Method for calculating parameterization of regulator of technical system

Abstract

The invention relates to a method for parameterizing a regulator of a computing technical system, comprising the steps of:-determining a characteristic of the regulator, where the characteristic comprises at least a description of a structure of the regulator and at least one differential equation, to map a dynamic behavior of the technical system using the differential equation, defining an objective function, the objective function being based on at least one requirement for a safety characteristic and / or a performance characteristic of the regulator and / or the technical system, establishing an optimization problem, the optimization problem being established based on the objective function and at least one additional condition, wherein at least one limit of at least one state of the technical system is ensured by the at least one additional condition,-calculating a parameterization of the regulator on the basis of the determined optimization problem. The invention also relates to a regulator, a computer program, a device and a storage medium for this purpose.

Description

Technical Field

[0001] The invention relates to a method for calculating parameterization of a controller of a technical system and also to a controller, a computer program, a device and a storage medium for this purpose. Background Art

[0002] The current process for calibrating regulators, in particular for automated driving functions, relies heavily on manual parameter settings. However, this approach not only requires extensive expertise, but also does not provide a priori guarantees that performance and safety standards are met. Verification of these standards is mostly done ex post facto through complex simulations and test drives, which are both time-consuming and costly. These manual calibration methods lack standardized, systematic optimization methods if the initially selected calibration does not meet performance and / or safety requirements. In this case, it is necessary to hire experienced experts who must re-calibrate with similar resource expenditure. Only in this way can compliance with performance and safety requirements be empirically verified again.

[0003] There are various methods for parameterizing controllers (e.g. the Ziegler-Nichols method for parameterizing PID controllers). These widespread methods often need to be implemented step by step in real systems, which involves costs and expenditures. In addition, some require specialized knowledge of the application and regulation. Some methods cannot be applied to multivariable systems at all. In addition to good performance (e.g. driver comfort or good guidance behavior), safety is also a core aspect of automated driving functions. This means that the regulation deviation must not exceed certain thresholds, for example to ensure that the vehicle does not leave the lane and thus does not collide. This requirement is not explicitly taken into account in classic parameterization methods and must be demonstrated by complex simulations and test drives. Therefore, parameterization in the prior art is only carried out, for example, by actual trials on real technical systems. Summary of the invention

[0004] The subject matter of the invention is a method with the features of claim 1, a controller with the features of claim 10, a computer program with the features of claim 11, a device with the features of claim 12 and a computer-readable storage medium with the features of claim 13. Further features and details of the invention are derived from the corresponding dependent claims, the description and the drawings. Features and details described in conjunction with the method according to the invention naturally also apply to the controller according to the invention, the computer program according to the invention, the device according to the invention and the computer-readable storage medium according to the invention, and vice versa, so that the disclosure of the various aspects of the invention is or can be referred to one another.

[0005] The subject matter of the invention is in particular a method for parameterizing a controller of a computational system, comprising the following steps, wherein the steps can be performed repeatedly and / or sequentially.

[0006] In a first step, the characteristics of the controller are preferably determined, wherein the characteristics include at least a description of the structure of the controller and at least one differential equation in order to map the dynamic behavior of the technical system using the differential equation. Preferably, at least one differential equation is assigned data, i.e. in particular specific values ​​are provided for which an identification method can be performed in order to identify the parameters of the at least one differential equation. For this purpose, the technical system can be stimulated, for example, by an excitation signal, in order to subsequently perform a measurement on or by the technical system.

[0007] In a further step, an objective function is preferably defined, wherein the objective function is based on at least one requirement for a safety characteristic and / or a performance characteristic of the regulator and / or the technical system. In the context of the present invention, a safety characteristic may also be referred to and understood as a safety requirement. The safety characteristic relates, for example, to the safety of a user of the technical system. For example, if the technical system is configured as a vehicle, the safety may be vehicle safety. In the context of the present invention, a performance characteristic may also be referred to and understood as a performance requirement. The performance characteristic may, for example, predetermine the type of regulation, whereby regulators may be provided with different properties, for example, in terms of performance, robustness, aggressiveness, comfort, optimization, guidance behavior and interference variable suppression.

[0008] In a further step, an optimization problem is preferably established, wherein the optimization problem is established based on the objective function and at least one additional condition, wherein at least one limitation of at least one state of the technical system is ensured by the at least one additional condition. Establishment can also be understood as determination of the optimization problem. The optimization problem can also be referred to and understood as an optimization task. In other words, limitations should be used to ensure that at least one state of the technical system does not exceed a certain threshold value. This threshold value can be predetermined by requirements or can be determined within the scope of the optimization. By means of limitations, the robustness of the control to disturbances can advantageously be ensured.

