Computer-implemented method and / or device for open-loop and / or closed-loop control of a physical system on the basis of at least one estimated state variable

Abstract

The invention relates to a computer-implemented method for open-loop and / or closed-loop control of a physical system on the basis of at least one state variable of a physical system; the method comprising: providing (S1) time-series-based measurement data of the physical system, at least one, in particular trained, physical model for estimating the at least one state variable on the basis of the provided time-series-based measurement data, and at least one data-based, in particular trained, machine learning model; estimating (S2) the at least one state variable by means of the at least one physical model on the basis of the provided time-series-based measurement data; identifying and / or determining (S3) at least one estimation error of the physical model by means of the at least one data-based machine learning model on the basis of the provided time-series-based measurement data and / or on the basis of the at least one estimated state variable; optimizing (S4) the at least one estimated state variable on the basis of the at least one estimation error; and performing open-loop and / or closed-loop control (S5) of the physical system on the basis of the at least one optimized estimated state variable.

Description

[0001] Description

[0002] title

[0003] Computer-implemented method and / or device for controlling and / or regulating a physical system based on at least one estimated state variable

[0004] The invention relates to a computer-implemented method for controlling and / or regulating a physical system based on at least one estimated state variable of the physical system. Furthermore, the invention relates to a device for controlling and / or regulating a physical system based on at least one state variable of the physical system.

[0005] State of the art

[0006] Estimating the steering rack force in a vehicle using physical models plays a significant role in vehicle development and control. These models are based on fundamental physical principles of mechanics and contribute to significantly improving vehicle performance and control. The steering rack force, which describes the interaction between the steering wheel and the wheels of a vehicle, is a key state variable for steering and handling.

[0007] The application of physical models to estimate rack force has undoubtedly enabled advances in the automotive industry. These models are based on assumptions and mathematical formulas that describe the relationship between steering inputs and the forces acting on the wheels. However, these models are not without their limitations. In an era where vehicles are becoming increasingly complex and connected, and new technologies such as electromobility and autonomous driving are becoming more prevalent, conventional physical models are reaching their limits.

[0008] This also generally applies to the estimation of state variables of a physical system using physical models, for example when no measured values ​​are available to measure the state variable, the installation of such sensors is not structurally possible, or the measurement of the state variable is technically highly complex.

[0009] The invention is therefore based on the object of specifying an improved method and / or an improved device for controlling and / or regulating a physical system on the basis of at least one estimated state variable of the physical system.

[0010] The object is achieved by a computer-implemented method for controlling and / or regulating a physical system based on at least one state variable of the physical system according to the features of patent claim 1. The object is achieved by a device for controlling and / or regulating a physical system based on at least one state variable of the physical system according to the features of patent claim 10.

[0011] Disclosure of the invention

[0012] According to a first aspect, a computer-implemented method for controlling and / or regulating a physical system based on at least one state variable of the physical system is proposed. For this state variable, for example, no sensory measurement data is available because, for example, the installation of measurement sensors is structurally impossible, and / or the measurement of the state variable can be technically highly complex. The method comprises the steps:

[0013] - Providing time series-based measurement data of the physical system, at least one, in particular trained, physical model for estimating the at least one state variable on the basis of the provided time series-based measurement data, and at least one data-based, in particular trained, machine learning model;

[0014] - Estimating the at least one state variable by the at least one physical model on the basis of the provided time series-based measurement data;

[0015] - Identifying and / or determining at least one estimation error of the physical model by the at least one data-based machine learning model on the basis of the provided time-series-based measurement data and / or on the basis of the at least one estimated state variable;

[0016] - Optimizing the at least one estimated state variable based on the at least one estimation error; and

[0017] - Controlling and / or regulating the physical system based on at least one optimised, estimated state variable.

[0018] This method enables the best possible model performance (accuracy, stability). Furthermore, this method enables high explainability through the use of physical models and clear task definitions, in contrast to data-based machine learning models. The individual models can thus remain functionally manageable (size, type). This enables the use of white-box models. The present cascading of the model architecture enables a higher overall model complexity, which nevertheless remains analyzable and / or comprehensible cascade-wise and / or individually due to the individual cascades. Overall, this approach is very robust against overfitting.

