The state vector $\overrightarrow{x}$

can be used in the state differential equation of the energy storage energy as follows: $$f_{\text{S.}}\left({\mathrm{F.}}_{\text{M.}},x\right)={\mathrm{E.}}_{\text{S.}}^{\text{'}}\left({\mathrm{F.}}_{\text{M.}},x\right)=-P_{\text{S.}}\left({\mathrm{F.}}_{\text{M.}},x\right)/\sqrt{2{\mathrm{E.}}_{\text{V}}/m},$$

wherein the chemical (ie internal) energy storage power P _S is defined as negative when the energy storage is charged. For accumulators, the energy storage capacity can also be referred to as battery capacity.

The energy storage model can have a series circuit comprising an ideal voltage source and an ohmic resistor. It follows from this, for example, that the chemical energy storage power, P _S , which can be limited for example by the constant power limits P _Smin and P _Smax , is the sum of the dissipative energy storage power P _{S, d} and the electrical power.

Die Klemmleistung resultiert beispielsweise aus der mechanischen Leistung, M_M, des Elektromotors wie folgt: $$P_{\text{M}}\left(F_{\text{M}},x\right)=M_{\text{M}}\left(F_{\text{M}}\right)\omega \left(x\right)=F_{\text{M}}\sqrt{2E_{\text{V}}/\text{m}}\mathrm{\gamma }\left(g\right),$$

sowie dessen dissipativer Leistung ${\text{P}}_{\text{M}\text{,d}}\left({\text{F}}_{\text{M}},\overrightarrow{x}\right),$

gegeben beispielsweise als statisches Kennfeld (siehe beispielsweise 3B).The energy storage capacity can be described as follows: $$P_{\text{S.}}\left({\mathrm{F.}}_{\text{M.}},x\right)=P_{\text{S.}\text{, d}}\left({\mathrm{F.}}_{\text{M.}\text{,}x}\right)+P_{\text{M.}}\left({\mathrm{F.}}_{\text{M.}},x\right)+P_{\text{M.}\text{, d}}\left({\mathrm{F.}}_{\text{M.}},x\right)\in \left[{\text{P}}_{\text{Smin}},{\text{P}}_{\text{Smax}}\right].$$

The clamping power results, for example, from the mechanical power, M _M , of the electric motor as follows: $$P_{\text{M.}}\left({\mathrm{F.}}_{\text{M.}},x\right)={\mathrm{M.}}_{\text{M.}}\left({\mathrm{F.}}_{\text{M.}}\right)\omega \left(x\right)={\mathrm{F.}}_{\text{M.}}\sqrt{2{\mathrm{E.}}_{\text{V}}/\text{m}}\mathrm{\gamma }\left(G\right),$$

as well as its dissipative performance ${\text{P}}_{\text{M.}\text{, d}}\left({\text{F.}}_{\text{M.}},\overrightarrow{x}\right),$

given for example as a static map (see for example 3B) .

und der Leerlaufspannung U(E_S) abhängen, z.B. wie folgt: $$P_{\text{S}\text{,d}}\left(F_{\text{M}},x\right)=\frac{{\left(U\left(E_{\text{S}}\right)-\sqrt{U^2\left(E_{\text{S}}\right)-4R\left(F_{\text{M}},x\right)\left(P_{\text{M}}\left(F_{\text{M}},x\right)+P_{\text{M}\text{,d}}\left(F_{\text{M}},x\right)\right)}\right)}^2}{4R\left(F_{\text{M}},x\right)}.$$

Der elektrische Widerstand des Energiespeichers (z.B. der Batteriewiderstand) kann beispielsweise zwei diskrete Werte annehmen, je nachdem ob der Energiespeicher geladen oder entladen wird, z.B. wie folgt: $$R\left(F_{\text{M}},x\right)=\{\begin{array}{cc}{\text{R}}_{+},& \text{f}ür{P}_{\text{S}}\left(F_{\text{M}},x\right)\le 0\\ R_{-},& \text{f}ü\text{r }{P}_{\text{S}}\left(F_{\text{M}},x\right)>0\end{array}.$$

The losses of the energy store can be caused by the electrical power, the ohmic resistance $\text{R.}\left({\text{F.}}_{\text{M.}},\overrightarrow{x}\right)$

and the open circuit voltage U (E _S ), e.g. as follows: $$P_{\text{S.}\text{, d}}\left({\mathrm{F.}}_{\text{M.}},x\right)=\frac{{\left(U\left({\mathrm{E.}}_{\text{S.}}\right)-\sqrt{U^2\left({\mathrm{E.}}_{\text{S.}}\right)-\mathrm{4th}\mathrm{R.}\left({\mathrm{F.}}_{\text{M.}},x\right)\left(P_{\text{M.}}\left({\mathrm{F.}}_{\text{M.}},x\right)+P_{\text{M.}\text{, d}}\left({\mathrm{F.}}_{\text{M.}},x\right)\right)}\right)}^2}{\mathrm{4th}\mathrm{R.}\left({\mathrm{F.}}_{\text{M.}},x\right)}.$$

The electrical resistance of the energy store (e.g. the battery resistance) can, for example, assume two discrete values, depending on whether the energy store is being charged or discharged, e.g. as follows: $$\mathrm{R.}\left({\mathrm{F.}}_{\text{M.}},x\right)=\{\begin{array}{cc}{\text{R.}}_{+},& \text{f}ür{P}_{\text{S.}}\left({\mathrm{F.}}_{\text{M.}},x\right)\le 0\\ {\mathrm{R.}}_{-},& \text{f}ü\text{r}{P}_{\text{S.}}\left({\mathrm{F.}}_{\text{M.}},x\right)>0\end{array}.$$

Energiespeicher-Energie (E_S), kinetische Energie (E_V), Reisezeit (t), Start/Stopp-System (σ), sowie Gang (g) ein Gütemaß definiert werden, wobei die Steuergrößen (u) des Antriebsstrangs des betrachteten Hybridelektrofahrzeugs berücksichtigt sind, nämlich Kraft des Verbrennungsmotors (F_E), Kraft des Elektromotors (F_M), Kraft der Bremse (F_B), Steuerung des Start/Stopp-Systems (u_σ) sowie Steuerung des Gangs (u_g).According to various embodiments, the system states $\left(\overrightarrow{x}\right),$

Energy storage energy (E _S ), kinetic energy (E _V ), travel time (t), start / stop system (σ), as well as gear (g) a quality measure can be defined, whereby the control variables (u) of the drive train of the hybrid electric vehicle under consideration are taken into account, namely the power of the internal combustion engine (F _E ), power of the electric motor (F _M ), power of the brake (F _B ), control of the start / stop system (u _σ ) and control of the gear (u _g ).

The quality measure can for example be formulated as follows: $$\begin{array}{c}\mathcal{J}\left(u,x\right)={\kappa }_{\text{S.}}\left({\mathrm{E.}}_{\text{S0}}-{\mathrm{E.}}_{\text{S.}}\left({\text{s}}_f\right)\right)\\ +{\displaystyle {\int }_{{\text{S.}}_0}^{{\text{S.}}_{\text{f}}}\left({\kappa }_{\text{E.}}\left({\mathrm{F.}}_{\text{E.}}+{\mathrm{F.}}_{\text{E.}\text{, d}}\left({\mathrm{F.}}_{\text{E.}\text{,}x}\right)\right)\sigma \mathrm{\gamma }\left(G\right)+\left|u_{\sigma }\right|{\beta }_{\sigma }+\left|u_G\right|{\beta }_G+a^2/\sqrt{2{\mathrm{E.}}_{\text{V}}/m{\beta }_{\text{a}}}\right)\text{ds}}.\end{array}$$

This is, for example, a so-called Bolzas quality measure, which is composed, for example, of a cost component for the target state and an integral cost component. The terms β _σ and β _g in the quality measure represent the loss of energy through the starting process of the internal combustion engine and friction losses in the clutch when shifting the gear. The term β _a adapts the driving behavior and prevents or allows strong acceleration of the hybrid electric vehicle. It goes without saying that other formulations of the model and the measure of quality are also possible, which lead to the same or similar results.

