An improved MPC adaptive time delay compensation method based on unscented Kalman filter

Abstract

An improved MPC adaptive time delay compensation method based on unscented Kalman filter belongs to the technical field of structural seismic test and is used for solving the problems of time delay, multi-actuator coupling and noise interference in multi-axis real-time hybrid test. The method comprises the following steps: offline calibration of system parameters and UKF initial value; seismic excitation input numerical substructure, and expected displacement of actuators is obtained through coordinate conversion; UKF optimal state estimation is taken as initial condition, and MPC rolling optimization is used to solve control instruction; physical substructure is loaded and measured displacement and counterforce are collected; measured data is input into UKF for nonlinear filtering, and updated state estimation is output; finally, state estimation and measured counterforce are fed back to the numerical substructure, expected displacement is updated, and the above steps are repeated to form a closed-loop adaptive compensation. The method can effectively improve the precision and robustness of multi-axis loading control and is suitable for complex structure seismic test in the field of civil engineering.

Description

Technical Field

[0001] This invention relates to the field of structural seismic testing technology, specifically to an improved MPC adaptive time delay compensation method based on unscented Kalman filtering. Background Technology

[0002] Real-time hybrid tests (RTHS) are a key technology for evaluating the seismic performance of structures, while multi-axis real-time hybrid tests (maRTHS) simulate multi-dimensional dynamic loads, which can more realistically reflect the seismic response of complex engineering structures (such as high-rise buildings and long-span bridges), providing accurate experimental basis for structural seismic design. However, time delay compensation in maRTHS faces the challenge of the complexity of multi-input multi-output systems. The inherent defects of servo loading systems and the dynamic delay and nonlinear characteristics of hydraulic servo actuators cause the system to have both time lag and amplitude deviation, resulting in asynchronous interface boundary responses between the numerical substructure and the physical substructure, which seriously affects the stability and accuracy of the test results.

[0003] Limitations of existing compensation methods: Linear Quadratic Gaussian (LQG) control method: As a benchmark method, it has poor adaptability to nonlinear systems, low compensation accuracy, and large overall performance index error.

[0004] The Distributed Unscented Kalman Filter Two-Stage Compensation (D-UKF-TAC) method can achieve high-precision state estimation and time delay and variable time delay compensation through UKF, but the overall performance still has some errors due to the neglect of the interaction between actuators by adopting distributed control. Some indicators are even worse than LQG.

[0005] Traditional Model Predictive Control (MPC) adaptive time delay compensation method: It improves the overall performance by adopting centralized control, but because it does not introduce a state estimator, the compensation accuracy is not as good as D-UKF-TAC, and it is easily affected by measurement noise and model uncertainty.

[0006] Therefore, there is an urgent need for a compensation method that can integrate "high-precision state estimation" and "global optimization control" to solve the bottleneck of "incompatibility between accuracy and global performance" in traditional methods, and to meet the comprehensive requirements of maRTHS for compensation accuracy, robustness and overall test performance. Summary of the Invention

[0007] To address the technical challenges in multi-axis real-time hybrid tests (maRTHS) where time lag and amplitude deviation, neglected multi-actuator coupling effects, measurement noise, and model uncertainty interference make it difficult for traditional compensation methods to balance compensation accuracy, robustness, and overall test performance, this invention provides an improved MPC adaptive time delay compensation method based on unscented Kalman filtering, comprising:

[0008] S1. Offline preparation stage: Build the maRTHS Benchmark model, divide the numerical substructure and physical substructure, determine the transmission system parameters composed of multi-axis hydraulic actuators and couplers, and calibrate the initial state mean, initial covariance matrix and system fixed time delay of the unscented Kalman filter through offline experiments.

[0009] S2. Desired Displacement Acquisition Stage: The seismic excitation is input into the numerical substructure, and the motion equation is solved to obtain the desired displacement including displacement and rotation. The desired displacement that the two hydraulic actuators can achieve translational motion is obtained through coordinate transformation.

[0010] S3.MPC Control Command Solving Stage: Using the prediction step size, control step size, error weight matrix, and control input weight matrix as initial conditions, the dynamic characteristics of the controlled system are described using a state-space model, and the optimal control command is solved through rolling optimization of model predictive control.