[0019] A cascade can be understood as a stage of an overall model comprising at least the physical model and the data-based machine learning model. The cascade or stage comprises either the physical model or the data-based machine learning model. The cascade or stage can be variably linked, in particular linked or connected, to at least one previous or subsequent cascade or stage of the overall model. The at least one data-based machine learning model is designed to estimate the estimation error made by the physical model and, based on this, to correct the output / estimated state variable of the physical model. This optimizes the estimated state variable because the absolute estimation error is reduced.Several data-based machine learning models can be connected in a cascaded manner in order to capture an error in the estimation of the estimation error from the previous cascade and to take it into account when optimizing the estimated state variable.

[0020] The wording “identifying and / or determining at least one estimation error of the physical model by the at least one data-based machine learning model on the basis of the provided time series-based measurement data” means that the at least one data-based machine learning model is operated in parallel to the at least one physical model and does not access output values ​​of the at least one physical model to determine the estimation error.

[0021] The phrase "identifying and / or determining at least one estimation error of the physical model by the at least one data-based machine learning model based on the provided time-series-based measurement data and based on the at least one estimated state variable" means that the at least one data-based machine learning model is operated in series with the at least one physical model and accesses output values ​​of the at least one physical model to determine the estimation error. In principle, the at least one physical model and the at least one data-based machine learning model can be operated in series and / or in parallel.It is also possible, particularly when multiple data-based machine learning models are used to optimize the estimation of the at least one state variable, for one of the data-based machine learning models to be used in series and another of the data-based machine learning models to be used in parallel. This can be designed variably and can vary for each cascade. For example, a further data-based machine learning model can determine an error in the estimation of the estimation error by the at least one data-based machine learning model based on the output of the state variable already optimized based on the estimation error and on the estimation error, i.e. it is operated or used in parallel to the physical model and in parallel to the at least one data-based machine learning model.

[0022] The invention thus utilizes a cascaded hybrid model structure, whereby the cascades can be structured differently, depending in particular on the hybrid model approach chosen, depending on the state variable to be estimated. Hybrid preferably means that both at least one physical model and at least one data-based machine learning model are used. The data-based machine learning model can, for example, comprise a neural network. In principle, however, only data-based machine learning models or only physical models can be used in cascading.

[0023] In principle, the models used in a subsequent cascade, be it a physical model and / or a data-driven machine learning model, can receive additional input parameters in addition to the time series-based measurement data. For example, these additional input parameters can include the output values ​​of a model from the previous cascade and / or additional parameters, such as additional measured values ​​and / or measured variables and / or domain information and / or hyperparameters.

[0024] It is understood that the steps according to the invention, as well as other optional steps, do not necessarily have to be performed in the order shown, but can also be performed in a different order. Furthermore, additional intermediate steps can be provided. The individual steps can also comprise one or more substeps without thereby departing from the scope of the method according to the invention.In one embodiment, the method further comprises: providing at least one further physical model and / or a further data-based machine learning model; identifying and / or determining at least one error of the estimation error based on the provided time-series-based measurement data and / or based on the at least one estimated state variable and / or based on the at least one optimized estimated state variable by the at least one further physical model and / or the at least one further data-based machine learning model; and optimizing the already optimized at least one estimated state variable based on the at least one error of the estimation error.In the step of identifying and / or determining the at least one error of the estimation error, an error of an overall model can be determined or identified based on the provided time-series-based measurement data and / or based on the at least one estimated state variable and / or based on the at least one optimized estimated state variable. The overall model comprises the physical model and the further physical model and / or the further data-based machine learning model.

[0025] If the overall model includes the physical model and the additional physical model, the error of the overall model is determined by the additional data-based machine learning model. If the overall model includes the physical model and the additional data-based machine learning model, the error of the overall model is determined by the additional physical model.

[0026] In one embodiment, the identification and / or determination of the at least one estimation error and / or the identification and / or determination of the at least one error of the estimation error takes place on the basis of at least one historical, estimated state variable and / or on the basis of at least one historical, optimized, estimated state variable and / or on the basis of at least one historical, multiply optimized, estimated state variable, and / or on the basis of at least one historical estimation error, and / or on the basis of at least one historical error of the estimation error. As a result, for example, transient relationships can be taken into account in the error evaluation by the at least one data-based, machine learning model, which can improve the accuracy of the error prediction. In addition, the feedback of previously estimated and thus historical measured variables and / or estimated variables may lead toto an increase in the prediction and / or estimation accuracy of at least one state variable.