[0009] In a further step, the parameterization of the controller is preferably calculated based on the optimization problem created. Various optimization methods known from the prior art can be used for this purpose.

[0010] Thus, the method advantageously allows efficient parameterization of the regulator without time-consuming manual calibration routines. Furthermore, at least one requirement for a safety characteristic and / or a performance characteristic can advantageously be taken into account during parameterization.

[0011] Furthermore, within the scope of the invention, at least one state can optionally reflect the time behavior of a corresponding controlled variable of the regulator and in particular specify the current value of the corresponding controlled variable. In the example of a vehicle as a technical system, the controlled variable can be, for example, the yaw angle error of the vehicle.

[0012] By regulating the at least one state by the regulator in such a way that the value of the at least one state remains in an invariant set, a limitation of at least one state of the technical system can be ensured. The invariant set is characterized in particular in that if a state vector is in the invariant set, the subsequent state vector is also in the set. It can thus be advantageously ensured that the regulation error of the at least one state does not exceed a critical threshold value and thus, for example, corresponding requirements for safety properties are ensured.

[0013] Furthermore, it can be provided that the at least one state is controlled by the controller in such a way that, in the case of disturbance variables bounded by a set of ellipsoids or polyhedra, the value of the state remains in an invariant set.

[0014] According to another possibility, it can be provided that the characteristic of the controller also defines the type of limitation of the state of the technical system, wherein the type is preferably based on an ellipsoidal or polyhedral function. Ellipsoidal and polyhedral functions are particularly advantageous for limiting the state of the technical system, and depending on the application, an ellipsoidal or polyhedral function may be more suitable and can be selected accordingly.

[0015] Optionally, it is contemplated that defining the objective function includes the following steps:

[0016] - determining a limit value or a limit range for at least one state based on at least one requirement for a safety property and / or a performance property of the controller and / or the technical system.

[0017] Thus, a specific and application-dependent limit value or limit range can advantageously be set for at least one state, which limit value or limit range should not be exceeded. Thus, a limitation of at least one state can be performed based on a specific limit value or limit range.

[0018] For example, it can be provided that at least one additional condition also defines a threshold value for at least one state and / or at least one input variable of the regulator, wherein the threshold value defined according to the additional condition must not be exceeded. Thus, it is advantageously possible to set a specific and application-dependent threshold value for at least one state or at least one input variable, which threshold value must not be exceeded. This can be ensured by calculating the parameterization based on the optimization problem. Thus, for example, additional states of at least one state and / or additionally at least one input variable can be advantageously taken into account.

[0019] Optionally, it may be provided that establishing the optimization problem may further include the following steps:

[0020] A cost function is defined, wherein within the scope of the calculation parameterization, a weight value is assigned to at least one state by means of the cost function in order to provide a priority of the state.

[0021] This makes it possible, for example, to adjust the controller in an advantageous manner with regard to its aggressiveness or responsiveness. Taking into account the cost function, for example, allows taking comfort into greater account as a performance characteristic in the parameterization of the controller and thereby also influencing the form of the invariant set in particular.

[0022] It is possible that at least one differential equation is a linear differential equation and that the dynamic behavior of the technical system is mapped by a combination of the at least one differential equation with at least one further linear differential equation. A linear differential inclusion can thus be present or implemented.

[0023] Furthermore, it can be provided that the behavior of the controller is determined by taking into account all state values, in particular measured values, in particular providing state feedback, or by taking into account some state values, in particular measured values, in particular providing output feedback.

[0024] Optionally, the method may further include the following steps:

[0025] - Implement parameterized regulators on technical systems.

[0026] The technical system is preferably a vehicle and the regulator is preferably used for lateral and / or longitudinal regulation of the vehicle. Therefore, the method according to the invention can be used in a vehicle. The vehicle can be configured, for example, as a motor vehicle and / or a passenger car and / or an autonomous vehicle. The vehicle can have a vehicle device, for example, for providing an autonomous driving function, and / or with a driver assistance system. The vehicle device can be designed to at least partially automatically control and / or accelerate and / or brake and / or steer the vehicle.

