EMB system closed-loop control method based on digital-analog dual-drive modeling and KF-UI estimation

Abstract

The invention belongs to the technical field of intelligent driving and vehicle control, and discloses an EMB system closed-loop control method based on digital-analog double-drive modeling and KF-UI estimation, and the method comprises the following steps: building a physical model of an EMB system according to the structure of the EMB system; based on the physical model, a data-driven friction torque linear modeling method is adopted to convert the nonlinear friction torque into a linear system model; designing a separation strategy of the clamping force based on the linear system model, decomposing a linear part in the clamping force, and correcting the linear part; constructing a state space model containing process noise and measurement noise by combining a linear system model and a separation strategy; joint estimation of the system state and unknown input is carried out on the state space model, and online estimation of the clamping force is achieved; the problems that in the prior art, non-linear modeling precision is insufficient, and clamping force estimation lacks self-adaptability are effectively solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent driving and vehicle control, and particularly relates to an EMB system closed-loop control method based on digital-analog dual-drive modeling and KF-UI estimation. BACKGROUND

[0002] As a core executive component of intelligent driving and new energy vehicles, the performance of an electronic mechanical brake (EMB) system directly affects braking safety and control accuracy. However, the EMB system has significant strong nonlinear characteristics, including friction, hysteresis effect, and transmission gap, etc. Traditional modeling methods based on physical laws are difficult to accurately describe these complex dynamic behaviors, resulting in a large deviation between the model and the actual system. In addition, existing clamping force estimation methods (such as polynomial fitting) rely on offline calibration data and cannot adapt to dynamic factors such as environmental temperature changes and mechanical wear, resulting in a significant decrease in estimation accuracy as the working condition changes. These problems seriously restrict the reliability of the EMB system in high-precision control and complex working conditions. Therefore, the existing technology has the problems of insufficient nonlinear modeling accuracy and lack of adaptability in clamping force estimation. SUMMARY

[0003] In view of the deficiencies of the prior art, the purpose of the present application is to provide an EMB system closed-loop control method based on digital-analog dual-drive modeling and KF-UI estimation, which solves the problems of insufficient nonlinear modeling accuracy and lack of adaptability in clamping force estimation in the prior art.

[0004] The purpose of the present application can be achieved by the following technical solutions: An EMB system closed-loop control method based on digital-analog dual-drive modeling and KF-UI estimation, comprising the following steps: According to the structure of the EMB system, a physical model of the EMB system is established; Based on the physical model, EMB system operation data is collected, and a data-driven friction torque linear modeling method is used to map the dynamic process of the nonlinear friction torque to a high-dimensional observation space, and a linear system model is obtained through data-driven identification; Based on the linear system model, a clamping force separation strategy is designed to decompose and correct the linear part of the clamping force; Combined with the linear system model and the separation strategy, a state space model containing process noise and measurement noise is constructed; The state space model is subjected to joint estimation of system state and unknown input to realize online estimation of the clamping force; According to the clamping force estimation result, a multi-loop closed-loop control strategy is used to perform closed-loop tracking control on the expected clamping force.

[0005] The physical model of the EMB system is established, specifically comprising the following steps: According to Ohm's law and electromagnetic characteristics of the motor, the dynamic model of the braking motor is established, and the specific expression is as follows: wherein, L is the motor inductance; is the motor current; is the motor internal resistance; is the back electromotive force; is the motor speed; is the motor input voltage; denotes the differential operator with respect to the time variable t ; According to Newton's second law, the torque balance equation of the system is established, and the specific expression is as follows: wherein, is the moment of inertia of the motor output shaft; denotes the torque constant of the motor; is the friction torque; is the braking clamping force; is the clamping force gain; denotes the angular acceleration of the motor.