[0027] In other words, a model in a cascade can predict an estimation error and / or a prediction of an error in estimating the estimation error based on input values ​​that lie in the past, i.e., those that can be assigned to past estimates. This can also be referred to as preprocessing. Such linking and / or feedback preferably occurs in a series connection between the models in different cascades.

[0028] In one embodiment, the at least one physical model and the at least one data-based machine learning model are trained sequentially, wherein the at least one physical model is trained before the at least one data-based machine learning model, and wherein the trained at least one physical model is used to provide training data for the subsequently trained at least one data-based machine learning model.

[0029] In other words, the models are trained sequentially per cascade, which is also referred to as model boosting. The trained models of a previous cascade are preferably treated as fixed models. The individual models are preferably connected sequentially. The individual models are preferably not designed to represent different areas of an input data space, but rather are a superimposition or redundancy of several models in the same input data space for a better representation of the output variable in the form of the at least one state variable. In one embodiment, the at least one physical model and the at least one data-based machine learning model are trained in parallel, in particular independently of one another and / or autonomously and / or independently.

[0030] In this embodiment, the resulting, particularly cascaded, model architecture is trained simultaneously and / or in parallel. Depending on the model components, backpropagation may be useful and possible. Due to the different model components (physical vs. data-based machine learning), joint training using, for example, backpropagation is not possible, as the models are not differentiable from one another. In such a case, it is preferable to use a different training concept. Furthermore, it may be preferable to optimize all model parameters, particularly those of all models, using an external optimizer, e.g., a search algorithm such as Sobol, Grid, or Random. In special cases, Bayesian optimization can also be performed.

[0031] In one embodiment, the at least one physical model and the at least one data-based machine learning model are trained cyclically sequentially, wherein the at least one physical model is trained stepwise and / or iteratively, and wherein the at least one data-based machine learning model is trained after each training step and / or after each training iteration of the at least one physical model on the basis of the stepwise and / or iteratively trained at least one physical model.

[0032] According to this embodiment, semi-simultaneous training of the models of all cascades is possible. Such training, in particular, allows for a separation of influences between the models through the specification of the cascades. This approach also represents a type of boosting, since a model error from a previous cascade is passed on to a subsequent cascade. Instead of training each model in a cascade individually to its respective optimum, according to this training concept, the respective model in a cascade is only trained stepwise or iteratively, whereby a step size can be a number of iterations in a gradient descent method or similar. This allows for a common optimal model solution to be sought, although the individual models continue to be trained independently of one another.

[0033] In one embodiment, the at least one physical model is trained based on a training data set comprising a plurality of time-series-based measurement data of the physical system and a plurality of associated state variables; wherein the data-based machine learning model is trained based on a training data set comprising the plurality of time-series-based measurement data of the physical system.

[0034] In one embodiment, the physical system comprises a motor vehicle with a vehicle steering system comprising a rack, and wherein the at least one state variable is a rack force.

[0035] In one embodiment, the time-series-based measurement data comprises a longitudinal acceleration and / or a lateral acceleration and / or a vehicle speed and / or a steering angle and / or a steering angular speed and / or a rack position and / or a rack speed and / or a rack acceleration and / or an engine torque and / or a hand torque.

[0036] According to a second aspect, a device for controlling and / or regulating a physical system based on at least one state variable of the physical system is proposed. For this state variable, for example, no sensory measurement data is available because, for example, the attachment of measurement sensors is structurally impossible, and / or the measurement of the state variable can be technically highly complex. The device comprises at least one evaluation and / or computing device configured to perform at least the following steps:

[0037] - Providing time series-based measurement data of the physical system, at least one, in particular trained, physical model for estimating the at least one state variable on the basis of the provided time series-based measurement data, and at least one data-based, in particular trained, machine learning model;

[0038] - Estimating the at least one state variable by the at least one physical model on the basis of the provided time series-based measurement data;

[0039] - Identifying and / or determining at least one estimation error of the physical model by the at least one data-based machine learning model on the basis of the provided time-series-based measurement data and / or on the basis of the at least one estimated state variable;

[0040] - Optimizing the at least one estimated state variable based on the at least one estimation error; and

[0041] - Controlling and / or regulating the physical system based on at least one optimised, estimated state variable.