[0027] The subject matter of the invention also relates to a controller for a technical system, wherein the controller is configured to carry out the method according to the invention or to be used within the scope of the method according to the invention.

[0028] The subject of the invention also relates to a computer program, in particular a computer program product, comprising instructions which, when executed by a computer, cause the computer to perform the method according to the invention. The computer program according to the invention thus brings the same advantages as described in detail with reference to the method according to the invention.

[0029] The subject matter of the invention also relates to a device for data processing, which is configured to carry out the method according to the invention. As the device, for example, a computer can be provided which executes the computer program according to the invention. The computer can have at least one processor for executing the computer program. A non-volatile data memory can also be provided, in which the computer program is stored and from which the processor can read the computer program for execution.

[0030] The subject matter of the present invention may also include a computer-readable storage medium having a computer program according to the present invention and / or comprising instructions which, when executed by a computer, cause the computer to perform the method according to the present invention. The storage medium is, for example, configured as a data memory, such as a hard disk drive and / or a non-volatile memory and / or a memory card. The storage medium may, for example, be integrated into a computer.

[0031] In addition, the method according to the present invention can also be implemented as a computer-implemented method. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Further advantages, features and details of the invention emerge from the following description, in which exemplary embodiments of the invention are described in detail with reference to the drawings. The features mentioned in the claims and the description may be essential to the invention individually or in any combination.

[0033] Figure 1 A schematic visualization of a method, a controller 1 , a technical system, an apparatus, a storage medium and a computer program according to an embodiment of the invention is shown,

[0034] Figure 2 A schematic diagram of a structure for lateral adjustment according to an embodiment of the present invention is shown,

[0035] Figure 3 shows a schematic visualization of an ellipsoidal function and a polyhedral function according to an embodiment of the present invention,

[0036] Figure 4 A schematic visualization of a flow chart of a method for parameterizing a controller according to an exemplary embodiment of the present invention is shown. DETAILED DESCRIPTION

[0037] Figure 1 A method 100 , a controller 1 , a technical system 2 , a device 10 , a storage medium 15 and a computer program 20 according to an embodiment of the present invention are schematically shown.

[0038] Figure 1In particular, an embodiment of a method 100 for parameterizing a regulator 1 of a technical system 2 is shown, which method comprises the following steps. In a first step 101, properties of the regulator 1 are determined, wherein the properties include at least a description of the structure of the regulator 1 and at least one differential equation in order to map the dynamic behavior of the technical system 2 using the differential equation. In a second step 102, an objective function is defined, wherein the objective function is based on at least one requirement for safety characteristics and / or performance characteristics of the regulator 1 and / or the technical system 2. In a third step 103, an optimization problem is established, wherein the optimization problem is established based on the objective function and at least one additional condition, wherein at least one restriction of at least one state of the technical system 2 is ensured by the at least one additional condition. In a fourth step 104, the parameterization of the regulator 1 is calculated based on the determined optimization problem.

[0039] In the scope of the invention, in particular, a method is proposed, which parameterizes a regulator 1, such as a lateral control, based on an invariant set. Using a dynamic model of a technical system 2, such as a vehicle, the regulator parameters can be set efficiently without time-consuming manual calibration routines. The maximum control deviations (e.g. lateral errors) for different states of the technical system 2 can be explicitly taken into account here, and safety requirements can therefore be met. In this way, performance requirements can also be taken into account (e.g. avoiding excessive steering angle influences to increase comfort). If there are multiple performance requirements, the priority of these performance requirements can also be determined by weights. The method can be applied in particular to different regulators 1 for which a dynamic model of the technical system 2 can be used.

[0040] The method according to an embodiment of the invention can bring various advantages. The method according to an embodiment in particular allows for efficient parameterization of the regulator 1 without time-consuming manual calibration routines. In addition, the maximum regulation deviation of different states of the system can be explicitly considered, thereby ensuring safety requirements. Disturbance variables and their influence on the technical system 2 can be explicitly considered in the parameterization. Linear differential inclusion (LDI) can be used in the method to explicitly consider model uncertainty. The method according to an embodiment can be applied to, for example, single variable systems (SISO: single input single output) and multivariable systems (MIMO: multiinputmulti output). By means of the method according to an embodiment, the performance of the technical system 2 can be flexibly adapted to different target standards. By minimizing the robust invariant set, the regulator 1 can be parameterized in a way that minimizes the regulation error. By maximizing the robust invariant set while adhering to the maximum regulation error, a less aggressive regulator 1 can be achieved, i.e., for example, a high level of comfort, where safety is still guaranteed. In addition, with the help of a cost function, the individual states and inputs can also be weighted, so that the performance can be set individually.