[0006] The EMB system operation data is collected, and the data-driven friction torque linear modeling method is adopted to map the dynamic process of the nonlinear friction torque to a high-dimensional observation space, and a linear system model is obtained through data-driven identification, which includes the following steps: The current , motor speed , motor angle and clamping force data during the motor operation are collected. The data-driven friction torque linear modeling method based on Koopman operator theory defines the system original state input, control input and observation output, which are as follows: wherein, is the system original state input of the Koopman operator space; is the corresponding control input; is the observation output of the Koopman operator; is the true friction torque of the system; The system original state input is mapped through the observation function The mapping to the high-dimensional observation space constructs the state of the system after dimensionality increase, and the specific expression is as follows: wherein, represents the state after dimensionality increase; Combined with the state after dimensionality increase , based on the Koopman operator theory, the dynamic process of the nonlinear friction torque is mapped to the high-dimensional observation space, and the theoretical framework of the linear state space model is established, and the expression of the theoretical framework is as follows: wherein, represents the system state input of the high-dimensional linear space; 、 、 、 together constitute a four-element linear parameter matrix set } to be solved by the system; 、 、 、 are respectively the coefficient matrices of the system state transition, control input mapping, observation output mapping and system direct input-output coupling of the high-dimensional linear space; Based on the historical operation data of the EMB system, a data set of state-input-output ) is constructed, and the following data matrices are defined: wherein, is the system state data set from 1 to M -1 moment; is the system state data set from 2 to M moment; is the system input data set from 1 to M -1 moment; is the system output data set from 1 to M -1 moment; According to the data matrix, the least square method is used to construct an optimization problem for solving the four-element linear parameter matrix set }, and the expression of the optimization problem is as follows: wherein, denotes the Frobenius norm of a matrix; substitute the obtained set of four linear parameter matrices into the theoretical framework to obtain a linear system model, and the linear system model is expressed as follows: wherein, denotes the training result of the friction torque; denotes the state at the next moment after dimensionality increase.

[0007] Based on the linear system model, a separation strategy of clamping force is designed to decompose the linear part of the clamping force and make corrections, which includes the following steps: The separation strategy is designed to decompose the clamping force into a linear part and a nonlinear part, and the mathematical expression of the separation strategy is as follows: wherein, is the total clamping force of the system; is the linear part of the clamping force, which reflects the linear response trend of the force with displacement; is the nonlinear part of the clamping force, which reflects the part caused by hysteresis, friction and structural deformation in the system; The linear part of the clamping force is obtained by taking the derivative of the time variable t to obtain: wherein, is the slope of the linear clamping force; denotes the change rate of the linear part of the clamping force; Since the actual operation process may switch frequently between clamping and releasing actions at any braking force during the braking process, the linear part of the clamping force change rate needs to be adjusted, and the mathematical expression of the adjustment process is as follows: wherein, denotes the correction term, denotes the clamping force error caused by the change of the switching position; is the dynamic change amount of the actual linear change rate relative to the ideal slope .

[0008] Combined with the linear system model and the separation strategy, a state space model containing system process noise and measurement noise is constructed, which includes the following steps: Combining a linear system model and a separation strategy, the forward Euler discretization method is used to select the system's state variables. x , ; Clamping force of the nonlinear part Unknown inputs modeled as state-space models Motor input voltage For the known input of the state-space model ; Define the control input of the state-space model as follows: ,but ; Define the output of the state-space model as y ,but ; Based on the control input and output of the state-space model, a state-space model containing system process noise and measurement noise is constructed, as shown in the following expression: in, A d , B d and C d These are the state matrix, control matrix, and output matrix of the EMB system. A d , B d and C d The expression is as follows: in, and These are system process noise and measurement noise, respectively.

[0009] The Kalman filter algorithm is used to jointly estimate the system state and unknown inputs of the state-space model. The specific steps include: Based on the state-space model, construct a system including state variables. x Estimating channels and unknown inputs An estimation framework for estimating channels; The estimation framework is initialized as follows: in, Represents the initial state variable Expectations ; Indicates initial unknown input Expectations ; Kalman gain coefficient K The value at time zero ; The initial covariance matrix is ​​given by the known state. For unknown input The initial covariance matrix; k State variable estimation is performed at any time, and the specific expression is as follows: In the formula, For based on k Always k+1 The estimation results of the system state at time t; for k The optimal estimation result of the time-series system; for k The estimated value of the input is controlled at all times; k+1 The system gain is calculated at each step, and the specific expression is as follows: In the formula, T This represents the matrix transpose operator; for k Time-state prediction covariance matrix; for k Update the covariance matrix at each time step; for r 3D identity matrix; and Let represent the covariance matrices of process noise and measurement noise, respectively; for K Kalman gain at time +1; for k The gain matrix related to the unknown input estimation at time +1; k+1 The estimation results are constantly being corrected, and the correction expression is as follows: wherein, is k the optimal estimation result of the state at time is k the estimation result of the unknown input at time k+1 the covariance matrix update at time wherein, is n a unit matrix of dimension is k+1 the state prediction covariance matrix at time Based on the Kalman filtering process, the clamping force estimation result can be obtained.