[0042] The statements made for the method apply, mutatis mutandis, to the present device and vice versa.

[0043] According to the invention, a control device is also claimed which is included in an autonomous vehicle and / or a robotic system and / or an industrial machine, and on which the present method can be carried out in any embodiment.

[0044] The invention also claims a computer program with program code for executing at least parts of the method according to the invention in one of its embodiments when the computer program is executed on a computer. In other words, the invention provides a computer program (product) comprising instructions that, when the program is executed by a computer, cause the computer to execute the method / steps of the method according to the invention in one of its embodiments.

[0045] According to the invention, a computer-readable data carrier with program code of a computer program is also proposed for executing at least parts of the method according to the invention in one of its embodiments when the computer program is executed on a computer. In other words, the invention relates to a computer-readable (storage) medium comprising instructions which, when executed by a computer, cause the computer to execute the method / steps of the method according to the invention in one of its embodiments.

[0046] The described designs and further training courses can be combined as desired.

[0047] Further possible embodiments, developments and implementations of the invention also include combinations of features of the invention described previously or below with regard to the embodiments that are not explicitly mentioned.

[0048] Short description of the drawings

[0049] The accompanying drawings are intended to provide a further understanding of embodiments of the invention. They illustrate embodiments and, in conjunction with the description, serve to explain principles and concepts of the invention.

[0050] Other embodiments and many of the aforementioned advantages will become apparent upon review of the drawings. The elements illustrated in the drawings are not necessarily drawn to scale.

[0051] They show:

[0052] Fig. 1 is a schematic flow diagram of an embodiment of the present method;

[0053] Fig. 2 is a schematic block diagram of a device according to an embodiment;

[0054] Fig. 3 shows a schematic block diagram of a device according to another embodiment; and Fig. 4 shows three different training approaches for training a cascaded model architecture.

[0055] In the figures of the drawings, the same reference symbols designate the same or functionally equivalent elements, parts or components, unless otherwise stated.

[0056] Figure 1 shows a schematic flow diagram of a computer-implemented method for controlling and / or regulating a physical system based on at least one state variable of the physical system.

[0057] In any embodiment, the method can be carried out at least partially by a device 100, which for this purpose can comprise several components not shown in detail, for example, one or more provision devices and / or at least one evaluation and computing device. It is understood that the provision device can be designed jointly with the evaluation and computing device or can be different from it. Furthermore, the device 100 can comprise a storage device and / or an output device and / or a display device and / or an input device.

[0058] According to the invention, the computer-implemented method comprises at least the following steps:

[0059] In a step S1, time series-based measurement data of the physical system, at least one, in particular trained, physical model for estimating the at least one state variable on the basis of the provided, time series-based measurement data, and at least one data-based, in particular trained, machine learning model are provided.

[0060] In a step S2, the at least one state variable is estimated by the at least one physical model based on the provided, time-series-based measurement data. In a step S3, at least one estimation error of the physical model is identified and / or determined by the at least one data-based machine learning model based on the provided, time-series-based measurement data and / or based on the at least one estimated state variable.

[0061] In a step S4, the at least one estimated state variable is optimized on the basis of the at least one estimation error.

[0062] In a step S5, the physical system is controlled and / or regulated on the basis of the at least one optimized, estimated state variable.

[0063] Fig. 2 shows an embodiment of a device 100 for controlling and / or regulating a physical system based on at least one state variable 1 of the physical system. The device 100 comprises at least one evaluation and / or computing device 10. The evaluation and / or computing device 10 is designed to provide time-series-based measurement data 12 of a physical system. The physical system can be, for example, a motor vehicle with a vehicle steering system comprising a rack. The at least one state variable 1 can be, for example, a rack force to be estimated.

[0064] In the case of a rack force estimation, the time series-based measurement data 12 may include a longitudinal acceleration and / or a lateral acceleration and / or a vehicle speed and / or a steering angle and / or a steering angular velocity and / or a rack position and / or a rack speed and / or a rack acceleration and / or an engine torque and / or a hand torque.

[0065] The evaluation and / or computing device 10 is designed to provide at least one, in particular trained, physical model 14 for estimating the at least one state variable 1 based on the provided time-series-based measurement data 12, and at least one (in this case two) data-based, in particular trained, machine learning model 16, 18. The models 14, 16, 18 are arranged in different cascade stages K1, K2, K3. The physical model can be, for example, a steering geometry model, alternatively an RFMD, RFMC, or an ESM.

