Method for determining system excitation by means of at least one input signal for model-based control of technical system

Abstract

The invention relates to a method for determining a system excitation by means of at least one input signal for model-based control of a technical system, comprising the following steps: providing at least one input signal, the at least one input signal physically influencing at least one parameter of the technical system; defining at least one distribution hypothesis for the at least one parameter, defining an objective function for optimizing the at least one input signal taking into account the at least one defined distribution hypothesis, the objective function optimizing the at least one input signal at least on the basis of a weighting of the sensitivity of the input signal, -determining a numerical algorithm for solving the defined objective function and an uncertainty quantification method for determining the sensitivity of the at least one input signal,-optimizing the defined objective function on the basis of the determined numerical algorithm and the determined uncertainty quantification method,-determining the system excitation on the basis of the optimized objective function. The invention further relates to a computer program, a device and a storage medium for this purpose.

Description

Technical Field

[0001] The invention relates to a method for determining a system excitation by means of at least one input signal for model-based regulation of a technical system and also to a computer program, a device and a storage medium for this purpose. Background Art

[0002] In the context of system identification in model-based control, system excitation is particularly important because it forms the basis for identifying system parameters. By using different excitations or input signals, the behavior of the system can be examined under different conditions. These data can then be used to create or calibrate a mathematical model of the system.

[0003] The quality of the system excitation can significantly affect the accuracy of the identified model. Suboptimal excitation can lead to a model that is not accurate enough to represent the actual dynamics of the system. Therefore, it is important to choose an excitation that is informative enough to appropriately map all relevant dynamics of the system.

[0004] The choice of the system excitation is therefore necessary for identifying the model parameters. The quality of the identifiability depends decisively on the selected system input. Since the choice of the excitation is dependent on various characteristic variables of the control loop of the system, the question regarding the system excitation can be very system-specific. There are a large number of so-called "measurement catalogues" for system identification based on expert knowledge. These measurement catalogues are more empirical in nature and have been optimized over many years of use. This is particularly problematic when transitioning to new technologies for which there are too few empirical values. Summary of the invention

[0005] The subject matter of the invention is a method having the features of claim 1, a computer program having the features of claim 8, a device having the features of claim 9 and a computer-readable storage medium having the features of claim 10. Further features and details of the invention are derived from the respective dependent claims, the description and the drawings. Features and details described in conjunction with the method according to the invention naturally also apply in conjunction with 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, respectively, so that with respect to the disclosure for the individual inventive aspects, reference is always made to one another or can be made to one another.

[0006] The subject matter of the invention is in particular a method for determining a system drive by means of at least one input signal for model-based regulation of a technical system, comprising the following steps, wherein the steps can be performed repeatedly and / or sequentially.

[0007] In a first step, in particular at least one input signal is provided, wherein the at least one input signal physically influences at least one parameter of the technical system. For example, the input signal can be a voltage or an engine torque. Within the scope of the present invention, the input signal can also be referred to and understood as an input variable. A possible parameter of the technical system is, for example, the inertia of the engine.

[0008] In a further step, at least one distribution hypothesis is preferably defined for at least one parameter. In one example, the distribution hypothesis may be a uniform distribution with a lower limit and an upper limit. Thus, prior knowledge about at least one parameter may advantageously be taken into account, and thereby the method enables a more accurate optimization of at least one input signal.

[0009] In a further step, an objective function for optimizing at least one input signal can be defined taking into account at least one defined distribution assumption. In this case, the objective function can optimize the at least one input signal at least based on a weighting of the sensitivity of the input signal. It is also possible that the objective function optimizes the ratio between the weighting of the sensitivity and the weighting of the input signal itself (i.e., for example, the level of the voltage if the input signal is a voltage). Within the scope of this step, an input-independent proxy model can also be determined, if necessary, by means of an Intrusive Polynomial Chaos Expansion (IPCE) method, whose output variable is directly a sensitivity measure.