[0010] A multi-loop closed-loop control strategy is adopted to perform closed-loop tracking control on the expected clamping force, which specifically includes the following steps: Based on the physical model and the clamping force estimation result , a three-loop cascade PID control algorithm including an outer clamping force control loop, a middle speed control loop and an inner current control loop is constructed, and the closed-loop tracking control process is as follows: The EMB system receives the braking instruction and calculates the error clamping force between the braking instruction and the outer clamping force estimation result . The error clamping force is taken as the input of the clamping force control loop, and the target motor speed is output through the PID regulator, which is specifically as follows: wherein, , , are the proportional gain coefficient, the integral gain coefficient and the differential gain coefficient of the clamping force control loop, respectively; The error speed between the target motor speed and the actual motor speed is taken as the input of the middle speed control loop, and the expected motor current is output through the PID regulation, which is specifically as follows: wherein, , , are the proportional gain coefficient, the integral gain coefficient and the differential gain coefficient of the speed control loop, respectively; The expected motor current Error current between the measured current As the input of the inner loop current control ring, the PID adjustment output motor input voltage of the EMB system , The specific expression is as follows: Wherein, , , The proportional gain coefficient, integral gain coefficient and differential gain coefficient of the current control ring respectively.

[0011] Advantages of the present application: 1. The present application effectively solves the problem of insufficient nonlinear modeling precision in the prior art by establishing a physical model of the EMB system and linearizing the nonlinear friction torque based on a data-driven method. The braking force is decomposed into linear and nonlinear parts by combining the clamping force separation strategy, significantly improving the adaptive ability of clamping force estimation. By constructing a state space model and a joint estimation algorithm, high-precision online estimation of the clamping force is realized. Finally, a multi-loop closed-loop control strategy is adopted to ensure stable tracking control of the expected clamping force, effectively solving the problems of insufficient nonlinear modeling precision and lack of adaptability of clamping force estimation in the prior art. 2. The high-dimensional linear space expression constructed based on the Koopman operator theory realizes accurate linearization expression of the nonlinear system by selecting an observation function to map the original state of the system to the elevated state. In the clamping force separation strategy, the linear clamping force rate is adjusted in real time through a dynamic correction term, effectively solving the problem of sudden change of braking force during working condition switching. The improved unknown input Kalman filter algorithm based on the constructed state space model simultaneously processes the system state variables and unknown input variables, significantly improving the robustness of the estimation process. The optimized three-loop cascade control architecture realizes the balance between fast response and accurate tracking of clamping force control under complex working conditions through the coordinated adjustment of the outer loop, the middle loop and the inner loop. BRIEF DESCRIPTION OF DRAWINGS

[0012] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced as follows. Obviously, for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

[0013] Figure 1 is the schematic diagram of the whole process of the control method of the present application; Figure 2 is the linear system model training result schematic diagram of the present application; ​Figure 3 is a schematic diagram of clamping force estimation result in an embodiment of the present application; Figure 4 is a schematic diagram of closed-loop tracking control real vehicle test result in an embodiment of the present application. DETAILED DESCRIPTION

[0014] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0015] As shown in the figure, an EMB system closed-loop control method based on digital-analog double drive modeling and KF-UI estimation includes the following steps: Figures 1 to 4 According to the structure of the EMB system, a physical model of the EMB system is established; Based on the physical model, EMB system operation data are collected, and a data-driven friction torque linear modeling method is used to map the dynamic process of the nonlinear friction torque to a high-dimensional observation space, and a linear system model is obtained through data-driven identification; Based on the linear system model, a clamping force separation strategy is designed to decompose the linear part of the clamping force and correct it; Combined with the linear system model and the separation strategy, a state space model containing process noise and measurement noise is constructed; The state space model is subjected to joint estimation of system state and unknown input to realize online estimation of clamping force; According to the clamping force estimation result, a multi-loop closed-loop control strategy is used to realize closed-loop tracking control of the expected clamping force. The physical model of the EMB system is established, specifically including the following steps:

[0016] According to Ohm's law and the electromagnetic characteristics of the motor, a dynamic model of the brake motor is established, and the specific expression is as follows: wherein, L is the motor inductance; is the motor current; is the motor internal resistance; is the back electromotive force; is the motor speed; is the motor input voltage; denotes the differential operator for the time variable t derivation; According to Newton's second law, a torque balance equation of the system is established, and the specific expression is as follows:​ in, The moment of inertia of the motor output shaft; This represents the torque constant of the motor; This is the frictional torque; This is the braking clamping force; For clamping force gain; This indicates the angular acceleration of the motor.