[0066] The evaluation and / or computing device 10 is designed to estimate the at least one state variable 1 by the at least one physical model 14 on the basis of the provided, time-series-based measurement data 12, as can be seen from the data flow in Fig. 2, which is indicated by corresponding arrows.

[0067] The evaluation and / or computing device 10 is configured to predict at least one estimation error 2 of the physical model 14 using the at least one data-based machine learning model 16 based on the provided time-series-based measurement data 12. The model 16 is connected in parallel to the model 14, but is arranged on a downstream cascade K2.

[0068] The evaluation and / or computing device 10 is configured to optimize and / or correct the at least one estimated state variable 1 based on the at least one estimation error 2. The optimized and / or corrected state variable is identified by reference numeral 3.

[0069] According to this embodiment, the evaluation and / or computing device 10 is further configured to identify and / or determine at least one error 3 of the estimation error 2 based on the provided time-series-based measurement data 12 and on the basis of the at least one optimized estimated state variable 3, and to further optimize the already optimized at least one estimated state variable 3 based on the at least one error of the estimation error 2. This further optimized state variable is designated by the reference numeral 4.

[0070] Model 18 receives both the measured data 12 and the optimized state variable as input parameters and is thus connected in series with models 14 and 16, but on a different cascade K3. Model 18 thus provides the final prediction of the state variables 1 and 4 and uses both the outputs of the preceding model 16 and the measured data 12.

[0071] The physical system can be controlled and / or regulated on the basis of the optimized state variable 3 or on the basis of the further optimized state variable 4.

[0072] The device 100 shown in Fig. 3 differs with regard to the model architecture within the three-stage cascade K1, K2, K3. According to this embodiment, the data-based machine learning model 18 determines the error 5 of the estimation error 2 solely based on the measurement data 12, without incorporating additional variables from the previous cascades. Model 18 is nevertheless arranged on cascade K3. Model 18 is thus connected in parallel to models 14, 16.

[0073] Fig. 4(a) shows a training procedure for training the cascaded model architecture according to the present invention. The at least one physical model 14 and the at least one data-based machine learning model 16, 18 are trained sequentially, i.e., in temporally successive training steps 1. Training step 1. TS, 2.

[0074] Training step 2. TS, ... Nth training step N. TS, trained. The at least one physical model 14 is trained before the at least one data-based machine learning model 16, 18. The trained, at least one physical model 14 is preferably used to provide training data for the subsequently trained, at least one data-based machine learning model 16, 18.

[0075] Fig. 4(b) shows a training procedure for training the cascaded model architecture according to the present invention. The at least one physical model 14 and the at least one data-based machine learning model 16, 18 are trained in parallel, in particular independently of one another and / or autonomously and / or autonomously.

[0076] Fig. 4(c) shows a training procedure for training the cascaded model architecture according to the present invention. The at least one physical model 14 and the at least one data-based machine learning model 16, 18 are trained cyclically and sequentially. The at least one physical model 14 is trained stepwise and / or iteratively, i.e., in temporally successive cycles of training steps TS (1st cycle 1 . Cy, 2nd cycle 2 . Cy, etc.). The at least one data-based machine learning model 16, 18 is trained after each training step and / or after each training iteration of the at least one physical model 14, preferably also based on the stepwise and / or iteratively trained at least one physical model.

[0077] Experiments and / or simulations have shown that the present method can achieve a significant improvement in the estimation compared to an estimation using a physical model.

Claims

Claims 1. Computer-implemented method for controlling and / or regulating (S5) a physical system based on at least one estimated state variable (3,4) of the physical system, comprising the steps: Providing (S1) time-series-based measurement data (12) of the physical system, at least one, in particular trained, physical model (14) for estimating the at least one state variable (1) on the basis of the provided, time-series-based measurement data (12), and at least one data-based, in particular trained, machine learning model (16, 18); Estimating (S2) the at least one state variable (1) by the at least one physical model (14) on the basis of the provided time-series-based measurement data (12); Identifying and / or determining (S3) at least one estimation error (2) of the physical model (14) by the at least one data-based machine learning model (16, 18) on the basis of the provided time-series-based measurement data (12) and / or on the basis of the at least one estimated state variable (1); Optimizing (S4) the at least one estimated state variable (1) based on the at least one estimation error (2); and controlling and / or regulating (S5) the physical system based on the at least one optimized estimated state variable (3, 4).