[0011] S4. Measured data acquisition stage: Send the optimal control command to the transmission system, load the physical substructure, and acquire the measured displacement and measured reaction force;

[0012] S5. UKF State Estimation Stage: The optimal control command and the measured displacement containing noise are input into the UKF estimator. The UKF algorithm is used to perform nonlinear estimation of the system state, filter out measurement noise and model uncertainty, and output the optimal state estimate.

[0013] S6. Closed-loop cycle stage: After the optimal state estimate is transformed by coordinate transformation, it is input into the numerical substructure along with the measured reaction force and the seismic excitation to update the new expected displacement. Then, with the new expected displacement and the optimal state estimate as the initial conditions, the process returns to S3 to repeat the MPC rolling optimization, forming a closed-loop cycle to achieve time delay compensation.

[0014] Furthermore, in S3, the initial conditions are specifically: prediction step size p=1, control step size m=1, error weight matrix Q=10I, and control input weight matrix R=100I.

[0015] Furthermore, in S3, the state-space model satisfies:

[0016]

[0017]

[0018] In the formula, Let k be the system state vector at time k; For control input; For measurement output; These are the system's state prediction matrix, input matrix, output matrix, and direct transfer matrix, respectively. and These are process noise and measurement noise, respectively, both of which follow a Gaussian distribution.

[0019] Furthermore, in S3, the objective function for the rolling optimization is:

[0020]

[0021] In the formula: For the desired output trajectory, Q is the state error weight matrix, used to minimize the tracking error; R is the control input weight matrix, used to adjust the degree of abrupt changes in the control input to ensure the stability of the control signal; P is the prediction time domain, which determines the number of steps for MPC to predict future states; m is the control movement time domain, which determines the number of steps for MPC to apply optimization control.

[0022] Furthermore, in S5, the parameters of the UKF estimator are set as follows: α=0.001, used to control the distribution range of sigma points; β=2, used to characterize the state distribution characteristics; γ=0, used to ensure that the covariance matrix is ​​positive semidefinite. The UKF estimator includes: an initial state covariance matrix. Measurement noise covariance matrix process noise covariance matrix .

[0023] Furthermore, in S5, the state equation and observation equation of the UKF algorithm satisfy:

[0024]

[0025]

[0026]

[0027] In the formula, h corresponds to the system's state equation and observation equation, respectively; The system state at step i includes the measured displacements. Time constant and amplitude gain The identification value needs to be solved using the UKF algorithm; For the input terms of the UKF state equations at step i-1; The i-th observation value is obtained from actual sensor measurements. and These are the process noise vector and the observation noise vector, respectively, both of which are zero-mean Gaussian white noise.

[0028] The beneficial effects of this invention are:

[0029] I. Significantly Improved Compensation Accuracy: By correcting the system state in real time through UKF, the actuator delay, normalized root mean square error and maximum peak error of IMPC-UKF are significantly reduced compared with the traditional MPC, approaching the high accuracy level of D-UKF-TAC.

[0030] II. Optimization of State Estimation Capability: The nonlinear estimation characteristics of UKF significantly reduce the system state estimation error. Specifically, the time delay of measured displacement and filtered displacement is reduced, and the node prediction displacement error is also significantly reduced compared with the traditional MPC, thus improving noise resistance and robustness.

[0031] III. Overall optimal performance: Under three seismic excitations (El Centro, Kobe, and Morgan) and different peak ground acceleration (PGA = 0.1-1.0 m / s²), the overall performance index error of IMPC-UKF is significantly lower than that of LQG and significantly lower than that of traditional MPC. The response error between the reference structure and the test structure and the peak error of the upper node are also reduced.

[0032] IV. Strong engineering applicability: No complex linearization processing is required. It is compatible with multiple types of seismic excitation and multi-degree-of-freedom maRTHS scenarios, and can be directly applied to the seismic performance evaluation of complex structures such as high-rise buildings and bridges. Attached Figure Description

[0033] Figure 1 The diagram shows the maRTHS Benchmark model.

[0034] Figure 2 This is a schematic diagram of the MPC adaptive compensation method.