[0041] For control functions in the field of autonomous driving, the hardware (e.g. sensor systems and actuator systems) and the structure of the control functions are already known, and the controller 1 should be parameterized according to the requirements. In this case, for example, the method proposed according to the embodiment can be used. If, for example, a recalibration of the controller 1 is required due to aging of the technical system 2, the method can also be used on site. The method can also be used as a service for the customer. If the customer is not satisfied with the behavior of the technical system 2, in particular the vehicle, the controller 1 can be recalibrated according to the customer's requirements by means of the method.

[0042] The method is explained below based on the example of a transverse control of a vehicle, in particular an autonomous vehicle. However, the transverse control is only one application example, and the method is not limited to this application example, but can generally be applied to different calibration tasks of the regulator 1 .

[0043] The model for the transverse regulation is preferably derived from a linearized single-track model.

[0044] Here, for example, the following state vector is defined where ψ e is the vehicle’s yaw angle error, β is the vehicle’s sideslip angle, y e is the lateral error of the vehicle, int(y e ) is the integrated lateral error of the vehicle, and δ is the steering angle of the vehicle.

[0045] For lateral adjustment, for example, it can be derived according to Figure 2 The state-space model includes the steering behavior of the steering gear (SRM: steering reference model), the linearized single track model (STM: single track model), the lateral error model (EM: error model) and the regulator 1 (FB: feedback controller).

[0046] In particular, the state-space model is given by:

[0047]

[0048] y=Cx

[0049] The state vector with input variable u = δ*(rated steering angle) The disturbance vector w preferably combines the angle error Δδ, the forces on the vehicle and the torque disturbance F dist 、M dist And the reference trajectory of the yaw angle

[0050] The regulator 1 is thus composed in particular of In general, this may mean not feeding back the complete state vector, but only the output y=Cx. This generally leads to the regulation law

[0051] u=Ky=KCx

[0052] Since the regulation can be carried out on the control unit and the regulator 1 can therefore be implemented in a time-discrete manner, the state space model is preferably discretized for parameterization of the regulator parameters.

[0053] This results in the discretized state space model

[0054] x(k+1)=Ax(k)+Bu(k)+Ew(k)

[0055] y(k)=Cx(k)

[0056] This state space model can be the basis of the method according to an embodiment of the invention. This maps in particular the dynamic behavior of the technical system 2. In addition to physical variables, the state vector x can also contain the state of the regulator 1, for example the integrated transverse error in the case of transverse control. This means, for example, that very different control structures can be introduced into this form, so that the method can be advantageously applied very universally.

[0057] If there are parameter uncertainties, the system can be modeled as a linear difference inclusion (LDI).

[0058] x(k+1)∈{Ax(k)+Bu(k)+Ew(k)|(A,B,E)∈co(Ω)}

[0059] Ω={(A i ,B i ,E i ),i=1,…,q}

[0060] co(Ω) preferably describes an operator of a convex envelope. This means in particular that the parameter uncertainty system matrix A is given by the combination of the vertex matrices

[0061]

[0062] This also applies to the input matrices B and E.

[0063] The object of the invention according to an embodiment may be to provide such a parameterization of the regulator 1 that it can be guaranteed that, for example, the regulation error does not exceed a certain threshold. To this end, the above-mentioned state space model can be designed so that the relevant regulation error appears as a state in the state vector x. For example, one concept that can give such a guarantee is the so-called invariant set. The invariant set M is characterized in particular in that if the starting state vector is in the set x(k)∈M, then the subsequent state vector is also in the set x(k+1)∈M taking into account possible interference variables and model uncertainties. It can thereby be ensured that the regulation error does not exceed a critical threshold, thereby ensuring safety.

[0064] In particular, the invariant set can be described as an ellipsoidal function3 or a polyhedral function4, such as Figure 3 As depicted in , where x1 and x2 are corresponding exemplary states of the technical system 2 .

[0065] The ellipsoid function 3 is specifically described mathematically as:

[0066] ε={x|x T Px≤1}

[0067] With a positive definite matrix P. The polyhedral function 4 can be described as:

[0068] Υ={x|H i x≤1,i∈{1,…,h}}

[0069] Among them, H i x≤1 describes a half-space. Alternatively, a polyhedron can be represented by vertices v i To describe, that is

[0070]

[0071] With vertex space vert(Υ)={v1,…,v p}.