[0017] Based on the physical model, operational data of the EMB system is collected, and a data-driven linear modeling method for friction torque is adopted to map the dynamic process of nonlinear friction torque to a high-dimensional observation space. The linear system model is then identified through data-driven identification, specifically including the following steps: Collect the current during motor operation Motor speed Motor rotation angle With clamping force data; A data-driven linear modeling method for friction torque based on Koopman operator theory is defined as follows: The system's initial state input, control input, and observed output are defined as follows: in, The system's original state input is given to the Koopman operator space; For the corresponding control input; For the observed output of the Koopman operator; This represents the actual frictional torque of the system. Through observation function Input the original state of the system Mapping to a higher-dimensional observation space, we construct the upgraded state of the system, as shown in the following expression: in, This represents the state after dimensional ascension; Combined with the state after dimensional upgrade Based on the Koopman operator theory, the dynamic process of nonlinear friction torque is mapped to a high-dimensional observation space, establishing a theoretical framework for a linear state-space model. The theoretical framework expression is as follows: in, The system state input represents a high-dimensional linear space; 、 、 、 The four sets of linear parameter matrices to be solved by the system }; 、 、 、 are the coefficient matrices of the system state transition, control input mapping, observation output mapping, and system direct input-output coupling in the high-dimensional linear space, respectively Based on the historical operation data of the EMB system, a data set of state-input-output (SIO) is constructed, and the following data matrices are defined: wherein, is the system state data set from time 1 to time M -1; is the system state data set from time 2 to time M -1; is the system input data set from time 1 to time M -1; is the system output data set from time 1 to time M -1; According to the data matrices, an optimization problem is constructed by using the least square method for solving the four sets of linear parameter matrices }, and the expression of the optimization problem is as follows: wherein, represents the Frobenius norm of a matrix; The four sets of linear parameter matrices } solved are substituted into the theoretical framework to obtain a linear system model, and the expression of the linear system model is as follows: wherein, represents the training result of the friction torque; represents the state at the next time after dimensionality increasing.

[0018] ​Based on the linear system model, a separation strategy of clamping force is designed to decompose the linear part of the clamping force and correct it, which includes the following steps: The separation strategy is designed to decompose the clamping force into linear and nonlinear parts, and the mathematical expression of the separation strategy is as follows: Wherein, is the total clamping force of the system; is the linear part of the clamping force, which reflects the linear response trend of force with displacement; is the nonlinear part of the clamping force, which reflects the part caused by hysteresis, friction and structural deformation in the system; The linear part of the clamping force is decomposed as The time variable t is differentiated to obtain: Wherein, is the slope of the linear clamping force; represents the change rate of the linear part of the clamping force; Because in the actual operation process, the braking process may switch frequently between clamping and releasing actions at any braking force, the change rate of the linear part of the clamping force needs to be modified, and the mathematical expression of the modification process is as follows: Wherein, represents the correction term, represents the clamping force error caused by the change of switching position; is the dynamic change amount of the actual linear change rate relative to the ideal slope .

[0019] Combined with the linear system model and the separation strategy, a state space model containing system process noise and measurement noise is constructed, which includes the following steps: Combined with the linear system model and the separation strategy, the forward Euler discrete method is used to select the state variables x of the system ; The nonlinear part of the clamping force is modeled as the unknown input of the state space model, and the motor input voltage is the known input of the state space model; The control input of the state space model is defined as , then ; The output of the state space model is defined as y , then ; Based on the state space model of control input, output, the state space model containing system process noise and measurement noise is constructed, the specific expression is as follows: Among them, A d , B d And C d The state matrix, control matrix and output matrix of EMB system are respectively, A d , B d And C d The expression is as follows: Among them, And The system process noise and measurement noise are respectively.