[0035] Figure 3 A schematic diagram of the improved MPC adaptive time delay compensation method for unscented Kalman filtering;

[0036] Figure 4 The flowchart shows the improved MPC adaptive time delay compensation method for unscented Kalman filtering. Detailed Implementation

[0037] The technical solution of the present invention will be further described below with reference to embodiments, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention. In the following embodiments, process equipment or devices not specifically specified are all conventional equipment or devices in the art. Unless specifically specified, the technical means used in the embodiments of the present invention are all conventional means well known to those skilled in the art.

[0038] Example 1: An improved MPC adaptive time delay compensation method based on unscented Kalman filtering, comprising:

[0039] S1. Offline preparation stage: Build the maRTHS Benchmark model, divide the numerical substructure and physical substructure, determine the transmission system parameters composed of multi-axis hydraulic actuators and couplers, and calibrate the initial state mean, initial covariance matrix and system fixed time delay of the unscented Kalman filter through offline experiments.

[0040] S2. Desired Displacement Acquisition Stage: The seismic excitation is input into the numerical substructure, and the motion equation is solved to obtain the desired displacement including displacement and rotation. The desired displacement that the two hydraulic actuators can achieve translational motion is obtained through coordinate transformation.

[0041] S3.MPC Control Command Solving Stage: Using the prediction step size, control step size, error weight matrix, and control input weight matrix as initial conditions, the dynamic characteristics of the controlled system are described using a state-space model, and the optimal control command is solved through rolling optimization of model predictive control.

[0042] S4. Measured data acquisition stage: Send the optimal control command to the transmission system, load the physical substructure, and acquire the measured displacement and measured reaction force;

[0043] S5. UKF State Estimation Stage: The optimal control command and the measured displacement containing noise are input into the UKF estimator. The UKF algorithm is used to perform nonlinear estimation of the system state, filter out measurement noise and model uncertainty, and output the optimal state estimate.

[0044] S6. Closed-loop cycle stage: After the optimal state estimate is transformed by coordinate transformation, it is input into the numerical substructure along with the measured reaction force and the seismic excitation to update the new expected displacement. Then, with the new expected displacement and the optimal state estimate as the initial conditions, the process returns to S3 to repeat the MPC rolling optimization, forming a closed-loop cycle to achieve time delay compensation.

[0045] Specifically, through Figure 1 It can be seen that the substructure of the multi-axis real-time hybrid test is divided and the system composition, signal flow and control logic are clearly defined, providing a unified benchmark for the comparison of the three compensation methods.

[0046] Figure 2 The diagram clearly reveals the closed-loop logic, module composition, and adaptation characteristics of model predictive control, providing intuitive support for understanding the working mechanism of the MPC adaptive time delay compensation method in maRTHS. At the same time, by clarifying the core framework of MPC, adapting to nonlinear scenarios, and supplementing engineering constraints, the diagram provides a basic framework reference, logical connection basis, and technical solution integrity support for the invention.

[0047] Figure 3The system reveals the closed-loop collaborative mechanism of "state awareness-rolling optimization", clarifies the functional positioning, data flow and adaptation characteristics of each module, and provides intuitive support for understanding the technical innovation and performance advantages of the method. At the same time, the diagram provides key theoretical support and logical connection for the invention by explaining the theoretical logic of performance improvement, strengthening the expression of technical novelty and improving the feasibility of the solution.

[0048] Figure 4 The system presents the complete implementation chain of the invention from offline preparation to real-time closed loop, clarifying the core tasks, parameter configurations and module collaboration relationships at each stage, providing clear guidance for the engineering implementation and reproduction of the method; at the same time, the diagram provides technical detail support, patent logic endorsement and scenario adaptation instructions for the invention by supplementing implementation details, strengthening logical rigor and making error control logic explicit.

[0049] Furthermore, in S3, the initial conditions are specifically: prediction step size p=1, control step size m=1, error weight matrix Q=10I, and control input weight matrix R=100I.

[0050] Furthermore, in S3, the state-space model satisfies:

[0051]

[0052]

[0053] In the formula, Let k be the system state vector at time k; For control input; For measurement output; These are the system's state prediction matrix, input matrix, output matrix, and direct transfer matrix, respectively. and These are process noise and measurement noise, respectively, both of which follow a Gaussian distribution.