[0072] The basis of the method according to the embodiment is in particular the following condition of robust positive invariance (RPI):

[0073]

[0074] For example, here the conditions for an elliptic robust invariant set are given. This condition means in particular that for every state x(k)∈ε and a finite disturbance variable w(k)∈W that is in the invariant set ε, the state continues to remain in the invariant set ε in all subsequent steps, i.e. x(k+1)∈ε. The set of possible disturbance variables W can be given by an ellipsoid or a polyhedron.

[0075] The condition x(k)∈ε can also be given by:

[0076]

[0077] In addition, for the sake of clarity, the following simplifications have been made:

[0078]

[0079] The following describes a method according to an exemplary embodiment of the present invention, in particular a method for parameterizing the controller 1 using a given structure of the controller 1 .

[0080] Different criteria may be important for parameterizing the controller 1. Six exemplary criteria are presented below, which can be linked to one another depending on the requirements of the control task. It will then be explained how these criteria can be taken into account when determining the controller gain.

[0081] The following criteria can be distinguished. Criterion 1 can be the type of restriction of the disturbance variable (e.g. a polyhedron or an ellipsoid). Criterion 2 can be the guarantee of compliance with state and input restrictions. Criterion 3 can be the consideration of cost functions. Criterion 4 can be the distinction between whether the regulator 1 has output feedback (i.e. u=KCx) or state feedback (i.e. u=Kx). Criterion 5 can be the target variable for the optimal regulator parameterization. Criterion 6 can be the consideration of parameter model uncertainty.

[0082] First, it is preferably assumed that the complete state vector x is fed back, ie u=Kx or C corresponds to the identity matrix.

[0083] Criterion 1: The mathematical conditions listed below allow the controller 1 to be parameterized in such a way that the state vector remains in an invariant set in the event of a disturbance. This ensures the robustness of the control to disturbances.

[0084] In the case of an ellipsoid as limiting disturbance variable, the set of possible disturbance variables w can be given here by:

[0085] W={w|w T Tw≤1}

[0086] The condition x(k+1)∈ε can be transformed into using the difference equation with the ellipsoid as the restricted disturbance variable:

[0087]

[0088] After mathematical transformation, the condition for robust positive invariance can be given by

[0089]

[0090] 1-μ-λ≥0,μ>0,λ>0

[0091] This is in particular a so-called linear matrix inequality (LMI), for which, for example, there are efficient optimization algorithms for solving this inequality. By solving this LMI, the matrices X>0, S and Y can be determined. The controller parameterization is in particular determined by K=YS -1 It follows that the ellipsoid is specifically defined by P = X -1 Parameterized.

[0092] In the case of a polyhedron-restricted disturbance variable, the condition x(k+1)∈ε can be transformed into using a difference equation in the case of a polyhedron-restricted disturbance variable (i.e., the set of possible disturbance variables is preferably given by the vertices of the polyhedron)

[0093]

[0094] After mathematical transformation, the condition for robust positive invariance can be given by

[0095]

[0096] By solving this LMI, the matrices X>0, S and Y can be determined. The controller parameterization is particularly given by =YS -1 It follows that the ellipsoid describing the invariant set is specifically defined by P = X -1 Parameterized.

[0097] Criterion 2: For example, if the absolute yaw angle error must not exceed a maximum value e max , then this can be expressed using the state vector It is described by the following two conditions

[0098] [1 / e max ,0,…,0]x≤1

[0099] [-1 / e max ,0,…,0]x≤1

[0100] In this way, safety limits can be defined for each relevant state. Such conditions can be summarized by the following set:

[0101] Υ x ={x|H i x≤1,i∈{1,…,n x}}

[0102] To ensure that this is always observed, the invariant set ε can be Υ x A subset of , ε∈Υ x . This can be described mathematically by the following condition:

[0103]

[0104] In combination with the conditions from criterion 1 , controller 1 can advantageously be parameterized in such a way that exceeding of the maximum control deviation is ensured in a robust manner.