[0010] In a further step, in particular a numerical algorithm for solving the defined objective function and an uncertainty quantification method for determining the sensitivity of at least one input signal are determined. For the numerical algorithm, a gradient-based method such as an interior point method or a trust region algorithm or a global optimization method such as simulated annealing or a genetic algorithm can be determined. For the uncertainty quantification method, a sampling-based method such as Monte Carlo, Latin hypercube or an intrusive uncertainty quantification method can be used. The numerical algorithm and the uncertainty quantification method can be determined, for example, depending on the type of technical system.

[0011] In a further step, the defined objective function is preferably optimized based on the determined numerical algorithm and the determined uncertainty quantification method. For example, the optimization may be a maximization or a minimization of the objective function.

[0012] In a further step, the system excitation is determined, in particular based on the optimized objective function.

[0013] At least one distribution hypothesis preferably predetermines at least one maximum and / or minimum value of at least one parameter and / or at least one characteristic for the admissibility of at least one input signal. The characteristic for the admissibility of at least one input signal can be, for example, an amplitude or slope constraint or another differentiable characteristic.

[0014] Furthermore, sensitivity describes in particular the rate at which at least one parameter of the technical system changes as a function of a change in at least one input signal. In simplified terms, sensitivity describes in particular the extent to which the output variable of the corresponding parameter changes when the input signal is changed.

[0015] A further advantage within the scope of the invention can be achieved if, within the scope of defining at least one objective function, it is provided whether the sensitivity of at least one parameter of the technical system is minimized or maximized. Thus, depending on the given application, the sensitivity of at least one parameter can advantageously be minimized or maximized.

[0016] Optionally, it is also conceivable that defining at least one target function further comprises the following steps:

[0017] The at least one input signal is weighted in order to optimize a defined target function, inter alia, taking into account the weighting of the at least one input signal.

[0018] The defined objective function is preferably optimized taking into account a weighting of at least one input signal, so that the input signal mathematically results in a penalty. In particular, the optimization of the defined objective function can thus be performed based on a ratio between the weighting of the sensitivity and the weighting of the input signal, for example in the sense of a quality measure g. In this case, the high quality measure g preferably results in the case of a high sensitivity and a low signal strength of the input signal.

[0019] Optionally, it is possible that the optimization of the defined target function further comprises the following steps:

[0020] - determining at least one degree of freedom for optimization, wherein the at least one degree of freedom describes at least one type of input signal.

[0021] The type of input signal can be, for example, a signal structure. In simplified terms, the use of the degrees of freedom is particularly to determine which possibilities exist for optimizing the input signal. Thus, given a given signal structure or a given initial function, a free optimization of the input signal or only a parameter optimization may be possible.

[0022] According to another possibility, it can be provided that the method further comprises the following steps:

[0023] - defining a termination criterion for optimizing the defined objective function, wherein the termination criterion specifies a threshold value of the sensitivity of the at least one input signal and / or a number of iterations for optimizing the defined objective function,

[0024] In this case, a defined objective function can be optimized iteratively until a defined termination criterion is met. This ensures that the sensitivity exceeds a threshold value and that a correspondingly optimized system excitation based on the input signal is possible. In addition, due to the number of iterations, the computational requirements can advantageously be adapted to the current application or the current technical system.

[0025] Optionally, it is conceivable that the method further comprises the following steps:

[0026] - applying the determined system excitation to the technical system in order to carry out a system identification of the technical system, wherein a value of at least one parameter of the technical system is determined based on the determined system excitation.

[0027] For example, the method can be applied to the system identification of a steering system with rack position control (RPC). At least one input signal of the system excitation can be used here to identify parameters at a prototype or within the scope of an end-of-line test.

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

[0029] The subject matter of the present invention is also a device for data processing, which is set up to carry out the method according to the invention. For example, a computer can be provided as the device, 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 computer program can be read out by the processor for execution.

[0030] The subject of the present invention may also be 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 designed, for example, as a data memory, such as a hard disk and / or a non-volatile memory and / or a memory card. The storage medium may, for example, be integrated into a computer.