[0054] Specifically, to predict the state and output at p future time points, the following formula is used to recursively calculate the state space model by expanding the conditional formula:

[0055]

[0056]

[0057]

[0058] The calculation formula is expressed in matrix form as follows:

[0059]

[0060] In the formula: State prediction matrix

[0061]

[0062] To control the input influence matrix:

[0063]

[0064] For the future state vector:

[0065]

[0066] For future control input vectors:

[0067]

[0068] The predicted system output at time p is:

[0069]

[0070] In the formula: Y is the predicted output for the next p steps:

[0071]

[0072] It is the matrix showing the influence of control inputs on future outputs; It is the matrix showing the influence of the initial state value on the future output.

[0073] Furthermore, in S3, the objective function for the rolling optimization is:

[0074]

[0075] In the formula: For the desired output trajectory, Q is the state error weight matrix, used to minimize the tracking error; R is the control input weight matrix, used to adjust the degree of abrupt changes in the control input to ensure the stability of the control signal; P is the prediction time domain, which determines the number of steps for MPC to predict future states; m is the control movement time domain, which determines the number of steps for MPC to apply optimization control.

[0076] Specifically, the output prediction formula is substituted into the MPC rolling optimization objective function, expanded and rearranged to obtain the standard quadratic optimization form, and the Hessian matrix is ​​defined. The problem of optimizing the MPC control output is ultimately transformed into a quadratic programming problem with actuator physical constraints (input upper and lower limits, input rate of change upper and lower limits) by using linear term vectors. The specific calculation process is as follows:

[0077] Substitute the objective function:

[0078]

[0079] Objective function expansion:

[0080]

[0081] Standard quadratic optimization form:

[0082]

[0083] Definitions of Hessian matrices and linear term vectors:

[0084]

[0085]

[0086] Standard quadratic programming form and constraints:

[0087]

[0088]

[0089]

[0090] In the formula: To control the upper and lower limits of the input, ensuring that the actuator does not exceed its physical limits; To constrain the rate of change of the input, the control signal must change too rapidly to prevent system oscillation. At each control moment, MPC applies only the first step of the optimal control sequence. Then, it proceeds to the next time step for re-optimization, thus forming a rolling optimization process. Finally, it is converted into a command displacement that can be executed by the actuator. .Will The data is sent to the transmission system to load the physical substructure and measure the actual displacement. and measured reaction force Then and measured displacement Input into the UKF estimator for noisy measured displacement State estimation is performed to obtain .

[0091] Furthermore, in S5, the parameters of the UKF estimator are set as follows: α=0.001, used to control the distribution range of sigma points; β=2, used to characterize the state distribution characteristics; γ=0, used to ensure that the covariance matrix is ​​positive semidefinite. The UKF estimator includes: an initial state covariance matrix. Measurement noise covariance matrix process noise covariance matrix .

[0092] Furthermore, in S5, the state equation and observation equation of the UKF algorithm satisfy:

[0093]

[0094]

[0095]

[0096] In the formula, h corresponds to the system's state equation and observation equation, respectively; The system state at step i includes the measured displacements. Time constant and amplitude gain The identification value needs to be solved using the UKF algorithm; For the input terms of the UKF state equations at step i-1; The i-th observation value is obtained from actual sensor measurements. and These are the process noise vector and the observation noise vector, respectively, both of which are zero-mean Gaussian white noise.

[0097] Specifically, the UKF algorithm executes as follows: Based on the offline calibrated initial parameters, Sigma points are generated through symmetric sampling and their corresponding weights are calculated. State prediction and covariance updates are then performed by combining the state equation and the observation equation. Finally, the optimal state estimate is obtained by fusing measured data. The core formula is as follows:

[0098] Sigma point generation and parameter λ calculation:

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] Sigma point weight calculation:

[0106]

[0107]

[0108]

[0109] In the formula: Let denot mean and covariance respectively, and β represent mean weights and covariance weights. Distribution of [something].

[0110] State and covariance prediction:

[0111]

[0112]

[0113] In the formula: Process noise covariance matrix.

[0114]

[0115] Predicting observed covariance and cross-covariance:

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] Kalman gain and state update:

[0122]

[0123]

[0124]

[0125] In the formula: Let h be the mean of the observations at step i-1, and h be the observation equation. For Kalman gain.

