A Linear Active Disturbance Rejection Control Method Based on Parameter Identification and Compensation
Through the linear self-immune disturbance control method based on parameter identification compensation, the problem of difficult balance between speed and stability of large inertia follow-up systems is solved, and effective resistance to nonlinear perturbations and dynamic response performance is improved.
Patent Information
- Application Number
- CN202411780718.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-05
- Publication Date
- 2025-04-08
AI Technical Summary
The prior art is difficult to balance the speed and stability, especially in complex operating conditions, and traditional PID control methods are difficult to improve the robustness and immunity of large-moment follow-up systems against nonlinear friction torque, load torque sudden change and load moment of inertia sudden change.
A linear self-immunity control method based on parameter identification compensation is adopted. By obtaining input parameters and control instructions, a linear self-immunity controller is loaded, and a parameter dynamic identification model is introduced through recursive least squares method and forgetting factor. Combining a second-order expanded state observer and error feedback control law, a linear self-immunity controller is constructed.
It significantly improves the dynamic response performance of the follow-up system, improves its resistance to nonlinear disturbances such as sudden load torque changes and moment of inertia changes, reduces adjustment time and debugging costs, and improves the performance of the overall control system.
Smart Images
Figure CN119781286A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of mechanical control, and in particular relates to a linear auto-disturbance rejection control method based on parameter identification and compensation. Background Art
[0002] The servo system is a core component of high-end equipment. In the existing technology, the large inertia servo system has high load capacity, good stability and wide applicability, but its development is limited by its slow dynamic response, difficult control and susceptibility to external disturbances. At the same time, the traditional PID control method is difficult to strike a balance between rapidity and stability when dealing with fast and precise maneuvering operations, especially under complex working conditions.
[0003] Therefore, a control method is needed to improve the robustness and anti-disturbance performance of the servo system to nonlinear friction torque, sudden changes in load torque and sudden changes in load rotational inertia, to solve the problem that traditional control methods are difficult to strike a balance between rapidity and stability, and to improve the overall performance of large inertia servo control systems. Summary of the invention
[0004] In order to solve the above technical problems, the present invention provides a linear active disturbance rejection control method based on parameter identification and compensation.
[0005] The present invention is achieved through the following technical solutions.
[0006] The present invention provides a linear active disturbance rejection control method based on parameter identification and compensation, comprising the following steps:
[0007] S1, obtaining input parameters and control instructions, wherein the input parameters include speed loop current output and speed loop speed output, and the control instructions include speed loop control speed instructions;
[0008] S2, load linear active disturbance rejection controller;
[0009] S3, inputting the input parameters and the control command into the linear active disturbance rejection controller to obtain the output control quantity, wherein the output control quantity includes the speed loop control current command;
[0010] S4. Control the follow-up system according to the output control quantity.
[0011] Preferably, before the loading, constructing a linear active disturbance rejection controller comprises the following steps:
[0012] S21, obtaining motor parameters, and constructing a motor mathematical model according to the motor parameters;
[0013] S22, obtaining a recursive least squares method;
[0014] S23, introducing a forgetting factor into the recursive least squares method to obtain a parameter dynamic identification model;
[0015] S24, introducing a parameter dynamic identification model into the motor mathematical model to obtain a first-order active disturbance rejection controller;
[0016] S25, obtaining a second-order extended state observer and establishing an error feedback control law;
[0017] S26. The first-order active disturbance rejection controller introduces a second-order extended state observer and an error feedback control law to obtain a linear active disturbance rejection controller.
[0018] Preferably, the motor mathematical model includes: a voltage equation, a flux equation, a torque equation and a mechanical motion equation.
[0019] Preferably, the voltage equation is expressed as follows:
[0020]
[0021] Among them, u d ,u q is the voltage of the motor in the dq coordinate system, i d ,i q is the current in the motor dq coordinate system, L d ,L q is the inductance of the motor in the dq coordinate system, R s is the motor resistance, ω e is the mechanical angular velocity of the motor, ψ f is the motor flux;
[0022] The expression of the magnetic flux equation is shown in the figure below:
[0023]
[0024] Among them, i d ,i q is the current in the motor dq coordinate system, L d ,L q is the inductance of the motor in the dq coordinate system, ψ d ,ψ q is the stator flux in the motor dq coordinate system, ψ f is the permanent magnet flux of the motor;
[0025] The expression of the torque equation is as follows:
[0026]
[0027] Among them, i q is the motor q-axis current, p nis the number of pole pairs of the three-phase permanent magnet synchronous motor, is the torque coefficient of the motor, ψ f is the permanent magnet flux of the motor;
[0028] The expression of the mechanical motion equation is as follows:
[0029]
[0030] Among them, ω m is the rotor mechanical angular velocity of the motor, θ m is the rotor mechanical angle of the motor, J is the moment of inertia, B is the damping coefficient, T L is the load torque, T e is the torque.