[0020] The Kalman filter (Kalman Filter with Unknown Input, KF-UI) algorithm is used to estimate the system state and unknown input of the state space model, which includes the following steps: Based on the state space model, the state variable x Estimate the channel and unknown input Estimate the estimation framework of the channel; Initialize the estimation framework, as follows: Among them, Indicates the expectation Of the initial state variable ; Indicates the expectation Of the initial unknown input ; The Kalman gain coefficient K At zero time ; The initial covariance matrix of known state; The initial unknown input The initial covariance matrix; k State variable estimation is performed at any time, and the specific expression is as follows: In the formula, For based on k Always k+1 The estimation results of the system state at time t; for k The optimal estimation result of the time-series system; for k The estimated value of the input is controlled at all times; k+1 The system gain is calculated at each step, and the specific expression is as follows: In the formula, T This represents the matrix transpose operator; for k Time-state prediction covariance matrix; for k Update the covariance matrix at each time step; for r 3D identity matrix; and Let represent the covariance matrices of process noise and measurement noise, respectively; for K Kalman gain at time +1; for k The gain matrix related to the unknown input estimation at time +1; k+1 The estimation results are constantly being corrected, and the correction expression is as follows: in, for k The optimal state estimation result at time +1; for k The estimation result of the unknown input at time +1; k+1 Time-varying covariance matrix update: In the formula, for n 3D identity matrix; for k+1 Time-state prediction covariance matrix; Based on the Kalman filtering process, the clamping force estimation result can be obtained .

[0021] A multi-loop closed-loop control strategy is adopted to perform closed-loop tracking control on the expected clamping force, specifically including the following steps: Based on the physical model and the clamping force estimation result , a three-loop cascade PID control algorithm including an outer loop clamping force control loop, a middle loop rotational speed control loop and an inner loop current control loop is constructed, and the closed-loop tracking control process is as follows: The EMB system receives the braking instruction , and calculates the error clamping force between the braking instruction and the outer loop clamping force estimation result ; ; The error clamping force is taken as the input of the clamping force control loop, and the target motor rotational speed is output through the PID regulator, specifically as follows: Among them, , , are the proportional gain coefficient, integral gain coefficient and differential gain coefficient of the clamping force control loop, respectively; The error rotational speed between the target motor rotational speed and the actual motor rotational speed is taken as the input of the middle loop rotational speed control loop, and the expected motor current is output through the PID regulation, specifically as follows: Among them, , , are the proportional gain coefficient, integral gain coefficient and differential gain coefficient of the rotational speed control loop, respectively; The error current between the expected current and the measured current is taken as the input of the inner loop current control loop, and the motor input voltage of the EMB system is output through the PID regulation, specifically as follows: Among them, , , are the proportional gain coefficient, integral gain coefficient and differential gain coefficient of the current control loop, respectively.

[0022] The verification results of the EMB system closed-loop control method based on digital-analog dual-drive modeling and KF-UI estimation in the present application are shown in Figures 2 to 4 As shown in Figure 2 , the training results of the clamping force sine (Asin, 4Asin) and the friction model under the M-type working condition are shown. Under the normalized scale, the friction torque modeling error is kept below 0.03, and the error peak value appears at the clamping and release switching moment. The comparison of the measured value and the estimated value curve shows that the model has good fitting ability for the Asin standard sine wave, the 4Asin high-frequency sine wave and the M-type step wave three working conditions, and the overall relative root mean square error (RRMSE) is 4.5%.

[0023] As shown in Figure 3 , the clamping force estimation results and the clamping force estimation error based on KF-UI are shown, including three test scenarios of M working condition, static working condition and dynamic working condition. As shown in part (a), the comparison curve of the clamping force estimated by KF-UI (solid line) and the real clamping force (dotted line) with time shows that under the M working condition, the static working condition and the dynamic working condition, the estimated value can well track the real value, and the trend of the two curves is basically consistent. Part (b) shows the corresponding clamping force estimation error, the error value fluctuates around the 0 value line, and the absolute value is less than 0.025 most of the time, indicating that the estimation accuracy is high. Overall, the KF-UI algorithm shows good tracking performance and estimation accuracy for the three working conditions within the time range of 0-50 seconds.

[0024] As shown in Figure 4 , the closed-loop tracking performance of the cascade PID control based on KF-UI estimation in the real vehicle test is shown. The three curves of the request value, the measured value and the error are clearly presented in the figure, corresponding to the M, Static and Dynamic three test stages. Under the normalized scale, the cascade PID control strategy based on KF-UI estimation of clamping force realizes effective tracking of the target braking force, and the relative root mean square error (RRMSE) of the overall tracking error is 6.5%, verifying the accuracy and feasibility of the PID control scheme.