[0126] Measured using UKF and MPC control commands Updated ,Will Perform coordinate transformation and output , feedback force and earthquake excitation The new desired displacement is obtained by inputting it again into the numerical substructure. Perform coordinate transformation to obtain the new desired displacement The MPC controller received and As an initial condition, rolling optimization is performed to obtain a new round of results. , control signal Apply it to the actuator. Repeat the above process to achieve the purpose of time delay compensation.

Claims

1. An improved MPC adaptive time delay compensation method based on unscented Kalman filtering, characterized in that, include: S1. Offline preparation stage: Build the maRTHS Benchmark model, divide the numerical substructure and physical substructure, determine the transmission system parameters composed of multi-axis hydraulic actuators and couplers, and calibrate the initial state mean, initial covariance matrix and system fixed time delay of the unscented Kalman filter through offline experiments. S2. Desired Displacement Acquisition Stage: The seismic excitation is input into the numerical substructure, and the motion equation is solved to obtain the desired displacement including displacement and rotation. The desired displacement that the two hydraulic actuators can achieve translational motion is obtained through coordinate transformation. S3.MPC Control Command Solving Stage: Using the prediction step size, control step size, error weight matrix, and control input weight matrix as initial conditions, the dynamic characteristics of the controlled system are described using a state-space model, and the optimal control command is solved through rolling optimization of model predictive control. S4. Measured data acquisition stage: Send the optimal control command to the transmission system, load the physical substructure, and acquire the measured displacement and measured reaction force; S5. UKF State Estimation Stage: The optimal control command and the measured displacement containing noise are input into the UKF estimator. The UKF algorithm is used to perform nonlinear estimation of the system state, filter out measurement noise and model uncertainty, and output the optimal state estimate. S6. Closed-loop cycle stage: After the optimal state estimate is transformed by coordinate transformation, it is input into the numerical substructure along with the measured reaction force and the seismic excitation to update the new expected displacement. Then, with the new expected displacement and the optimal state estimate as the initial conditions, the process returns to S3 to repeat the MPC rolling optimization, forming a closed-loop cycle to achieve time delay compensation.

2. The improved MPC adaptive time delay compensation method based on unscented Kalman filtering according to claim 1, characterized in that, In S3, the initial conditions are specifically: prediction step size p=1, control step size m=1, error weight matrix Q=10I, and control input weight matrix R=100I.

3. The improved MPC adaptive time delay compensation method based on unscented Kalman filtering according to claim 1, characterized in that, In S3, the state-space model satisfies: In the formula, Let k be the system state vector at time k; For control input; For measurement output; These are the system's state prediction matrix, input matrix, output matrix, and direct transfer matrix, respectively. and These are process noise and measurement noise, respectively, both of which follow a Gaussian distribution. for The system state vector at time step.

4. The improved MPC adaptive time delay compensation method based on unscented Kalman filtering according to claim 1, characterized in that, In S3, the objective function for the rolling optimization is: In the formula: For the desired output trajectory, Q is the state error weight matrix, used to minimize the tracking error; R is the control input weight matrix, used to adjust the degree of abrupt changes in the control input to ensure the stability of the control signal; P is the prediction time domain, which determines the number of steps for MPC to predict future states. m represents the control movement time domain, which determines the number of steps for MPC to apply optimal control. for Time-based measurement output, for Control input at all times.

5. The improved MPC adaptive time delay compensation method based on unscented Kalman filtering according to claim 1, characterized in that, In S5, the parameters of the UKF estimator are set as follows: α = 0.001, used to control the range of sigma point distribution; β = 2, used to characterize the state distribution characteristics; γ = 0, used to ensure that the covariance matrix is ​​positive semidefinite. The UKF estimator includes: an initial state covariance matrix. Measurement noise covariance matrix process noise covariance matrix .

6. The improved MPC adaptive time delay compensation method based on unscented Kalman filtering according to claim 1, characterized in that, in S5, the state equation and observation equation of the UKF algorithm satisfy: In the formula, h corresponds to the system's state equation and observation equation, respectively; The system state at step i includes the measured displacements. Time constant and amplitude gain The identification value needs to be solved using the UKF algorithm; For the input terms of the UKF state equations at step i-1; The i-th observation value is obtained from actual sensor measurements. and These are the process noise vector and the observation noise vector, respectively, both of which are zero-mean Gaussian white noise. For the first Step system status.

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