• minimiere $$\mathcal{J}\left(u,x\right)$$
  
• unter den Bedingungen $$x_{\text{c}}^{\text{'}}=f_{\text{c}}\left(u,x\right)$$
  
  $$x_{\text{d}}^{+}=x_{\text{d}}+u_{\text{d}}$$
  
  $$\begin{array}{cc}x\left({\text{s}}_0\right)=x_0,& t\left({\text{s}}_{\text{f}}\right)<=t_{\text{f}}\end{array}$$
  
  $$E_{\text{V}}^{\text{'}}\in \text{m}\left[{\text{a}}_{\text{min}},{\text{a}}_{\text{max}}\right]$$
  
  $$E_{\text{S}}^{\text{'}}\in -\left[{\text{P}}_{\text{Smin}},P_{\text{Smax}}\right]/\sqrt{2E_{\text{V}}/m}$$
  
  $$x\in \left[x_{\text{min}},x_{\text{max}}\right]$$
  
  $$u_{\text{c}}\in \left[u_{\text{c}\text{,min}}\left(x\right),u_{\text{c}\text{,max}}\left(x\right)\right]$$
  
  $$u_{\sigma },u_g\in \left\{-\mathrm{1,0,1}\right\}.$$
  

With the quality measure, the optimal control problem can be summarized as follows:

• minimize $$\mathcal{J}\left(u,x\right)$$
  
• under the conditions $$x_{\text{c}}^{\text{'}}=f_{\text{c}}\left(u,x\right)$$
  
  $$x_{\text{d}}^{+}=x_{\text{d}}+u_{\text{d}}$$
  
  $$\begin{array}{cc}x\left({\text{s}}_0\right)=x_0,& t\left({\text{s}}_{\text{f}}\right)<=t_{\text{f}}\end{array}$$
  
  $${\mathrm{E.}}_{\text{V}}^{\text{'}}\in \text{m}\left[{\text{a}}_{\text{min}},{\text{a}}_{\text{Max}}\right]$$
  
  $${\mathrm{E.}}_{\text{S.}}^{\text{'}}\in -\left[{\text{P}}_{\text{Smin}},P_{\text{Smax}}\right]/\sqrt{2{\mathrm{E.}}_{\text{V}}/m}$$
  
  $$x\in \left[x_{\text{min}},x_{\text{Max}}\right]$$
  
  $$u_{\text{c}}\in \left[u_{\text{c}\text{, min}}\left(x\right),u_{\text{c}\text{,Max}}\left(x\right)\right]$$
  
  $$u_{\sigma },u_G\in \left\{-\mathrm{1.0.1}\right\}.$$
  

The function f _c (u, x) = (f _s , f _v , f _t ) combines the state differential equations of all continuous system states.

To solve the formulated optimal control problem with the discrete solution method, for example, the path coordinates can be discretized and the continuous system states x _{c can be} quantized.

• Minimiere $$\begin{array}{l}\begin{array}{cc}& \mathcal{J}\left(u\left(k\right),x\left(k\right),k\right)\end{array}\\ ={\kappa }_{\text{S}}\left({\mathrm{<figure-callout\; id="0"\; label="E\; S"\; filenames="DE102019105665A1\_0089.png,DE102019105665A1\_0092.png"\; state="\{\{state\}\}">E</figure-callout>}}_S-E_{\text{S}}\left(N_{\text{k}}\right)\right)\\ +{\displaystyle \sum _{k=1}^{N_k}({\kappa }_{\text{E}}\left(F_{\text{E}}\left(k\right)+F_{\text{E}\text{,d}}\left(F_{\text{E}}\left(k\right),x\left(k\right)\right)\sigma \left(k\right)\mathrm{\gamma }\left(g\left(k\right)\right)+a^2\left(k\right)/\sqrt{2E_{\text{V}}\left(k\right)/m}{\beta }_{\text{a}}\right)\mathrm{\Delta }\text{s}\left(k\right)}\\ +{\displaystyle \sum _{k=1}^{N_{\text{k}}}\left(\left|u_{\sigma }\left(k\right)\right|{\beta }_{\sigma }+\left|u_{\text{g}}\left(k\right)\right|{\beta }_{\text{g}}\right)}\end{array}$$
  
• unter den Bedingungen $$x_{\text{c}}\left(k+1\right)=x_{\text{c}}\left(k\right)+f_{\text{c}}\left(u,\mathbf{x}\right)\mathrm{\Delta }\text{s}$$
  
  $$x_{\text{d}}\left(k+1\right)=x_{\text{d}}\left(k\right)+u_{\text{d}}$$
  
  $$\begin{array}{cc}x\left(0\right)=x_0,& t\left(N_k\right)<=t_{\text{f}}\end{array}$$
  
  $$f_{\text{V}}\left(k\right)\in \text{m}\left[{\text{a}}_{\text{min}},{\text{a}}_{\text{max}}\right]$$
  
  $$f_{\text{S}}\left(k\right)\in -\left[{\text{P}}_{\text{Smin}},{\text{P}}_{\text{Smax}}\right]/\sqrt{2E_{\text{V}}\left(k\right)/m}$$
  
  $$x\in \left[x_{\text{min}},x_{\text{max}}\right]$$
  
  $$u_{\text{c}}\in \left[x_{\text{min}},x_{\text{max}}\right]$$
  
  $$u_g,u_{\sigma }\in \left\{-\mathrm{1,0,1}\right\},$$
  

wobei k ein diskreter Punkt der Wegkoordinate s ist.Thus, a discrete optimal control problem arises as follows:

• Minimize $$\begin{array}{l}\begin{array}{cc}& \mathcal{J}\left(u\left(k\right),x\left(k\right),k\right)\end{array}\\ ={\kappa }_{\text{S.}}\left({\mathrm{E.}}_{\mathrm{S.}0}-{\mathrm{E.}}_{\text{S.}}\left(N_{\text{k}}\right)\right)\\ +{\displaystyle \sum _{k=1}^{N_k}({\kappa }_{\text{E.}}\left({\mathrm{F.}}_{\text{E.}}\left(k\right)+{\mathrm{F.}}_{\text{E.}\text{, d}}\left({\mathrm{F.}}_{\text{E.}}\left(k\right),x\left(k\right)\right)\sigma \left(k\right)\mathrm{\gamma }\left(G\left(k\right)\right)+a^2\left(k\right)/\sqrt{2{\mathrm{E.}}_{\text{V}}\left(k\right)/m}{\beta }_{\text{a}}\right)\mathrm{\Delta }\text{s}\left(k\right)}\\ +{\displaystyle \sum _{k=1}^{N_{\text{k}}}\left(\left|u_{\sigma }\left(k\right)\right|{\beta }_{\sigma }+\left|u_{\text{G}}\left(k\right)\right|{\beta }_{\text{G}}\right)}\end{array}$$
  