2. The method of claim 1, further comprising: Providing at least one further physical model and / or one further data-based machine learning model (18); Identifying and / or determining at least one error (5) of the estimation error (2) on the basis of the provided time series-based measurement data (12) and / or on the basis of the at least one estimated state variable (1) and / or on the basis of the at least one optimized estimated state variable (3) by the at least one further physical model and / or the at least one further data-based machine learning model (18); Optimizing the already optimized, at least one, estimated state variable (3) on the basis of the at least one error (5) of the estimation error (2).

3. The method according to claim 1 or 2, wherein the identification and / or determination of the at least one estimation error (2) and / or the identification and / or determination of the at least one error (5) of the estimation error (2) is carried out on the basis of at least one historical estimated state variable and / or on the basis of at least one historical, optimized, estimated state variable and / or on the basis of at least one historical, multiply optimized, estimated state variable, and / or on the basis of at least one historical estimation error, and / or on the basis of at least one historical error of the estimation error.

4. The method according to any one of claims 1 to 3, wherein the at least one physical model (14) and the at least one data-based machine learning model (16, 18) are trained sequentially, wherein the at least one physical model (14) is trained before the at least one data-based machine learning model (16, 18), and wherein the trained at least one physical model (14) is used in particular to provide training data for the subsequently trained at least one data-based machine learning model (16, 18).

5. The method according to one of claims 1 to 3, wherein the at least one physical model (14) and the at least one data-based machine learning model (16, 18) are trained in parallel, in particular independently of one another and / or autonomously and / or independently.

6. The method according to one of claims 1 to 3, wherein the at least one physical model (14) and the at least one data-based, machine learning model (16, 18) are trained cyclically sequentially, wherein the at least one physical model (14) is trained stepwise and / or iteratively, and wherein the at least one data-based, machine learning model (16, 18) is trained after each training step and / or after each training iteration of the at least one physical model (14), in particular on the basis of the stepwise and / or iteratively trained at least one physical model (14).

7. The method according to any one of the preceding claims, wherein the at least one physical model (14) is trained based on a training data set comprising a plurality of time-series-based measurement data (12) of the physical system and a plurality of associated state variables (1); wherein the data-based machine learning model (16, 18) is trained based on a training data set comprising the plurality of time-series-based measurement data (12) of the physical system.

8. The method according to any one of the preceding claims, wherein the physical system comprises a motor vehicle with a vehicle steering system comprising a rack, and wherein the at least one state variable (1, 3, 4) comprises a rack force.

9. The method according to claim 8, wherein the time-series-based measurement data (12) comprise a longitudinal acceleration and / or a lateral acceleration and / or a vehicle speed and / or a steering angle and / or a steering angular speed and / or a rack position and / or a rack speed and / or a rack acceleration and / or an engine torque and / or a hand torque.

10. Device (100) for controlling and / or regulating (S5) a physical system on the basis of at least one estimated state variable (3, 4) of the physical system, the device (100) comprising at least one evaluation and / or computing device (10) which is designed to carry out at least the following steps: Providing time-series-based measurement data (12) of the physical system, at least one, in particular trained, physical model (14) for estimating the at least one state variable (1) on the basis of the provided, time-series-based measurement data (12), and at least one data-based, in particular trained, machine learning model (16, 18); Estimating the at least one state variable (1) by the at least one physical model (14) on the basis of the provided time-series-based measurement data (12); Identifying and / or determining at least one estimation error (2) of the physical model (14) by the at least one data-based machine learning model (16) on the basis of the provided time-series-based measurement data (12) and / or on the basis of the at least one estimated state variable (1); Optimizing the at least one estimated state variable (1) based on the at least one estimation error (2); and controlling and / or regulating the physical system based on the at least one optimized estimated state variable (3, 4).

11. A computer program comprising program code for executing at least parts of a method according to any one of claims 1 to 9 when the computer program is executed on a computer.

12. A computer-readable data carrier with program code of a computer program for carrying out at least parts of a method according to one of claims 1 to 9 when the computer program is executed on a computer.

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