[0025] In the description of the present specification, the description of the terms "one embodiment", "example", "specific example" and the like means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are contained in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0026] ​The above shows and describes the basic principles, main features and advantages of the present application. Those skilled in the art should understand that the present application is not limited to the above-mentioned embodiments, and the above-mentioned embodiments and descriptions in the specification are only to illustrate the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application.

Claims

1. An EMB system closed-loop control method based on digital-analog dual drive modeling and KF-UI estimation, characterized in that, The method comprises the following steps: According to the structure of the EMB system, a physical model of the EMB system is established; Based on the physical model, EMB system operation data is collected, and a data-driven friction torque linear modeling method is used to map the dynamic process of the nonlinear friction torque to a high-dimensional observation space, and a linear system model is obtained through data-driven identification; Based on the linear system model, a clamping force separation strategy is designed to decompose and correct the linear part of the clamping force; Combined with the linear system model and the separation strategy, a state space model containing process noise and measurement noise is constructed; The joint estimation of system state and unknown input is performed on the state space model to realize online estimation of clamping force; According to the clamping force estimation result, a multi-loop closed-loop control strategy is adopted to realize closed-loop tracking control of the expected clamping force.

2. The EMB system closed-loop control method based on DQ dual-drive modeling and KF-UI estimation according to claim 1, characterized in that, The physical model of the EMB system is established, specifically including the following steps: According to Ohm's law and the electromagnetic characteristics of the motor, the dynamic model of the brake motor is established, and the specific expression is as follows: wherein, L is the motor inductance; is the motor current; is the motor internal resistance; is the back electromotive force; is the motor rotational speed; is the motor input voltage; denotes the differential operator for the time variable t derivation; According to Newton's second law, the torque balance equation of the system is established, and the specific expression is as follows: wherein, is the moment of inertia of the motor output shaft; denotes the moment constant of the motor; is the friction torque; is the brake clamping force; is the clamping force gain; denotes the motor angular acceleration.

3. The EMB system closed-loop control method based on DQ dual-drive modeling and KF-UI estimation according to claim 2, characterized in that, EMB system operation data is collected, and a data-driven friction torque linear modeling method is used to map the dynamic process of the nonlinear friction torque to a high-dimensional observation space, and a linear system model is obtained through data-driven identification, specifically including the following steps: Collecting current during operation of the motor , motor rotational speed , motor rotational angle and clamping force data; Based on the data-driven friction torque linear modeling method of Koopman operator theory, the original state input, control input and observation output of the system are defined, specifically as follows: wherein, is the system original state input for the Koopman operator space; is the corresponding control input; is the observation output for the Koopman operator; is the system real friction torque; By observing function The original state of the system is input Map to high-dimensional observation space, build the state of the system after dimensionality, the specific expression is as follows: wherein represents the state after the dimensionality increase; Combined with the state after dimensionality increase Based on the Koopman operator theory, the dynamic process of the nonlinear friction torque is mapped to a high-dimensional observation space, and a theoretical framework of a linear state space model is established. The theoretical framework expression is as follows: wherein, represents the system state input of the high-dimensional linear space; , 、 、 together constitute a set of four linear parameter matrices of the system to be solved }; 、 、 、 are respectively the coefficient matrices of the system state transition, control input mapping, observation output mapping, and system direct input-output coupling of the high-dimensional linear space. Based on the historical operation data of the EMB system, a data set of state-input-output (SIO) is constructed, and the following data matrix is defined: ) wherein, is 1 to M the system state data set at time -1; is the system state data set at time 2 to M; is 1 to M the system input data set at time -1; is 1 to M the system output data set at time -1; According to the data matrix, an optimization problem is constructed by using a least square method, and a set of four-element linear parameter matrices is solved }The expression of the optimization problem is as follows: wherein denotes the Frobenius norm of a matrix; The four-element linear parameter matrix set { } obtained by solving is substituted into the theoretical framework to obtain a linear system model, and the linear system model expression is as follows: wherein, the training result of the friction torque; denotes the state at the next time after the dimensionality increase.