• under the conditions $$x_{\text{c}}\left(k+1\right)=x_{\text{c}}\left(k\right)+f_{\text{c}}\left(u,\mathbf{x}\right)\mathrm{\Delta }\text{s}$$
  
  $$x_{\text{d}}\left(k+1\right)=x_{\text{d}}\left(k\right)+u_{\text{d}}$$
  
  $$\begin{array}{cc}x\left(0\right)=x_0,& t\left(N_k\right)<=t_{\text{f}}\end{array}$$
  
  $$f_{\text{V}}\left(k\right)\in \text{m}\left[{\text{a}}_{\text{min}},{\text{a}}_{\text{Max}}\right]$$
  
  $$f_{\text{S.}}\left(k\right)\in -\left[{\text{P}}_{\text{Smin}},{\text{P}}_{\text{Smax}}\right]/\sqrt{2{\mathrm{E.}}_{\text{V}}\left(k\right)/m}$$
  
  $$x\in \left[x_{\text{min}},x_{\text{Max}}\right]$$
  
  $$u_{\text{c}}\in \left[x_{\text{min}},x_{\text{Max}}\right]$$
  
  $$u_G,u_{\sigma }\in \left\{-\mathrm{1.0.1}\right\},$$
  

where k is a discrete point of the path coordinate s.

The discrete optimal control problem can for example be calculated with the aid of a numerical algorithm (e.g. DP). This DP algorithm starts, for example, with k = 1 and calculates for each state x (k + 1) the sum of state transition costs based on the possible predecessor states at k and the cumulative costs from the start to the respective predecessor state at k. For example, only the previous states can be considered that meet the secondary conditions in order to keep the computing time small. The state transition costs depend, for example, on the control variables, which are determined by reversing the state differential equations. This means that u is deduced from the difference x (k + 1) -x (k). It is assumed, for example, that the control variables do not change in the interval [s _k , s _{k + 1} ], which corresponds to an instantaneous value sampling. When all possible total costs have been calculated for a state x (k), the lowest value is stored in the cost tensor and the index of the corresponding predecessor. This algorithm can be implemented, for example, with interleaved loops which, for example, examine all possible state transitions in order to calculate the state change costs. For this purpose, for example, all possible E _V (k), E _S (k), σ (k) and g (k) can be iterated.

According to various embodiments, the optimization based on a combined solution of the DP with Pontryagin's maximum principle takes place in the second stage of the MPC.

Details of the Pontryagin maximum principle (PMP) are described below by way of example. Since the optimum is usually defined as the minimum in the optimum control, the maximum principle can be converted to a minimum principle by changing the sign. It can clearly be understood as an extremal principle.

wobei F(x, u, t) das Gütemaß ist, was mit der Zustandsdifferentialgleichung f(x, u, t) über Lagrange-Multiplikatoren (ψ) zusammengeführt wird. Der Vektor der Lagrange-Multiplikatoren ψ(s)=(ψ_s(s), ψ_v(s), ψ_t(s)) enthält die Kozustände ψ_s(s), ψ_v(s) und ψ_t(s) für die jeweiligen Systemzustände E_S, E_V und t.According to various embodiments, a corresponding Hamilton function can be defined as follows: $$H\left(\mathbf{x},\psi ,u,s\right)=\mathrm{F.}\left(x,u,s\right)+{\psi }^T\mathbf{f}\left(x,u,s\right),$$

where F (x, u, t) is the measure of quality, which is combined with the state differential equation f (x, u, t) via Lagrange multipliers (ψ). The vector of the Lagrange multipliers ψ (s) = (ψ _s (s), ψ _v (s), ψ _t (s)) contains the co-states ψ _s (s), ψ _v (s) and ψ _t (s) for the respective system states E _S , E _V and t.

To apply the PMP to the optimal control problem, the discrete states g and σ can be neglected and only their control variables can be retained in the problem description. An adjusted quality measure can be as follows: $$\begin{array}{c}\mathcal{L.}\left(x,u,s\right)={\kappa }_{\text{S.}}{\mathrm{F.}}_{\text{S.}}\left(s\right)+{\kappa }_{\text{E.}}\left({\mathrm{F.}}_{\text{E.}}\left(s\right)+{\mathrm{F.}}_{\text{E.}\text{, d}}\left({\mathrm{F.}}_{\text{E.}},x,s\right)\right)\sigma \left(s\right)\mathrm{\gamma }\left(G\left(s\right)\right)\\ +\left|u_{\sigma }\right|{\beta }_{\sigma }+\left|u_G\right|{\beta }_G+a^2\left(s\right)/\sqrt{2{\mathrm{E.}}_{\text{V}}\left(s\right)/m}{\beta }_{\text{a}}\end{array}$$

• minimiere $$\mathcal{H}\left(x,\psi ,u,s\right)$$
  
• unter den Bedingungen $$\psi \text{'}\left(s\right)=-\frac{\partial \mathcal{H}\left(x,\psi ,u,s\right)}{\partial x_{\text{c}}\left(s\right)}$$
  
  $$x_{\text{d}}^{+}=x_{\text{d}}+u_{\text{d}}$$
  
  $$\begin{array}{cc}x\left({\text{s}}_0\right)=x_0,& t\left({\text{s}}_{\text{f}}\right)<=t_{\text{f}}\end{array}$$
  
  $$E_{\text{V}}^{\text{'}}\left(s\right)\in \text{m}\left[{\text{a}}_{\text{min}},{\text{a}}_{\text{max}}\right]$$
  
  $$E_{\text{S}}^{\text{'}}\left(s\right)\in -\left[{\text{P}}_{\text{Smin}},{\text{P}}_{\text{Smax}}\right]/\sqrt{2E_{\text{V}}\left(s\right)/m}$$
  
  $$x\left(s\right)\in \left[x_{\text{min}},x_{\text{max}}\right]$$
  
  $$u_{\text{c}}\left(s\right)\in \left[u_{\text{c}\text{,min}}\left(x\right),u_{\text{c}\text{,max}}\left(x\right)\right]$$
  
  $$u_g,u_{\sigma }\in \left\{-\mathrm{1,0,1}\right\}$$
  

The optimal control problem can thus be formulated as follows:

• minimize $$\mathcal{H}\left(x,\psi ,u,s\right)$$
  
• under the conditions $$\psi \text{'}\left(s\right)=-\frac{\partial \mathcal{H}\left(x,\psi ,u,s\right)}{\partial x_{\text{c}}\left(s\right)}$$
  
  $$x_{\text{d}}^{+}=x_{\text{d}}+u_{\text{d}}$$
  
  $$\begin{array}{cc}x\left({\text{s}}_0\right)=x_0,& t\left({\text{s}}_{\text{f}}\right)<=t_{\text{f}}\end{array}$$
  
  $${\mathrm{E.}}_{\text{V}}^{\text{'}}\left(s\right)\in \text{m}\left[{\text{a}}_{\text{min}},{\text{a}}_{\text{Max}}\right]$$
  
  $${\mathrm{E.}}_{\text{S.}}^{\text{'}}\left(s\right)\in -\left[{\text{P}}_{\text{Smin}},{\text{P}}_{\text{Smax}}\right]/\sqrt{2{\mathrm{E.}}_{\text{V}}\left(s\right)/m}$$
  
  $$x\left(s\right)\in \left[x_{\text{min}},x_{\text{Max}}\right]$$
  
  $$u_{\text{c}}\left(s\right)\in \left[u_{\text{c}\text{, min}}\left(x\right),u_{\text{c}\text{,Max}}\left(x\right)\right]$$
  
  $$u_G,u_{\sigma }\in \left\{-\mathrm{1.0.1}\right\}$$
  

In order to determine the piece-wise constant course of the respective Ko-state, the problem can be solved with a recursive algorithm that divides the horizon into segments at the points where the violation of the energy storage limits with a constant ψ _s in the segment is greatest. From this, for example, a piecewise constant Ko-state follows, which can represent the globally optimal solution.