[0031] Furthermore, 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 are apparent from the following description, in which exemplary embodiments of the invention are described in detail with reference to the accompanying drawings. The features mentioned in the claims and in the description may be essential to the invention individually or in any combination. Among them:

[0033] Figure 1 Schematic visualizations of methods, technical systems, devices, storage media and computer programs according to embodiments of the present invention are shown.

[0034] Figure 2 A schematic diagram showing a method according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0035] exist Figure 1 , a method 100 , a technical system 1 , a device 10 , a storage medium 15 and a computer program 20 according to an embodiment of the present invention are schematically shown.

[0036] Figure 1 In particular, an embodiment of a method 100 for determining a system excitation by means of at least one input signal for model-based regulation of a technical system 1 is shown. In a first step 101, at least one input signal is provided, wherein the at least one input signal physically influences at least one parameter of the technical system 1. In a second step 102, at least one distribution assumption is defined for at least one parameter. In a third step 103, an objective function for optimizing the at least one input signal is defined taking into account the at least one defined distribution assumption, wherein the objective function optimizes the at least one input signal at least based on a weighted optimization of the sensitivity of the input signal. In a fourth step 104, a numerical algorithm for solving the defined objective function and an uncertainty quantification method for determining the sensitivity of the at least one input signal are determined. In a fifth step 105, the defined objective function is optimized based on a specific numerical algorithm and a specific uncertainty quantification method. In a sixth step 106, the system excitation is determined based on the optimized objective function.

[0037] With the invention according to an embodiment, it is in particular possible to determine a system excitation which is tailored for identifying specific unknown parameters of the technical system 1. This can be used to check a certain number of existing input signals with regard to their suitability for identifying these parameters. As long as the existing input signals can be parameterized, the degrees of freedom can be optimized according to the current situation. In addition, new optimal system excitations can also be generated. The invention according to an embodiment makes it possible to use in particular existing expertise (for example in the form of a measurement catalog) when transferring to new application situations. In addition, the integrity of the measurement catalog can be verified by checking whether all relevant parameters have experienced sufficient excitation.

[0038] Compared with the prior art, the present invention according to the embodiment provides the following advantages, for example. An excitation signal for identifying a specific model parameter can be generated for the existing prior knowledge about the technical system. This includes, in particular, maximizing the sensitivity of the parameter to be identified and minimizing the influence of other parameters, which should affect the estimation result as little as possible. Existing expertise (for example, in the form of a "measurement catalog") can be checked in view of the suitability and completeness for identifying specific parameters. This can include the following aspects: if there are degrees of freedom in the existing excitation signal, the degrees of freedom can be optimized for the existing system. If a specific parameter cannot be fully identified using an existing excitation or input signal, a specific optimal excitation signal can be systematically extended to the measurement catalog. When transitioning to another system (for example, a new generation of products), the existing measurement catalog can be adapted to the new system. For example, this supports the transfer of existing expertise to new technologies. For special system categories, it is possible to solve the signal generation problem - similar to the case of a solution for model prediction regulation. For example, as long as the system allows corresponding excitation during operation, online optimization or adaptability to parameter fluctuations can be achieved.

[0039] The present invention according to an embodiment is particularly relevant in the context of system identification within the scope of model-based regulation. The purpose of the system identification is preferably to determine the parameters of the technical system 1. The system design or system analysis of the system excitation used for this is an aspect of the present invention according to an embodiment. This is in particular the basis for model-based regulation.

[0040] The basis of the method according to the exemplary embodiment is in particular the model A description of the system's behavior, the model Based on the system input to be designed Measurement / output parameters And related parameters The relationship between

[0041]

[0042] If the model M is a dynamic state space model with internal states, further simplifications may be necessary, as will be explained below. The parameters are preferably interpreted as uncertain quantities and described by probabilistic assumptions p ~ Q. In the following, in particular without limiting the generality, the estimates are given with upper and lower limits p - ≤p≤p + Uniform distribution The upper and lower limits restrict the expected parameter range. The target variable for the optimization of the input variable is based, for example, on a global sensitivity analysis of the measured variable. i About parameter p j Sensitivity S ij(t) can be determined by the Sobol sequence:

[0043]

[0044] Among them, ~j especially represents the addition of p j All parameters except . The first-order Sobol index is used as the sensitivity measure S ij Other metrics, such as the total effect Sobol index, are also possible. To calculate the sensitivity according to equation (2) for a specific input, various uncertainty quantification methods (UQ) can be used, such as sampling-based Monte Carlo simulations, Latin hypercube sampling, (adaptive) pseudospectral projections or intrusive polynomial chaotic evolution (IPCE).