[0031] Preferably, the expression of the recursive least squares method is as follows:
[0032]
[0033] in, is the parameter estimate at time k, K(k) is the gain vector at time k, y(k) is the observed value at time k, is the regression vector at time k.
[0034] Preferably, the expression for introducing the forgetting factor in the recursive least squares method is as follows:
[0035]
[0036] Among them, y(k) is the observation value at time k, is the regression vector at time k, K(k)
[0037] is the gain vector at time k, P(k) is the error covariance matrix at time k, and λ represents the forgetting factor.
[0038] Preferably, the expression of the parameter dynamic identification model is as follows:
[0039]
[0040] Among them, ω m is the speed, T e is the torque, a, b 1 , c is the system parameter to be identified, y(k) is the observed value at time k, is the regression vector at time k, and θ(k) is the parameter estimate at time k.
[0041] Preferably, the state equation of the first-order active disturbance rejection controller is as follows:
[0042]
[0043] Among them, b 0 System parameters, i q * is the q-axis current, h is the system expansion state, is the external estimated compensation value, x 2 is the unknown interference f dotal ;
[0044] The unknown interference f dotal The expression is as follows:
[0045]
[0046] Among them, b,b 0 is the system parameter, is the q-axis current, T L ,B,J, is the parameter identification value, is an unknown value.
[0047] Preferably, the expression of the second-order extended state observer is as follows:
[0048]
[0049] Among them, z 1 ,z 2 The output ω is m and unknown interference f dotal The estimated value of m is the output, b 0 is the system parameter, is the external estimated compensation value, β 1 ,β 2 It is a system adjustable parameter.
[0050] Preferably, the expression of the error feedback control law is as follows:
[0051]
[0052] Among them, u 0 is the linear active disturbance rejection control law, e 1 is the error signal, k p is the proportional coefficient of the control law, is the control system reference input, z 1 Output ω m The estimated value of .
[0053] The beneficial effects of the present invention are:
[0054] 1. The control strategy is adjusted in real time through parameter identification, which improves the dynamic response performance of the servo system and reduces the adjustment time of the servo system.
[0055] 2. The compensation mechanism based on parameter identification significantly improves the servo system's ability to resist nonlinear disturbances such as sudden change in load torque and change in moment of inertia.
[0056] 3. Introduce the forgetting factor to improve the accuracy of the recognition algorithm and the data updating ability.
[0057] 4. Due to the combination of parameter identification and anti-disturbance control, the need for manual debugging of the servo system is reduced, thereby reducing the debugging cost and time. BRIEF DESCRIPTION OF THE DRAWINGS
[0058] Figure 1 is a flow chart of a method provided by an embodiment of the present invention;
[0059] Figure 2 It is one of the schematic diagrams of the linear active disturbance rejection controller simulation model provided by an embodiment of the present invention;
[0060] Figure 3 This is the second schematic diagram of the linear active disturbance rejection controller simulation model provided by an embodiment of the present invention;
[0061] Figure 4 It is a schematic diagram of the change of the speed curve under the influence of nonlinear friction in the simulation experiment provided by the embodiment of the present invention;
[0062] Figure 5 It is a schematic diagram of a load torque variation identification curve of a simulation experiment provided by an embodiment of the present invention;
[0063] Figure 6 It is a schematic diagram of a damping coefficient change identification curve of a simulation experiment provided by an embodiment of the present invention;
[0064] Figure 7 It is a schematic diagram of the rotational inertia change identification curve of the simulation experiment provided by an embodiment of the present invention. DETAILED DESCRIPTION
[0065] The technical solution of the present invention is further described below, but the scope of protection claimed is not limited to the description.
[0066] like Figure 1 As shown, a linear active disturbance rejection control method based on parameter identification and compensation includes the following steps:
[0067] S1, obtaining input parameters and control instructions, wherein the input parameters include speed loop current output and speed loop speed output, and the control instructions include speed loop control speed instructions;
[0068] The speed loop current output and the speed loop speed output are the current output and speed output of the speed loop model, and the speed loop control speed command is the control command of the speed loop model. Among them, the speed loop is an important link in controlling the follow-up system. In the present invention, the linear active disturbance rejection controller is the speed loop model, and the linear active disturbance rejection controller obtains the output control quantity through the output calculation of the speed loop model, that is, the self-disturbance rejection of the follow-up system is realized.