An exemplary algorithm is described below in which the energy storage energy and the travel time can be removed from the optimal control problem by, for example, specifying values for the corresponding Ko states ψ _s and ψ _t . This specification of the co-states ψ _s and ψ _t can clearly be realized by the first stage of the MPC described herein based on an SQP-based algorithm.

According to various embodiments, a higher-level algorithm can solve the ko states by solving a 2-point boundary value problem with segmentation of the horizon. This algorithm is in 5 and 6th exemplified, with the optimal control problem 500p is resolved.

• Minimiere $${\displaystyle \sum _{k=k_0}^{k_{\text{f}}}\left(\mathcal{L}\left(u,x,k\right)+{\psi }_{\text{S}}{f}_{\text{S}}\left(u,x\right)+{\psi }_{\text{t}}{f}_{\text{t}}\left(u,x,k\right)\right)\mathrm{\Delta }\text{s}}$$
  
• unter den Bedingungen $$E_{\text{V}}\left(k+1\right)=E_{\text{V}}\left(k\right)+f_{\text{V}}\left(k\right)\mathrm{\Delta }\text{s}$$
  
  $$x_{\text{d}}\left(k+1\right)=x_{\text{d}}\left(k\right)+u_{\text{d}}\left(k\right)$$
  
  $$x\left(k_0\right)=x_0,$$
  
  $$t\left(N_k\right)\approx t_{\text{f}}$$
  
  $$E_{\text{S}}\left(N_{\text{k}}\right)\approx E_{\text{S}\text{,f}}$$
  
  $$f_{\text{V}}\left(k\right)\in \text{m}\left[{\text{a}}_{\text{min}},{\text{a}}_{\text{max}}\right]$$
  
  $$f_{\text{S}}\left(k\right)\in -\left[{\text{P}}_{\text{Smin}},{\text{P}}_{\text{Smax}}\right]/\sqrt{2E_{\text{V}}\left(k\right)m}$$
  
  $$\stackrel{⌣}{x}\left(k\right)\in \left[{\stackrel{⌣}{x}}_{\text{min}},{\stackrel{⌣}{x}}_{\text{,max}}\right]$$
  
  $$u_{\text{c}}\left(k\right)\in \left[u_{\text{c}\text{,min}}\left(x\right),u_{\text{c}\text{,max}}\left(x\right)\right]$$
  
  $$u_{\sigma },u_g\in \left\{-\mathrm{1,0,1}\right\}$$
  
  wobei die Lösung iterativ erfolgt mit: $$\stackrel{⌣}{x}=\left(E_{\text{V}},x_{\text{d}}\right).$$
  

The optimal control problem 500p can for example be formulated as follows:

• Minimize $${\displaystyle \sum _{k=k_0}^{k_{\text{f}}}\left(\mathcal{L.}\left(u,x,k\right)+{\psi }_{\text{S.}}{f}_{\text{S.}}\left(u,x\right)+{\psi }_{\text{t}}{f}_{\text{t}}\left(u,x,k\right)\right)\mathrm{\Delta }\text{s}}$$
  
• under the conditions $${\mathrm{E.}}_{\text{V}}\left(k+1\right)={\mathrm{E.}}_{\text{V}}\left(k\right)+f_{\text{V}}\left(k\right)\mathrm{\Delta }\text{s}$$
  
  $$x_{\text{d}}\left(k+1\right)=x_{\text{d}}\left(k\right)+u_{\text{d}}\left(k\right)$$
  
  $$x\left(k_0\right)=x_0,$$
  
  $$t\left(N_k\right)\approx t_{\text{f}}$$
  
  $${\mathrm{E.}}_{\text{S.}}\left(N_{\text{k}}\right)\approx {\mathrm{E.}}_{\text{S.}\text{, f}}$$
  
  $$f_{\text{V}}\left(k\right)\in \text{m}\left[{\text{a}}_{\text{min}},{\text{a}}_{\text{Max}}\right]$$
  
  $$f_{\text{S.}}\left(k\right)\in -\left[{\text{P}}_{\text{Smin}},{\text{P}}_{\text{Smax}}\right]/\sqrt{2{\mathrm{E.}}_{\text{V}}\left(k\right)m}$$
  
  $$\stackrel{⌣}{x}\left(k\right)\in \left[{\stackrel{⌣}{x}}_{\text{min}},{\stackrel{⌣}{x}}_{\text{,Max}}\right]$$
  
  $$u_{\text{c}}\left(k\right)\in \left[u_{\text{c}\text{, min}}\left(x\right),u_{\text{c}\text{,Max}}\left(x\right)\right]$$
  
  $$u_{\sigma },u_G\in \left\{-\mathrm{1.0.1}\right\}$$
  
  where the solution is iterative with: $$\stackrel{⌣}{x}=\left({\mathrm{E.}}_{\text{V}},x_{\text{d}}\right).$$
  

The target conditions for travel time and energy storage energy are specified, since each value for the ko states causes exactly one target value for the respective state.

7th illustrates route data as an example 103 with a predefined gradient and a predefined speed limit curve.

8th illustrates a diagram as an example 800 , which represents the solution quality relative to the calculation effort of the PMP-DP for a predefined route and a corresponding discretization Δs of the route.

With the aim of further reducing the computational effort to solve the optimal control problem, the optimal control problem is formulated below as a quadratic problem (QP). By solving the QP in an SQP scheme, for example, the linearization error caused by approximations can be kept low.

• Minimiere $$f_0\left(\tilde{x}\right)$$
  
• unter den Bedingungen $$f_i\left(\tilde{x}\right)\le 0$$
  
  $$h_j\left(\tilde{x}\right)=0$$
  
  $$\tilde{x}\in C.$$
  
  wobei die Zustände x̃ in der konvexen Menge C liegen müssen.

For the SQP, the optimal control problem can be formulated as follows:

• Minimize $$f_0\left(\tilde{x}\right)$$
  
• under the conditions $$f_i\left(\tilde{x}\right)\le 0$$
  
  $$H_j\left(\tilde{x}\right)=0$$
  
  $$\tilde{x}\in \mathrm{C.}.$$
  
  where the states x̃ must lie in the convex set C.

For example, integer states cannot be considered in a QP, which is why the start / stop system and the gear selection of the transmission are removed from the mixed-integer problem. For this purpose, the internal combustion engine is assumed to be switched on permanently (σ = 1) and a gear change is assumed to be instantaneously without penalty term g.