[0105] By establishing corresponding additional conditions, it is also possible to ensure that input limits (or actuator limits) are respected. For example, the input limits are given in the form of a polyhedron:

[0106] Υ u = {u|G i u≤1,i∈{1,…,n u}}

[0107] To ensure that this is always observed, the invariant set ε can be Υ u A subset of , ε∈Υ u This can be described by the following condition

[0108]

[0109] Therefore, during calibration, compliance with the input restrictions within the invariant set can be explicitly taken into account. The same optimization variables X>0, S and Y as in criterion 1 can appear in the additional conditions for compliance with the state and input restrictions, so that these can be directly combined with each other.

[0110] Criterion 3: In order to be able to take into account requirements regarding performance characteristics, such as comfort, for the parameterization of the controller 1, a cost function can be defined. This allows the aggressiveness of the controller 1 to be set and states (such as lateral errors) to be weighted to different degrees, which involves a kind of prioritization.

[0111] In general, the cost function can be given by

[0112]

[0113] It has positive definite weight matrices Q and R, which are, for example, diagonal matrices.

[0114] Through the corresponding mathematical transformation, in particular, the following conditions are obtained

[0115]

[0116] 1-μ-λ≥0,μ>0,λ>0

[0117] This condition ensures the robust positive invariance of the ellipsoid ε under disturbance variables limited by the ellipsoid, wherein the cost function J should preferably be minimized. By solving this LMI, the matrices X>0, S and Y can be determined. The controller parameterization is in particular given by K=YS -1 It follows that the ellipsoid is specifically defined by P = X -1 Parameterized.

[0118] For disturbance variables restricted to polyhedra, the LMI additional conditions can be adapted according to criterion 1, so that here, in addition to the disturbance variables restricted to polyhedra, a cost function is also taken into account.

[0119] Taking into account the cost function may allow taking into account requirements on performance characteristics (eg comfort) in the regulator parameterization and influence the form of the invariant set.

[0120] Criterion 4: In general, in particular, not all states are always measurable or are not taken into account in the control law, i.e. u=KCx. Therefore, the following additional condition can be established, which allows the parameterization of the controller 1 in the case of incomplete state feedback. In this case, the same approach as in criterion 1 is preferably followed in the case of an ellipsoid as a limiting disturbance variable. By solving the following condition

[0121]

[0122] VC=CS

[0123] 1-μ-λ≥0,μ>0,λ>0

[0124] A robust invariant set can be determined, wherein in particular the matrices X>0, S, V and U are determined. The controller parameterization is in particular determined by K=UV -1 It follows that the ellipsoid is specifically defined by P = X -1 Parameterization. This process of taking into account output feedback can also be combined with other criteria.

[0125] Criterion 5: Depending on the specific application, different target variables may be important. Possible target variables according to embodiments and how these can be combined with criteria 1 to 4 are described below. The target variable is preferably optimized, ie in particular minimized, in the optimization problem set up.

[0126] If the influence of disturbance variables should be compensated to the greatest extent possible, minimization of the robust invariant set is a possible objective variable. In particular, the ellipsoid ε = {x|x T The volume of Px≤1} and (detP) -1 / 2 = proportional. Therefore, by minimizing -logdetP, the volume of the ellipsoid can be minimized. Alternatively, the trace of the matrix P can be used, which corresponds to the sum of the squares of the semi-axes of the ellipsoid. Therefore, by minimizing -SpurP, the size of the ellipsoid is also minimized. Since the optimization variable X=P is given in particular under the above conditions -1 , so the objective function Spur X can be used to minimize the robust invariant set. This objective function is particularly advantageous in combination with the conditions of criterion 1. Minimization of the robust invariant set can lead to an aggressive regulator 1.

[0127] For high-dimensional systems with more than three to five states, the global minimization of the volume of the invariant set for a specific application may lead to undesirable results, because, for example, disproportionate regulator deviations in the individual states will lead to the lowest overall volume. In this case, the invariant set can be minimized in a targeted manner in a predetermined direction D i ∈R n ,i=1,2,…,n d The expansion of |D i |Direction D i The minimization on is weighted proportionally. To establish such a cost function, in the first step, the invariant set ε is moved in the direction D i The maximum expansion d i It can be expressed as the following condition

[0128]

[0129] In the second step, this condition can be obtained by means of the objective function ∑ i d i Make ε expand in the corresponding direction D i Minimize directly.

[0130] In the optimization problem, the maximization of the robust invariant set can be achieved by the objective function -logdetX or -SpurX. This maximum robust invariant set is determined, for example, so that, according to the requirements, the maximum regulation deviation is still ensured by the conditions from criterion 2. The invariance of this set can be ensured by the conditions from criterion 1. Through this process, a regulator 1 that tends to be less aggressive can be determined, i.e., in particular a higher level of comfort, wherein safety is still guaranteed.