[0069] In this embodiment, the speed loop current output refers to the speed loop q-axis current output.
[0070] S2, load linear active disturbance rejection controller;
[0071] Before the loading, constructing a linear active disturbance rejection controller includes the following steps:
[0072] S21, obtaining motor parameters, and constructing a motor mathematical model according to the motor parameters;
[0073] In this embodiment, the motor parameters include motor electrical parameters, motor mechanical motion parameters, motor flux parameters and motor torque parameters.
[0074] The motor parameters need to be acquired according to the actual operation of the motor, and all parameters that may cause interference can be acquired to achieve the effect of self-interference rejection, which is not limited to this embodiment. Similarly, the motor mathematical model needs to be constructed according to the actual motor, which is not limited to this embodiment.
[0075] The motor mathematical model includes: voltage equation, flux equation, torque equation and mechanical motion equation.
[0076] The input and output of the motor mathematical model can be obtained by deducing the voltage equation, magnetic flux equation, torque equation and mechanical motion equation.
[0077] The expression of the voltage equation is as follows:
[0078]
[0079] Among them, u d ,u q is the voltage of the motor in the dq coordinate system, i d ,i q is the current in the motor dq coordinate system, L d ,L q is the inductance of the motor in the dq coordinate system, R s is the motor resistance, ω e is the mechanical angular velocity of the motor, ψ f is the motor flux;
[0080] The expression of the magnetic flux equation is as follows:
[0081]
[0082] Among them, i d ,i q is the current in the motor dq coordinate system, L d ,L q is the inductance of the motor in the dq coordinate system, ψ d ,ψ q is the stator flux in the motor dq coordinate system, ψ f is the permanent magnet flux of the motor;
[0083] The expression of the torque equation is as follows:
[0084]
[0085] Among them, i q is the motor q-axis current, p n is the number of pole pairs of the three-phase permanent magnet synchronous motor, is the torque coefficient of the motor, ψ f is the permanent magnet flux of the motor;
[0086] The expression of the mechanical motion equation is as follows:
[0087]
[0088] Among them, ω m is the rotor mechanical angular velocity of the motor, θ m is the rotor mechanical angle of the motor, J is the moment of inertia, B is the damping coefficient, T L is the load torque, T e is the torque.
[0089] The equation of the motor mathematical model above is the equation after Clark and Park coordinate transformation. It can be found that the number of parameters of the permanent magnet synchronous motor in the rotating coordinate system dq is reduced, and the decoupling of the relationship between the motor parameters is achieved. The relationship between the parameters is clear, which lays the foundation for the subsequent construction of the linear active disturbance rejection controller.
[0090] S22, obtaining a recursive least squares method;
[0091] The traditional least squares method is improved and the recursive least squares method is used to identify the parameters.
[0092] Assume that the traditional least squares parameter estimate at time k is for:
[0093]
[0094] in, is the data vector matrix, Output vector matrix for the system.
[0095] The recursive least squares expression can be obtained by recursion.
[0096] The expression of the recursive least squares method is as follows:
[0097]
[0098] in, is the parameter estimate at time k, K(k) is the gain vector at time k, y(k) is the observed value at time k, is the regression vector at time k.
[0099] S23, introducing a forgetting factor into the recursive least squares method to obtain a parameter dynamic identification model;
[0100] The parameters contained in the actual control system are all time-varying, and the recursive least squares method is more suitable for identifying constant parameters. In order to prevent the "data saturation" phenomenon that occurs as the number of recursive iterations continues to increase, the concept of forgetting factor is introduced to improve the accuracy of the identification algorithm and the data updating ability.
[0101] Here we take the performance index function as:
[0102]
[0103] Among them, λ is the forgetting factor, which is generally set to λ = 0~1, y(k) is the observation value at time k, is the regression vector at time k.
[0104] In summary, the expression for introducing the forgetting factor in the recursive least squares method is as follows:
[0105]
[0106] Among them, y(k) is the observation value at time k, is the regression vector at time k, K(k) is the gain vector at time k, P(k) is the error covariance matrix at time k, and λ represents the forgetting factor.