These assumptions make it possible, for example, to select the gear in advance, so that fuel consumption is minimal when the internal combustion engine is operated only (that is, neglecting the influence of the electric motor). For this purpose, for example, instead of the consumption map of the internal combustion engine, a corresponding map can be created for the internal combustion engine-transmission unit, which generates the drive force F̃ _{E, W} on the wheels. 9 illustrates an example of a map 900 (eg a fuel consumption map) for the internal combustion engine-transmission unit for a fuel-optimized gear selection. The map 900 was approximated, for example, by an analytical function.

wobei die Kosten als quadratische konvexe Funktion ausgedrückt sein können.The quality measure can then be formulated as follows: $$\begin{array}{l}J\left(\tilde{t},{\widetilde{\mathrm{E.}}}_{\text{V}},{\widetilde{\mathrm{F.}}}_{\text{E.}\text{, W}},{\widetilde{\mathrm{E.}}}_{\text{S.}}\right)={\kappa }_{\mathrm{E.}\mathrm{S.}}\left({\widetilde{\mathrm{E.}}}_{\text{S0}}-{\widetilde{\mathrm{E.}}}_{\text{S.}}\left(s_{\text{f}}\right)\right)+{\kappa }_{\text{E.}}{\displaystyle {\int }_{s_0}^{s_{\text{f}}}\frac{{\tilde{P}}_{\text{E.}}}{v}\text{d}s}\\ ={\kappa }_{\text{S.}}\left({\widetilde{\mathrm{E.}}}_{\text{S0}}-{\widetilde{\mathrm{E.}}}_{\text{S.}}\left(s_{\text{f}}\right)\right)+{\kappa }_{\mathrm{E.}}{\zeta }_0{\displaystyle {\int }_{s_0}^{s_{\text{f}}}\frac{1}{v}\text{d}s+{\kappa }_{\text{E.}}{\zeta }_1{\displaystyle {\int }_{s_0}^{s_{\text{f}}}\text{d}s}}\\ +{\kappa }_{\text{E.}}\sqrt{\frac{m}{2}}{\displaystyle {\int }_{s_0}^{s_{\text{f}}}\left({\zeta }_2{\widetilde{\mathrm{E.}}}_{\text{V}}+{\zeta }_3{\widetilde{\mathrm{F.}}}_{\text{E.}\text{, W}}+{\zeta }_{\mathrm{4th}}{\widetilde{\mathrm{F.}}}_{\text{E.}\text{, W}}^2+{\zeta }_5{\widetilde{\mathrm{E.}}}_{\text{V}}^2\right)\text{d}s}\\ ={\kappa }_{\text{S.}}\left({\widetilde{\mathrm{E.}}}_{\text{S0}}-{\widetilde{\mathrm{E.}}}_{\text{S.}}\left(s_{\text{f}}\right)\right)+{\kappa }_{\text{E.}}{\zeta }_0\left(\tilde{t}\left(s_{\text{f}}\right)-{\tilde{t}}_0\right)+{\kappa }_{\text{E.}}{\zeta }_1\left(s_{\text{f}}-s_0\right)\\ +{\kappa }_{\text{E.}}\sqrt{\frac{m}{2}}{\displaystyle {\int }_{s_0}^{s_{\text{f}}}\left({\zeta }_2{\widetilde{\mathrm{E.}}}_{\text{V}}+{\zeta }_3{\widetilde{\mathrm{F.}}}_{\text{E.}\text{, W}}+{\zeta }_{\mathrm{4th}}{\widetilde{\mathrm{F.}}}_{\text{E.}\text{, W}}^2+{\zeta }_5{\mathrm{E.}}_{\text{V}}^2\right)\text{d}s},\end{array}$$

where the cost can be expressed as a quadratic convex function.

The maximum force which the internal combustion engine-transmission unit delivers to the wheels can be a strongly non-linear and piecewise discrete function. This can be taken into account, for example, by performing a piecewise non-linear inner approximation, e.g. in the form: $${\widetilde{\mathrm{F.}}}_{\text{E.}\text{, Wmax}}=\text{min}\left(\begin{array}{l}{\zeta }_{\text{W.}\text{,1}}+{\zeta }_{\text{W.}\text{, 2}}{\widetilde{\mathrm{E.}}}_{\text{V}},\hfill \\ {\zeta }_{\text{W.}\text{, 3}},\hfill \\ {\zeta }_{\text{W.}\text{, 4}}+{\zeta }_{\text{W.}\text{, 5}}/\sqrt{{\widetilde{\mathrm{E.}}}_{\text{V}}}\hfill \end{array}\right)$$

sowie die untere Grenze $${\tilde{F}}_{\text{M}\text{,Wmin}}=\text{max}\left(\begin{array}{l}{\zeta }_{\text{M}\text{,4}}\hfill \\ {\zeta }_{\text{M}\text{,5}}+{\zeta }_{\text{M}\text{,6}}/\sqrt{{\tilde{E}}_{\text{V}}}\hfill \end{array}\right)$$

können beispielsweise mit zwei Teilstücken approximiert werden.The electric motor can also be combined with the transmission to form a unit. The upper limit of the power of this EM gear unit $${\widetilde{\mathrm{F.}}}_{\text{M.}\text{, Wmax}}=\text{min}\left(\begin{array}{l}{\zeta }_{\text{M.}\text{,1}}\hfill \\ {\zeta }_{\text{M.}\text{, 2}}+{\zeta }_{\text{m}\text{, 3}}/\sqrt{{\widetilde{\mathrm{E.}}}_{\text{V}},}\hfill \end{array}\right)$$

as well as the lower limit $${\widetilde{\mathrm{F.}}}_{\text{M.}\text{, Wmin}}=\text{Max}\left(\begin{array}{l}{\zeta }_{\text{M.}\text{, 4}}\hfill \\ {\zeta }_{\text{M.}\text{, 5}}+{\zeta }_{\text{M.}\text{, 6}}/\sqrt{{\widetilde{\mathrm{E.}}}_{\text{V}}}\hfill \end{array}\right)$$

can for example be approximated with two parts.

An energy storage force F̃ _S = P _S / v can also be defined corresponding to the forces for the internal combustion engine-transmission unit and the electric motor-transmission unit, which can be understood as a longitudinal force that acts on the vehicle when drive power is drawn from the energy storage unit.

As a result, the electrical power balance can be described as a balance of forces by modeling the energy store with a constant efficiency for charging η _{s, chr} and discharging η _{S, dis,} e.g. as follows: $${\widetilde{\mathrm{F.}}}_{\text{S.}}\ge \text{Max}\left(\begin{array}{l}{\widetilde{\mathrm{F.}}}_{\text{M.}\text{, W}}/\left({\eta }_{\text{M.}\text{, mot}}{\eta }_{\text{G}}{\eta }_{\text{S.}\text{, dis}}\right),\hfill \\ {\widetilde{\mathrm{F.}}}_{\text{M.}\text{, W}}{\eta }_{\text{M.}\text{,gene}}{\eta }_{\text{G}}{\eta }_{\text{S.}}\text{chr}\hfill \end{array}\right).$$

In addition to the energy storage force, a further control signal, z, can be used, for example, to form the state differential equation as follows: $$\begin{array}{l}\tilde{t}\text{'}=z\\ z\ge 1/\sqrt{2{\widetilde{\mathrm{E.}}}_{\text{V}}/\text{m}}.\end{array}$$

The nonlinear control signal, z, can for example be approximated by means of two affine parts: $$\tilde{z}\ge \text{Max}\left(\begin{array}{l}{\zeta }_{\text{t}\text{,1}}+{\zeta }_{\text{t}\text{, 2}}{\widetilde{\mathrm{E.}}}_{\text{V}},\hfill \\ {\zeta }_{\text{t}\text{, 3}}+{{\rm Z}}_{\text{t}\text{, 3}}{\widetilde{\mathrm{E.}}}_{\text{V}}\hfill \end{array}\right),$$

The resulting optimal control problem can thus have linear state differential equations, e.g. as follows: $$\begin{array}{l}{\mathrm{E.}}_{\text{S.}}^{\text{'}}=-{\widetilde{\mathrm{F.}}}_{\text{S.}}\\ {\widetilde{\mathrm{E.}}}_{\text{V}}^{\text{'}}={\widetilde{\mathrm{F.}}}_{\text{M.}\text{, W}}+{\widetilde{\mathrm{F.}}}_{\text{E.}\text{, W}}-{\widetilde{\mathrm{F.}}}_{\text{B.}}-2{\text{c}}_{\text{a}}{\widetilde{\mathrm{E.}}}_{\text{V}}/\text{m}-c_{\alpha }\\ \tilde{t}\text{'}=\tilde{z}.\end{array}$$

By means of linearization around a reference trajectory eine _V , a convex inner approximation can be formulated as follows: $$1/\sqrt{\widetilde{\mathrm{E.}}}\approx f_{\text{lin}}\left({\widetilde{\mathrm{E.}}}_{\text{V}},{\overline{\widetilde{\mathrm{E.}}}}_{\text{V}}\right).$$

The model is therefore fully approximated by quadratic functions, which enables the development of an SQP.