[0045] In particular, the input signal u(t) is determined by the optimal control problem

[0046]

[0047] In this case, the optimal input signal is determined in particular by optimizing a target function, in particular by maximizing an overall quality measure g as a function of the sensitivity S and the input u. In particular, a possible target function in the form of a quality measure g can have the following structure:

[0048]

[0049] The first term in particular represents the optimization of the sensitivity, for example by means of a weighted square norm. Through the diagonal entries of the matrix Q, it can be selected whether a particular parameter should be maximized (Q ii >0) or minimize (Q ii <0). Off-diagonal entries Q may also be used ji =Q ij <0 is used to simultaneously penalize the maximization of different sensitivities. If there are multiple measurement variables q≥1, the sensitivity S i，(·) The second addend in equation (4) allows, in particular, for example via the weighting matrix R, to penalize the signal energy of the input signal. In addition, the set Preferably describes the allowed input signals. For example, this may include amplitude or slope constraints or other differentiable properties:

[0050]

[0051] If there is a parameterizable signal structure u(t,θ) with degrees of freedom θ, e.g. as a linear combination The optimization problem according to equation (3) can then be performed directly via the degrees of freedom θ instead of via the time function u(t).

[0052] For a specific model class of linear and nonlinear dynamic systems according to equation (1), the sensitivity measure can be determined particularly efficiently by the intrusive UQ method. This makes it possible in particular to implement the method according to the embodiment in real time and to express it by way of example using a linear state space model:

[0053]

[0054] y(t)=C(p)x(t)+D(p)u(t).

[0055] With the help of the Intrusive Polynomial Chaos Expansion (IPCE) method, an input-independent proxy model can be determined, whose output parameter is directly a sensitivity measure according to equation (2).

[0056]

[0057] S(t)=VX(t)

[0058] This enables, for example, the sensitivity to be determined by simulating the proxy model only according to equation (7) and the potentially computationally expensive determination of the matrices A′, B′, W′, V′ within the scope of a preprocessing step. In particular, it is then not necessary to perform a sampling-based method to determine the sensitivity measure S(t) at optimization time.

[0059] According to one embodiment, by Figure 2 The determination of the optimal input signal is carried out in the following steps as explained in . In a first step 201, a distribution hypothesis for at least one parameter of the technical system 1 is defined. This includes, for example, a probability measure for the parameter p to be considered, such as a maximum or minimum value to be expected and / or a definition of permissible excitations, for example the set of permissible input signals according to equation (5) And / or optionally, a proxy model is determined according to step 201′, for example, equation (7), as long as a system class suitable for this, such as equation (6) exists. In a second step 202, the objective function of the optimization is defined, for example in the form of equation (4). Here, the weighting of the sensitivity is determined, that is, in particular, a definition is provided regarding which parameter of the sensitivity should be maximized or minimized (see weighting matrix Q). If multiple parameters should be identified using system excitation, the parameters can be identified together with an input signal or with separate input signals. The latter means, in particular, that for each configuration, the further steps 203 to 205 are experienced multiple times. In addition, the input signal is weighted, for example, by a weighting matrix R, ∈. In a third step 203, the degrees of freedom of the optimization are defined, in particular the time range of the optimization problem and the type of input signal, that is, for example, whether a free optimization or parameter optimization of the input signal is performed under a given signal structure or a given initial function. In a fourth step 204 according to the first alternative, the optimization problem is solved according to equation (3). Here, a numerical algorithm is determined 2041, for example a gradient-based method such as an interior point method or a trust region algorithm, or a global optimization method such as simulated annealing or a genetic algorithm. In addition, an uncertainty quantification method (UQ method) is determined 2042 for determining a sensitivity measure for an input signal determined by the numerical algorithm according to equation (2). Here, sampling-based methods such as Monte Carlo, Latin hypercube or invasive UQ methods can be used. As long as the proxy model is determined in step 1, the sensitivity measure can be determined directly by the invasive UQ method. In addition, in this step, the optimization problem is iteratively solved according to equation (3) using a specific numerical algorithm and an uncertainty quantification method until a termination criterion 2043 is reached. In a fifth step 205, one or more input signals can be applied to the technical system 1.