[0107] The expression of the parameter dynamic identification model is as follows:
[0108]
[0109] Among them, ω m is the speed, T e is the torque, a, b 1, c is the system parameter to be identified, y(k) is the observed value at time k, is the regression vector at time k, and θ(k) is the parameter estimate at time k.
[0110] S24, introducing a parameter dynamic identification model into the motor mathematical model to obtain a first-order active disturbance rejection controller;
[0111] The state equation of the first-order active disturbance rejection controller is as follows:
[0112]
[0113] Among them, b 0 System parameters, iq* is the q-axis current, h is the system expansion state, is the external estimated compensation value, x 2 is the unknown interference f dotal ;
[0114] The unknown interference f dotal The expression is as follows:
[0115]
[0116] Among them, b,b 0 is the system parameter, is the q-axis current, T L ,B,J, is the parameter identification value, is an unknown value.
[0117] S25, obtaining a second-order extended state observer and establishing an error feedback control law;
[0118] The system state and disturbances are estimated in real time through a linear extended state observer, and these disturbances are dynamically compensated by a linear state error feedback control law.
[0119] The expression of the second-order extended state observer is as follows:
[0120]
[0121] Among them, z 1 ,z 2 The output ω is m and unknown interference f dotal The estimated value of m is the output, b 0 is the system parameter, is the external estimated compensation value, β 1 ,β 2 It is a system adjustable parameter.
[0122] Reasonable configuration of system adjustable parameters β1 ,β 2 The state variables of the extended state observer LESO can track the system state variables in real time and accurately, thereby effectively tracking and observing disturbances.
[0123] The expression of the error feedback control law is as follows:
[0124]
[0125] Among them, u 0 is the linear active disturbance rejection control law, e 1 is the error signal, k p is the proportional coefficient of the control law, is the control system reference input, z 1 Output ω m The estimated value of .
[0126] By configuring the appropriate k p The response speed of the control system can be increased so that the observation error of the control system observing the total disturbance converges quickly to 0.
[0127] S26. The first-order active disturbance rejection controller introduces a second-order extended state observer and an error feedback control law to obtain a linear active disturbance rejection controller.
[0128] The simulation model of the linear active disturbance rejection controller is as follows: Figure 2 , 3 As shown in the figure, based on parameter identification and compensation, the accurate identification of key parameters such as moment of inertia, load torque and damping coefficient is ensured. In the case of changes in moment of inertia, sudden changes in moment of inertia and sudden changes in load torque, the uncertainty of the control system can be compensated to improve the anti-disturbance and robustness performance of the control system.
[0129] S3, inputting the input parameters and the control command into the linear active disturbance rejection controller to obtain the output control quantity, wherein the output control quantity includes the speed loop control current command;
[0130] In this embodiment, the speed loop control current command refers to the speed loop control q-axis current command.
[0131] S4. Control the follow-up system according to the output control quantity.
[0132] The present invention realizes the experimental verification of the linear anti-disturbance controller based on parameter identification and compensation through a follow-up semi-physical simulation platform. The semi-physical simulation platform is mainly composed of a control driver, a motor under test, a loading motor, a power supply, and an RCP fast response prototype. The follow-up semi-physical simulation platform creates a control interface model, downloads the control model to the RCP real-time simulator, runs the parameter identification algorithm, and performs online identification of the system's moment of inertia, load torque, and damping coefficient. The speed regulation, steering performance, and anti-disturbance performance of the controller are experimentally verified. The experiment simulates nonlinear friction torque and load torque interference, collects and analyzes the operating data, and some experimental results are as follows. Figures 4 to 7 As shown, Figure 4 The change of speed curve under the influence of nonlinear friction, Figure 5 Identify waveforms for load torque changes, Figure 6 Identify waveforms for damping coefficient changes, Figure 7 The waveform is used to identify the change of moment of inertia. The results show that the controller has significant improvements in stability and anti-interference compared with the traditional PID controller, confirming its potential for application in practical control systems.
[0133] The present invention adjusts the control strategy in real time through parameter identification, thereby improving the dynamic response performance of the servo system and reducing the adjustment time of the servo system; based on the compensation mechanism of parameter identification, the resistance of the servo system to nonlinear disturbances such as sudden change of load torque and change of moment of inertia is significantly improved; the forgetting factor is introduced to improve the accuracy of the identification algorithm and the data updating capability; due to the combination of parameter identification and anti-disturbance control, the need for manual debugging of the servo system is reduced, thereby reducing the debugging cost and time.