• minimiere $$J\left(\tilde{x}\left(\tilde{k}\right),\tilde{u}\left(\tilde{k}\right)\right)+Q\left(\tilde{x}\left(\tilde{k}\right),\tilde{u}\left(\tilde{k}\right)\right)$$
  
• unter den Bedingungen $$\tilde{x}\left(\tilde{k}+1\right)=A\left(\tilde{k}\right)\tilde{x}\left(\tilde{k}\right)+B\left(\tilde{k}\right)\tilde{u}\left(\tilde{k}\right)+w\left(\tilde{k}\right)$$
  
  $$C\left(\tilde{k}\right)\tilde{x}\left(\tilde{k}\right)+D\left(\tilde{k}\right)\tilde{u}\left(\tilde{k}\right)\le \mathbf{b}\left(\tilde{k}\right)$$
  
  $$\begin{array}{cc}\tilde{x}\left(0\right)={\tilde{x}}_0,& \tilde{t}\left(N_k\right)<={\tilde{t}}_{\text{f}}\end{array}$$
  
  $$\begin{array}{cc}\tilde{x}\left(\tilde{k}\right)\in \left[{\tilde{\text{x}}}_{\text{min}}\left(\tilde{k}\right),{\tilde{x}}_{\text{max}}\left(\tilde{k}\right)\right],& \tilde{u}\left(\tilde{k}\right)\in \left[{\tilde{u}}_{\text{min}}\left(\tilde{k}\right),{\tilde{u}}_{\text{max}}\left(\tilde{k}\right)\right].\end{array}$$
  

For this purpose, the state vector x̃ = (Ẽ _S , E _V , t̃) and the control vector ũ = (F̃ _{E, W} , F _{M, W} , F̃ _B , F̃ _S , z̃) are defined as described above and s, analogously as for the DP and PMP-DP described, discretized with instantaneous value sampling. Consequently, the QP that is solved in each SQP iteration can be described as follows:

• minimize $$J\left(\tilde{x}\left(\tilde{k}\right),\tilde{u}\left(\tilde{k}\right)\right)+Q\left(\tilde{x}\left(\tilde{k}\right),\tilde{u}\left(\tilde{k}\right)\right)$$
  
• under the conditions $$\tilde{x}\left(\tilde{k}+1\right)=\mathrm{A.}\left(\tilde{k}\right)\tilde{x}\left(\tilde{k}\right)+\mathrm{B.}\left(\tilde{k}\right)\tilde{u}\left(\tilde{k}\right)+w\left(\tilde{k}\right)$$
  
  $$\mathrm{C.}\left(\tilde{k}\right)\tilde{x}\left(\tilde{k}\right)+\mathrm{D.}\left(\tilde{k}\right)\tilde{u}\left(\tilde{k}\right)\le \mathbf{b}\left(\tilde{k}\right)$$
  
  $$\begin{array}{cc}\tilde{x}\left(0\right)={\tilde{x}}_0,& \tilde{t}\left(N_k\right)<={\tilde{t}}_{\text{f}}\end{array}$$
  
  $$\begin{array}{cc}\tilde{x}\left(\tilde{k}\right)\in \left[{\tilde{\text{x}}}_{\text{min}}\left(\tilde{k}\right),{\tilde{x}}_{\text{Max}}\left(\tilde{k}\right)\right],& \tilde{u}\left(\tilde{k}\right)\in \left[{\tilde{u}}_{\text{min}}\left(\tilde{k}\right),{\tilde{u}}_{\text{Max}}\left(\tilde{k}\right)\right].\end{array}$$
  

The matrices A, B, C, D and the vectors w, b, x̃ _min , x̃ _max can be set up as described above. These matrices and vectors depend, for example, on k̃, since the slope and the limits of Ẽ _V and the approximation of zhängen depend on the path. The distance between two sample values does not have to be constant and can be adapted depending on the reference speed, eg a coarser sample can be used for higher speeds.

According to various embodiments, the SQP and the PMP-DP can be or will be implemented as a pure control method. In order to include model deviations, a simulation model can be used that is based on the control model described above and supplemented by further dynamics. These additional dynamics cause, for example, a discrepancy between the control and simulation model, which is why a pure control that calculates the states with the aid of the control model causes an error in the prediction of the states that arise in the simulation model.

Due to the discrepancy between reality and the control model, it can be helpful to update the specifications for the control variables with a comparatively high frequency (eg with more than 0.5 Hz). For this purpose, the two-stage MPC described here can be used, which as an energy management strategy with efficient longitudinal guidance online in the hybrid electric vehicle 200 can be used. The division of tasks between the upper (high-level MPC) and lower (low-level MPC) level is in 10 illustrated schematically.

The route data 103 (e.g. trajectories for gradient, minimum and maximum kinetic energy) can be used as well as the current system states. The first (upper) MPC stage can be set up, for example, in such a way that the general tendency of the energy storage energy and the trajectory of the travel time to the end of the route are determined. The second (lower) MPC stage can for example be set up in such a way that, based on the trajectories determined by the first stage Objectives for a shorter forecast horizon can be determined and thus the control parameters including the discrete decisions can be determined with a higher level of detail.

In the second (low-level) MPC stage, for example, the horizon can be divided into sections that are short enough to be calculated, for example, by means of PMP-DP in a predefined time (eg in less than 1 s). The problem can be solved, for example, in sections, that is to say by continuously optimizing short forecast horizons, so that it is helpful, for example, to specify values for the desired target time and target energy storage energy for the respective section. Target conditions are specified, for example, by the first (high-level) MPC stage, which the energy management calculates for a horizon that extends to the end of the route. The results of the first MPC stage, optimized for example, are used to determine the target values for the energy storage energy Ẽ _{s, f} and the target time t̃ _f for the limited forecast horizon of the second MPC stage. Both the first and the second MPC stage can, according to various embodiments, take into account the current system states, which are returned as start states. The update rate of the current system states can be adapted to the duration of the iterations. Additional input signals can be, for example, as already described, the trajectories of the gradient (α) and the speed limits (E _Vmin and E _Vmax ) for the current route.

According to various embodiments, comparatively long forecast horizons can be calculated in the first MPC stage, which can be particularly desirable for the sensible use of high-capacity energy storage devices such as plug-in hybrid vehicles, so that the horizon extends to the end of the route. Such an MPC can be very computational. Therefore, according to various embodiments, an SQP scheme can be used for this. The SQP scheme can be implemented as a real-time iteration. For example, the real-time iteration can take advantage of the iterative nature of the MPC by spreading the SQP iterations over the MPC updates. According to various embodiments, only one QP can be solved each time the MPC is updated, which reduces the calculation effort and enables the use of a conventional QP solver.