[0060] If the optimization is to be performed in real time, according to a second alternative, an iterative sequence of steps 204' and 205' with steps 2041', 2042' and 2043' can be provided. In this case, the system response of the last cycle is preferably used as the initial value x0 or X0 for the next iteration.

[0061] The invention can be used in any technical context based on model-based control functions. One possible application is in particular the identification of parameters in steering systems, i.e. for rack position control, for example for steer-by-wire systems. In this case, the model according to equation (1) maps in particular the relationship between the engine torque and the rack position or the engine angle.

[0062] Another possible application is the detection of the lateral and / or longitudinal steering behavior of the vehicle. Here, for example, the steering angle and the desired acceleration are the input signals, and the yaw rate, the slip angle or the vehicle position and speed are the relevant parameters. Other possible applications are (large space) robotics or motor control.

[0063] The above explanations of the embodiments describe the invention only within the scope of examples. Of course, the individual features of the embodiments can be freely combined with one another as far as technically reasonable, without departing from the scope of the invention.

Claims

1. A method (100) for determining a system excitation by means of at least one input signal for model-based regulation of a technical system (1), comprising the following steps: - providing (101) at least one input signal, wherein the at least one input signal physically influences at least one parameter of the technical system (1), - defining (102) at least one distribution hypothesis for at least one parameter, - defining (103) an objective function for optimizing at least one input signal taking into account at least one defined distribution assumption, wherein the objective function optimizes at least one input signal based at least on a weighting of the sensitivities of the input signal, - determining (104) a numerical algorithm for solving the defined objective function and an uncertainty quantification method for determining the sensitivity of at least one input signal, - optimizing (105) the defined objective function based on the determined numerical algorithm and the determined uncertainty quantification method, - Determining (106) system excitations based on the optimized objective function.

2. The method (100) according to claim 1, characterized in that: At least one distribution hypothesis predetermines at least one maximum and / or minimum value of at least one parameter and / or at least one characteristic for the admissibility of at least one input signal, and / or Sensitivity describes the rate at which at least one parameter of a technical system (1) changes as a function of a change in at least one input signal.

3. The method (100) according to any one of the preceding claims, characterized in that In the context of defining (103) at least one objective function, it is specified whether the sensitivity of at least one parameter of the technical system (1) is to be minimized or maximized.

4. The method (100) according to any one of the preceding claims, characterized in that Defining (103) at least one objective function further comprises the following steps: - weighting the at least one input signal in order to carry out an optimization of the defined objective function taking into account the weighting of the at least one input signal (105).

5. The method (100) according to any one of the preceding claims, characterized in that Optimizing the objective function defined by (105) further comprises the following steps: - determining at least one degree of freedom for optimization, wherein the at least one degree of freedom describes at least one type of input signal.

6. The method (100) according to any one of the preceding claims, characterized in that The method further comprises the following steps: - defining a termination criterion for optimizing the target function defined in (105), wherein the termination criterion specifies a threshold value of the sensitivity of at least one input signal and / or a number of iterations for optimizing the target function defined in (105), The objective function defined in (105) is optimized iteratively until a defined termination criterion is met.

7. The method (100) according to any one of the preceding claims, characterized in that The method further comprises the following steps: - applying the determined system excitation to the technical system (1) in order to carry out a system identification of the technical system (1), wherein a value of at least one parameter of the technical system (1) is determined based on the determined system excitation.

8. 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 6.

9. A device (10) for data processing, which is configured to carry out the method (100) according to any one of claims 1 to 6.

10. 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 6.

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