Claims
1. A linear active disturbance rejection control method based on parameter identification and compensation, characterized in that: The following steps are involved: S1, obtaining input parameters and control instructions, wherein the input parameters include speed loop current output and speed loop speed output, and the control instructions include speed loop control speed instructions; S2, load linear active disturbance rejection controller; S3, inputting the input parameters and the control command into the linear active disturbance rejection controller to obtain the output control quantity, wherein the output control quantity includes the speed loop control current command; S4. Control the follow-up system according to the output control quantity.
2. The linear active disturbance rejection control method according to claim 1, characterized in that: Before the loading, constructing a linear active disturbance rejection controller includes the following steps: S21, obtaining motor parameters, and constructing a motor mathematical model according to the motor parameters; S22, obtaining a recursive least squares method; S23, introducing a forgetting factor into the recursive least squares method to obtain a parameter dynamic identification model; S24, introducing a parameter dynamic identification model into the motor mathematical model to obtain a first-order active disturbance rejection controller; S25, obtaining a second-order extended state observer and establishing an error feedback control law; S26. The first-order active disturbance rejection controller introduces a second-order extended state observer and an error feedback control law to obtain a linear active disturbance rejection controller.
3. The linear active disturbance rejection control method according to claim 2, characterized in that: The motor mathematical model includes: voltage equation, flux equation, torque equation and mechanical motion equation.
4. The linear active disturbance rejection control method according to claim 3, characterized in that: The expression of the voltage equation is as follows: Among them, u d ,u q is the voltage of the motor in the dq coordinate system, i d ,i q is the current in the motor dq coordinate system, L d ,L q is the inductance of the motor in the dq coordinate system, R s is the motor resistance, ω e is the mechanical angular velocity of the motor, ψ f is the motor flux; The expression of the magnetic flux equation is as follows: Among them, i d ,i q is the current in the motor dq coordinate system, L d ,L q is the inductance of the motor in the dq coordinate system, ψ d ,ψ q is the stator flux in the motor dq coordinate system, ψ f is the permanent magnet flux of the motor; The expression of the torque equation is as follows: Among them, i q is the motor q-axis current, p n is the number of pole pairs of the three-phase permanent magnet synchronous motor, is the torque coefficient of the motor, ψ f is the permanent magnet flux of the motor; The expression of the mechanical motion equation is as follows: Among them, ω m is the rotor mechanical angular velocity of the motor, θ m is the rotor mechanical angle of the motor, J is the moment of inertia, B is the damping coefficient, T L is the load torque, T e is the torque.
5. The linear active disturbance rejection control method according to claim 2, characterized in that: The expression of the recursive least squares method is as follows: in, is the parameter estimate at time k, K(k) is the gain vector at time k, y(k) is the observed value at time k, is the regression vector at time k.
6. The linear active disturbance rejection control method according to claim 2, characterized in that: The expression for introducing the forgetting factor in the recursive least squares method is as follows: Among them, y(k) is the observation value at time k, is the regression vector at time k, K(k) is the gain vector at time k, P(k) is the error covariance matrix at time k, and λ represents the forgetting factor.
7. The linear active disturbance rejection control method according to claim 2, characterized in that: The expression of the parameter dynamic identification model is as follows: Among them, ω m is the speed, T e is the torque, a, b1, c are the system parameters to be identified, y(k) is the observed value at time k, is the regression vector at time k, and θ(k) is the parameter estimate at time k.
8. The linear active disturbance rejection control method according to claim 2, characterized in that: The state equation of the first-order active disturbance rejection controller is as follows: Among them, b0 system parameters, i q * is the q-axis current, h is the system expansion state, is the external estimated compensation value, x2 is the unknown interference f dotal ; The unknown interference f dotal The expression is as follows: Among them, b, b0 are system parameters, is the q-axis current, T L ,B,J, is the parameter identification value, is an unknown value.
9. The linear active disturbance rejection control method according to claim 2, characterized in that: The expression of the second-order extended state observer is as follows: Among them, z1 and z2 are the output ω m and unknown interference f dotal The estimated value of m is the output, b0 is the system parameter, is the external estimated compensation value, β1, β2 are the system adjustable parameters.
10. The linear active disturbance rejection control method according to claim 2, characterized in that: The expression of the error feedback control law is as follows: Among them, u0 is the linear anti-disturbance control law, e1 is the error signal, k p is the proportional coefficient of the control law, is the reference input of the control system, z1 is the output ω m The estimated value of .