[0131] If a cost function is defined, it should in particular be minimized, which can be achieved by the objective function SpurP or -SpurX. This minimizes the upper limit of the cost function, for example. In order to ensure robust invariance, the conditions from criterion 3 can be considered together. In general, this objective function can lead to the maximization of the robust invariant set. By increasing the weight matrices Q and R, the volume of the invariant set can be reduced. In addition, the weight matrix can be used to influence performance characteristics (i.e., for example, interference suppression or comfort). This can also have an impact on the form of the invariant set. In addition, the conditions in criterion 2 can be added to the optimization to ensure the maximum regulation deviation.

[0132] If there is only one output feedback, the conditions can be adapted according to criterion 4. This can be combined with all objective functions from criterion 5.

[0133] Criterion 6: If there is parametric uncertainty, and the uncertain model is described as a linear differential inclusion (LDI), then linear matrix inequalities can be established for all q vertex matrices of the LDI. This procedure can be combined with all criteria 1-4.

[0134] Figure 4 The sequence of a method 200 for parameterizing a controller according to an exemplary embodiment is shown.

[0135] In a first step 201, all relevant information is detected. The following information can be provided in order to apply the method according to the embodiment based on this. The technical system 2 to be regulated can be described by a differential equation endowed with data that maps the dynamic behavior (for example, modeling of the lateral dynamics based on the linearized differential equation of the single-track model and its identification). First, for example, the differential equation of the single-track model can be established as described above. This is preferably done based on the corresponding physical equations. The parameters of the differential equation can then be identified by corresponding identification methods. This is done, for example, based on measurements of the technical system 2, in particular vehicle measurements. The parameters to be identified can be fully stimulated in the cycle being performed. In addition, a mathematical description of the regulator structure can preferably be provided in a non-parametric manner. The structure of the lateral regulation can be described by mathematical equations. These equations can be dynamic and / or static equations. This is preferably done in a time-discrete form. In addition, the overall model of the technical system 2 to be regulated and the regulator 1 can be established in the following form

[0136] x(k+1)=Ax(k)+Bu(k)+Ew(k)

[0137] y(k)=Cx(k)

[0138] Including parameterization of A, B, E and C. The differential equation of the lateral dynamics is discretized, in particular, using the sampling time used, and combined with the lateral control equation of the entire system. As a result, the technical system 2 of the lateral dynamics and the control structure can be combined in one differential equation, so that the control part to be parameterized can be represented by u=Ky. As a result, if a dynamic regulator 1 with its own state is used, such as a PI regulator 1, the total order can be increased compared to the order of the lateral dynamics. In addition, the limitation of the disturbance w can be mathematically described by a polyhedron or an ellipsoid. Here, in particular, it should be identified in which value ranges the disturbance occurs. For example, what is relevant to the lateral control is which maximum lateral disturbance force acts on the vehicle.

[0139] In a further step 202, the target function is defined. In this case, for example, the target variables from standard 5 should be defined according to the requirements of the control task. It may be relevant here which safety requirements must be met or which requirements on performance characteristics (e.g. comfort) must be given. For example, for lateral control, a maximum permissible lateral error y can be set.e Additionally, the steering angle δ and its derivative can be defined as limits to ensure a certain degree of comfort. These requirements can be taken into account in the controller parameterization by means of additional conditions according to criterion 2. In order to obtain a controller 1 that is not unnecessarily aggressive, which could, for example, make the driver of the vehicle uncomfortable, the invariant set can be maximized while respecting the defined limits. Alternatively, the goal can be to minimize the lateral error in cases where accurate lateral tracking is important.

[0140] In a further step 203, an optimization problem is preferably established. Depending on the requirements for the regulator 1, relevant additional conditions from criteria 1 to 4 and 6 should be defined. Here, in addition to the mathematical description of the objective function, other additional conditions can also be established. These additional conditions in particular ensure that the regulator parameters are optimized so that a robust invariant set is obtained according to the objective function. Here, depending on the type of interference set, additional conditions according to criterion 1 may be required, such as the lateral interference force of the wind on the lateral regulation, which will be described by a polyhedron. The objective function can be defined according to criterion 5. In order to be able to ensure the maximum deviation of each state (such as lateral error), criterion 2 can be used. Criterion 4 can also be used in the embodiment of lateral regulation because there can be output feedback here. If the cost function should be minimized, criterion 3 can be considered. There may usually be parameter uncertainty, such as the constantly changing mass of the vehicle, which can be integrated by criterion 6. This particularly derives an optimization problem including the objective function and a series of additional conditions.