The second MPC level below can be used to calculate shorter forecast horizons than with the first MPC level. This allows the PMP-DP to be used to calculate the actual control, which promises a significantly higher quality of the solution, since the discrete states and control variables are also optimized and can be calculated with a non-convex model.

In order to follow the objectives of the first MPC stage (MPC-1), the algorithm of the second MPC stage (MPC-2) can be set up, for example, in such a way that a 2-point boundary value problem is solved by ψ _s and ψ _t respectively determine. For example, the bisection can be used as a single shooting method. For example, the single-shot process is performed while the hybrid electric vehicle is on 200 moved. For this purpose, the MPC is shot once with a fixed value for ψ _s and ψ _t with each iteration, whereby a prediction of the states at the end of the short horizon of the second MPC stage (MPC-2) can be calculated. For the next shot of the single-shot method, for example, the deviation of this prediction from the state specifications of the first MPC stage (MPC-1) can be saved and used the next time the second MPC stage (MPC-2) is called to either ψ _s or ψ _t Help adjust the bisection. For example, if ψ _{t was} adjusted in the last iteration, a new value for ψ _s can be determined, and vice versa.

11 shows the second MPC stage (MPC-2) of the control device 100 in a schematic representation, according to various embodiments.

For example, the second MPC stage (MPC-2) can have a non-linear proportional controller (NPR), for example in order to avoid possible violations of the energy storage limits. By means of the non-linear proportional controller (NPR), for example, a new value for the Ko-state zustand _{S, lim} can be determined, which, for example, can guarantee realizable control in the PMP-DP. For this purpose, the non-linear proportional controller (NPR) receives the value for ψ _s from the single-shot process block (EVB) as well as the current charge / discharge status and the energy storage limits. If the charge / discharge state of the energy store is, for example, close to its lower limit, W _{S, lim is} increased, thus forcing the energy store to be charged, and vice versa. This controller behavior can be achieved by implementing a tangent function 1200 , such as in 12 shown, can be realized.

In the following, various examples are described which relate to what has been described above and what is shown by way of example in the figures.

Example 1 is a method for regulating a drive system of a hybrid vehicle, the method comprising: determining auxiliary optimization data based on a first model by means of a first optimization method, the first model having: a first continuous state parameter, which indicates a charge / discharge state of a Energy storage of the drive system represents, a second continuous state parameter which represents a travel time, a first control parameter set which represents continuous control variables of the drive system, and wherein the auxiliary optimization data represent a course of the first state parameter and the second state parameter assigned to a predefined route, wherein the The first optimization method has sequential quadratic programming for determining the auxiliary optimization data based on route data and actual control variable data, taking into account the er first and second continuous state parameters and the first control parameter set; Determining default control variable data based on a second model by means of a second optimization method, the second model having: a first state parameter which represents the charge / discharge state of the energy store, a second state parameter which represents the driving time, a first control parameter set , which represents the continuous control variables of the drive system, and a second set of control parameters, which represents discrete control variables of the drive system, the default control variable data representing a default course of the continuous control variables and the discrete control variables of the drive system for part of the predefined route, wherein the second optimization method has dynamic programming using the Pontryagin maximum principle, and using the determined auxiliary optimization data, target values for the first state parameter and the second Zu state parameters of the second model are determined for the part of the predefined route to determine the default control variable data based on the route data, the actual control variable data and the determined auxiliary optimization data, taking into account the first and second continuous state parameters and the first and second set of control parameters; and outputting the default control variable data for operating the drive system based on the output default control variable data.

In example 2, the method according to example 1 can furthermore have the route data representing at least one predefined gradient profile and a predefined speed limit profile assigned to the predefined route.

In example 3, the method according to example 1 or 2 can furthermore have the actual control variable data representing a respective actual state of the control variables of the first and second control variable sets.

In example 4, the method according to one of examples 1 to 3 can further include that at least one control parameter of the second control parameter set is not optimized in the first optimization method.

In example 5, the method according to one of examples 1 to 4 can furthermore have a horizon up to the end of the journey being taken into account in the first optimization method, preferably up to a horizon of more than 50 km.

In example 6, the method according to one of examples 1 to 5 can furthermore have a horizon of less than 10 km, preferably of less than 5 km, being taken into account in the second optimization method.

In example 7, the method according to one of examples 1 to 6 can furthermore have that the first optimization method has an update interval in a range from 10 s to 300 s.

In example 8, the method according to one of examples 1 to 7 can furthermore have that the first optimization method has a discretization of the horizon in a range from 1 m to 100 m, preferably less than 50 m.

In example 9, the method according to one of examples 1 to 8 can furthermore have that the second optimization method has an update interval in a range from 0.01 s to 5 s, preferably less than 1 s.

In example 10, the method according to one of examples 1 to 9 can furthermore have that the second optimization method has a discretization of the horizon in a range from 10 m to 100 m, preferably less than 100 m.

In example 11, the method according to one of examples 1 to 10 can furthermore have that the second optimization method has a quantization of the acceleration in a range from 0.1 m / s ² to 1 m / s ² , preferably less than 1 m / s ² .

In example 12, the method according to one of examples 1 to 11 can further comprise that the first control parameter set has one or more control parameters that represent one or more of the following continuous control variables: torque or force of an internal combustion engine of the drive system; Torque or power of an electric motor of the drive system; Torque or force of a braking system of the drive system.

In example 13, the method according to one of examples 1 to 12 can further include that the second control parameter set has one or more control parameters that represent one or more of the following discrete control variables: state of a start / stop system of an internal combustion engine of the drive system; State of a transmission in the drive system.

In example 14, the method according to one of examples 1 to 13 can further comprise that the control parameters of the second control parameter set are integer and wherein the control parameters of the first control parameter set are non-integer, preferably fractional-rational.

In example 15, the method according to one of examples 1 to 14 can further include that the first and the second optimization method are carried out by means of a computing system, the computing system having a computing power of less than 100 TFLOPS.

In example 16, the method according to one of examples 1 to 15 can furthermore have that the second optimization method has a non-linear proportional controller for taking into account energy storage limits of the energy storage.

In example 17, the method according to one of examples 1 to 16 can further include that the second optimization method is set up such that a 2-point boundary value problem is solved, the auxiliary optimization data representing target values for the 2-point boundary value problem.

In example 18, the method according to one of examples 1 to 17 can furthermore have the auxiliary optimization data representing target specifications for the charge / discharge state of the energy store and the driving time based on a section of the predefined driving route taken into account in the second optimization method.

Example 19 is a control device ( 100 ) to control a drive system ( 202 ) of a hybrid vehicle ( 200 ), where the control device ( 100 ) is set up: Route data ( 103 ), whereby the route data ( 103 ) represent a predefined gradient curve and a predefined speed limit curve assigned to a predefined route; Actual control variable data ( 105i ), whereby the actual control variable data ( 105i ) an actual state of at least one continuous control variable of the drive system ( 202 ) and at least one discrete control variable of the drive system ( 202 ) represent; based on a first model (M1) using a first optimization method (OPT1) auxiliary optimization data ( 105h ), wherein the first model (M1) has: a first state parameter which defines a charge / discharge state of an energy store ( 216 ) of the drive system ( 202 ) represents a second state parameter, which represents a travel time (t), and at least one first control parameter, which the at least one continuous control variable of the drive system ( 202 ), and where the auxiliary optimization data ( 105h ) represent a course of the first state parameter and the second state parameter, the first optimization method (OPT1) having sequential quadratic programming (SQP); based on a second model (M2) by means of a second optimization method (OPT2) default control variable data ( 105s ), wherein the second model (M2) has: a first state parameter, which the charge / discharge state of the energy store ( 216 ) represents a second state parameter which represents the driving time (t), at least one first control parameter which the at least one continuous control variable of the drive system ( 202 ) represents, and at least one second control parameter, which the at least one discrete control variable of the drive system ( 202 ), and where the default control variable data ( 105s ) a specification curve of the at least one first control variable and the at least one second control variable of the drive system ( 202 ) represent for a respective section of the predefined route, the second optimization method (OPT2) having dynamic programming (DP) using the Pontryagin maximum principle (PMP), and using the determined auxiliary optimization data ( 105h ) Target values for the first state parameter and the second state parameter of the second model (M2) are determined for the respective partial route; and the default control variable data ( 105s ) output to operate the drive system ( 202 ) based on the output specification control variable data ( 105s ).