4. The EMB system closed-loop control method based on Digi-Model Dual-Drive Modeling and KF-UI Estimation according to claim 3, characterized in that, Based on the linear system model, a clamping force separation strategy is designed to decompose and correct the linear part of the clamping force, specifically including the following steps: The separation strategy is designed to decompose the clamping force into linear and nonlinear parts, and the mathematical expression of the separation strategy is as follows: wherein, is the total clamping force of the system; is the linear portion of the clamping force, representing a linear response trend of the force with displacement; is the nonlinear portion of the clamping force, reflecting the portion of the system caused by hysteresis, friction, and structural deformation; Clamping force of linear portion Time variable t Taking derivative, we get: wherein, is the linear clamping force slope; represents the linear portion clamping force rate of change; Due to the actual operation process, the brake process may frequently switch between clamping and releasing actions at any braking force, and the linear part of the clamping force change rate needs to be modified, and the mathematical expression of the modification process is as follows: wherein, represents a correction term, represents a clamping force error caused by a change in switching position; is a dynamic change amount of the actual linear change rate with respect to the ideal slope .

5. The EMB system closed-loop control method based on DQ dual-drive modeling and KF-UI estimation according to claim 4, characterized in that, Combined with the linear system model and the separation strategy, a state space model containing system process noise and measurement noise is constructed, specifically including the following steps: Combining linear system model and separation strategy, forward Euler discrete method is adopted to select state variable of system x , ; Clamping force of nonlinear portion Unknown input modeled as a state space model Motor input voltage Known input for state space model ; The control input representation defining the state space model is denoted as then ; The output representation of the state space model is defined as y then ; Based on the control input and output of the state space model, a state space model containing system process noise and measurement noise is constructed, and the specific expression is as follows: wherein, A d , B d and C d are the state matrix, control matrix and output matrix of the EMB system, respectively, A d , B d and C d the expressions of which are as follows: wherein with are the system process noise and measurement noise, respectively.

6. The EMB system closed-loop control method based on DQ dual-drive modeling and KF-UI estimation according to claim 5, characterized in that, The joint estimation of system state and unknown input is performed on the state space model using Kalman filter algorithm, specifically including the following steps: Based on the state space model, a state variable x Estimation of the channel and unknown inputs Estimation framework for estimating the channel; Initialize the estimation framework, specifically as follows: wherein represents the initial state variable ; ; represents the initial unknown input ; ; is a Kalman gain coefficient K at time zero ; is an initial covariance matrix of the known state is an initial covariance matrix of the unknown input ; k The state variable estimation is performed at every time instant, and the specific expression is as follows: wherein is based on k the estimate of the system state at time k+1 the estimate of the system state at time is k the optimal estimate of the system at time is k the estimate of the control input at time k+1 The system gain at time t is calculated as follows: wherein T denotes the matrix transpose operator; is k the state prediction covariance matrix at time k; is k the state update covariance matrix at time k; is r the n x n identity matrix; and denote the covariance matrices of the process noise and measurement noise, respectively; is K the Kalman gain at time k + 1; is k the gain matrix related to the unknown input estimate at time k + 1; k+1 The estimation result is corrected at the moment, and the correction expression is as follows: wherein, is k the optimal estimation result of the state at time is k the estimation result of the unknown input at time k+1 Time-varying covariance matrix update: wherein is n identity matrix; is k+1 time state prediction covariance matrix; Based on a Kalman filtering process, a clamp force estimate can be obtained .

7. The EMB system closed-loop control method based on DQ dual-drive modeling and KF-UI estimation according to claim 6, characterized in that, A multi-loop closed-loop control strategy is adopted to realize closed-loop tracking control of the expected clamping force, specifically including the following steps: Based on the physical model and the clamping force estimation results , a three-loop cascade PID control algorithm including an outer loop clamping force control loop, a middle loop rotating speed control loop and an inner loop current control loop is constructed, and the closed-loop tracking control process is as follows: The EMB system receives a braking command and calculates a braking command with an error clamping force between the outer loop clamping force estimate ; With error clamping force As an input to the clamping force control loop, the target motor speed is output by a PID regulator Specifically as follows: wherein, , , Kp, Ki, and Kd are proportional, integral, and derivative gain coefficients of the clamp force control loop, respectively. The target motor speed The error speed between the target motor speed and the actual motor speed is input to the PID regulator to output the desired motor current as follows: wherein, , , are the proportional gain coefficient, the integral gain coefficient and the derivative gain coefficient of the speed control loop, respectively; with the error current between the measured current and the desired current as input, the PID regulation outputs the motor input voltage of the EMB system , the specific expression is as follows: wherein, , , are the proportional, integral and derivative gain coefficients of the current control loop, respectively.

Images