[0141] In a fourth step 204 , an optimization problem is preferably solved. For this purpose, corresponding optimization tools known from various examples in the prior art can be used, and thus the parameterization of the regulator 1 can be calculated.

[0142] In a fifth step 205 according to this exemplary embodiment, the controller 1 can be implemented in a technical system 2, for example, in a control unit of a vehicle. After the controller parameterization has been calculated, the controller 1 can be implemented on the control unit or a new parameterization can be loaded onto the control unit. After the controller 1 has been put into operation with the optimized parameterization in a real technical system 2 (for example, a vehicle), it can also be evaluated whether the required guarantees can be met.

[0143] The above explanations of the embodiments describe the present invention only within the scope of examples. Of course, the individual features of the embodiments can be freely combined with each other without departing from the scope of the present invention if technically reasonable.

Claims

1. A method (100) for calculating a parameterization of a controller (1) of a technical system (2), comprising the following steps: - determining (101) characteristics of the controller (1), wherein the characteristics include at least a description of the structure of the controller (1) and at least one differential equation in order to map the dynamic behavior of the technical system (2) using the differential equation, - defining (102) an objective function, wherein the objective function is based on at least one requirement for a safety property and / or a performance property of the controller (1) and / or the technical system (2), - establishing (103) an optimization problem, wherein the optimization problem is established based on the objective function and at least one additional condition, wherein at least one restriction of at least one state of the technical system (2) is ensured by the at least one additional condition, - Calculating the parameterization of the regulator (1) based on the determined optimization problem.

2. The method (100) according to claim 1, It is characterized in that The at least one state reflects the time behavior of the respective manipulated variable of the regulator (1) and in particular specifies the current value of the respective manipulated variable. Therein, a limitation of at least one state of the technical system (2) is ensured by regulating the at least one state by the regulator (1) in such a way that the value of the at least one state remains in an invariant set.

3. The method (100) according to any one of the preceding claims, It is characterized in that The characteristics of the regulator (1) also define the limiting type of the state of the technical system (2), wherein the type is preferably based on an ellipsoidal or polyhedral function (4).

4. The method (100) according to any one of the preceding claims, It is characterized in that Defining (102) the objective function includes the following steps: - determining a limit value or a limit range for the at least one state based on at least one requirement for a safety property and / or a performance property of the controller (1) and / or the technical system (2).

5. The method (100) according to any one of the preceding claims, It is characterized in that The at least one additional condition also defines a threshold value for the at least one state and / or at least one input variable of the regulator (1), wherein the threshold value defined according to the additional condition must not be exceeded.

6. The method (100) according to any one of the preceding claims, It is characterized in that Determining (103) the optimization problem also includes the following steps: - defining a cost function, wherein a weight value is assigned to the at least one state by means of the cost function within the scope of the calculation (104) parameterization in order to provide a priority of the state.

7. The method (100) according to any one of the preceding claims, It is characterized in that The at least one differential equation is a linear differential equation and the dynamic behavior of the technical system (2) is mapped by a combination of the at least one differential equation with at least one further linear differential equation.

8. The method (100) according to any one of the preceding claims, It is characterized in that The characteristic of the controller (1) is determined by taking into account the values ​​of all states or the values ​​of a subset of states.

9. The method (100) according to any one of the preceding claims, It is characterized in that The method (100) further comprises the following steps: - a parameterized controller (1) implemented on the technical system (2), The technical system (2) is preferably a vehicle, and the regulator (1) is used for lateral and / or longitudinal adjustment of the vehicle.

10. A controller (1) for a technical system (2), wherein the controller (1) is configured to carry out a method (100) according to any one of claims 1 to 8 or to be used in a method (100) according to any one of claims 1 to 8.

11. A computer program (20) comprising instructions which, when the computer program (20) is executed by a computer (10), cause the computer (10) to perform the method (100) according to any one of claims 1 to 8.

12. A device (10) for data processing, arranged to perform the method (100) according to any one of claims 1 to 8.

13. A computer-readable storage medium (15) comprising instructions which, when executed by a computer (10), cause the computer to perform the steps of the method (100) according to any one of claims 1 to 8.

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