Example 20 is a method for regulating a drive system of a hybrid vehicle, the method comprising: determining auxiliary optimization data based on a first model by means of a first optimization method, the first optimization method having sequential quadratic programming for determining the auxiliary optimization data based on route Data and actual control variable data taking into account parameters which represent the drive system of the hybrid drive vehicle, and wherein the auxiliary optimization data represent a course of a subset of the parameters assigned to a predefined route; Determination of default control variable data based on a second model by means of a second optimization method, the default control variable data representing a default curve of control variables of the drive system for a section of the predefined route, the second optimization method being dynamic programming using the Pontryagin's maximum principle, and based on the determined auxiliary optimization data, target values for one or more parameters of the second model for the section are determined to determine the default control variable data based on the route data, the actual control variable data taking into account parameters which represent the drive system of the hybrid drive vehicle; and outputting the default control variable data for operating the drive system based on the output default control variable data.

Example 21 is a non-volatile storage medium having instructions which, executed by at least one processor, execute the method for regulating a drive system of a hybrid electric vehicle according to one of Examples 1 to 18 or 20.

It goes without saying that functions, algorithms, etc. which are described herein with reference to a method can also be implemented in the same way in a control device and vice versa.

Claims (10)

Method for controlling a drive system of a hybrid vehicle, the method comprising: Determination of auxiliary optimization data based on a first model by means of a first optimization method, the first model having: a first continuous state parameter which represents a charge / discharge state of an energy store of the drive system, a second continuous state parameter which represents a travel time, a first control parameter set which represents continuous control variables of the drive system, and wherein the auxiliary optimization data represent a course of the first state parameter and the second state parameter assigned to a predefined route, wherein the first optimization method has sequential quadratic programming to determine the auxiliary optimization data based on Route data and actual control variable data taking into account the first and second continuous state parameters and the first control parameter set; Determination of default control variable data based on a second model by means of a second optimization method, the second model having: a first state parameter which represents the charge / discharge state of the energy store, a second state parameter which represents the driving time, a first control parameter set, which represents the continuous control variables of the drive system, and a second control parameter set, which represents discrete control variables of the drive system, the default control variable data representing a default course of the continuous control variables and the discrete control variables of the drive system for part of the predefined route, the second optimization method having dynamic programming using the Pontryagin maximum principle , and with the aid of the determined auxiliary optimization data, target values for the first state parameter and the second state parameter of the second model for the part of the predefined route are determined to determine the default control variable data based on the route data, the actual control variable data and the determined auxiliary optimization data taking into account the first and second continuous state parameters and the first and second control parameter sets; and o Outputting the default control variable data for operating the drive system based on the output default control variable data. Procedure according to Claim 1 , wherein the route data represent at least one predefined gradient curve and a predefined speed limit curve assigned to the predefined route. Procedure according to Claim 1 or 2 , wherein the actual control variable data represent a respective actual state of the control variables of the first and second control variable sets. Method according to one of the Claims 1 to 3 wherein at least one control parameter of the second control parameter set is not optimized in the first optimization method. Method according to one of the Claims 1 to 4th , wherein the first control parameter set has one or more control parameters which represent one or more of the following continuous control variables: torque or force of an internal combustion engine of the drive system; • Torque or power of an electric motor of the drive system; • Torque or force of a braking system of the drive system; and wherein the second control parameter set has one or more control parameters which represent one or more of the following discrete control variables: state of a start / stop system of an internal combustion engine of the drive system; • State of a gearbox in the drive system. Method according to one of the Claims 1 to 5 wherein the control parameters of the second control parameter set are integers and wherein the control parameters of the first control parameter set are non-integer, preferably fractional-rational. Method according to one of the Claims 1 to 6th , wherein the auxiliary optimization data represent target specifications for the charge / discharge status of the energy store and the driving time based on a section of the predefined driving route taken into account in the second optimization method, and / or the second optimization method is set up in such a way that a 2-point Boundary value problem is solved, the auxiliary optimization data representing target specifications for the 2-point boundary value problem. Control device (100) for controlling a drive system (202) of a hybrid vehicle (200), wherein the control device (100) is set up: To receive route data (103), the route data (103) having a predefined gradient and a predefined Represent speed limit profile assigned to a predefined route; o receive actual control variable data (105i), the actual control variable data (105i) representing an actual state of at least one continuous control variable of the drive system (202) and at least one discrete control variable of the drive system (202); o to determine auxiliary optimization data (105h) based on a first model (M1) by means of a first optimization method (OPT1), the first model (M1) having: a first state parameter, which indicates a charge / discharge state of an energy store (216 ) of the drive system (202) represents, • a second state parameter, which represents a travel time (t), and • at least one first control parameter, which represents the at least one continuous control variable of the drive system (202), and wherein the auxiliary optimization data (105h) represent a course of the first state parameter and the second state parameter, the first optimization method (OPT1) having sequential quadratic programming (SQP); o to determine default control variable data (105s) based on a second model (M2) by means of a second optimization method (OPT2), the second model (M2) having: a first state parameter, which indicates the charge / discharge state of the energy store (216) represents • a second state parameter which represents the driving time (t), • at least one first control parameter which represents the at least one continuous control variable of the drive system (202), and • at least one second control parameter which the at least one discrete control variable of the drive system (202) represents, and the default control variable data (105s) representing a default course of the at least one first control variable and the at least one second control variable of the drive system (202) for a respective section of the predefined route, the second optimization method (OPT2) being dynamic programming ( DP) using the Pontryagin maximum principle (PMP), and wherein target values for the first state parameter and the second state parameter of the second model (M2) for the respective section are determined by means of the determined auxiliary optimization data (105h); and o output the default control variable data (105s) for operating the drive system (202) based on the output default control variable data (105s). Method for controlling a drive system of a hybrid vehicle, the method comprising: Determination of auxiliary optimization data based on a first model by means of a first optimization method, the first optimization method having sequential quadratic programming to determine the auxiliary optimization data based on route data and actual control variable data, taking into account parameters that the drive system of the hybrid drive vehicle, and wherein the auxiliary optimization data represent a course of a subset of the parameters assigned to a predefined route; o Determination of default control variable data based on a second model by means of a second optimization method, the default control variable data representing a default course of control variables of the drive system for a section of the predefined route, the second optimization method using dynamic programming of the Pontryagin maximum principle, and based on the determined auxiliary optimization data, target values for one or more parameters of the second model for the section are determined to determine the default control variable data based on the route data, the actual control variable Data taking into account parameters representing the drive system of the hybrid drive vehicle; and o Outputting the default control variable data for operating the drive system based on the output default control variable data. Non-volatile storage medium having instructions which, executed by at least one processor, the method for regulating a drive system of a hybrid electric vehicle according to one of Claims 1 to 7th or 9 To run.

Images