Active-disturbance-rejection decoupling control method and device based on Kalman filter under flywheel energy storage system

Abstract

The invention provides an active-disturbance-rejection decoupling control method and device based on a Kalman filter under a flywheel energy storage system, and relates to the field of flywheel energy storage systems, and the method comprises the steps: building a body kinetic model of a hybrid magnetic bearing; designing and analyzing an active-disturbance-rejection decoupling controller based on the established body dynamic model of the hybrid magnetic bearing; a state equation and an observation equation required by a Kalman filter are established, a displacement signal output by a hybrid magnetic bearing body is collected and input into the Kalman filter for noise elimination, and then the signal is transmitted to an active-disturbance-rejection decoupling controller to eliminate low-frequency disturbance to obtain a control result.

Description

Technical Field

[0001] The present invention relates to the field of flywheel energy storage systems, and particularly to a self-disturbance rejection decoupling control method and device based on a Kalman filter for a flywheel energy storage system. Background Art

[0002] Flywheel energy storage has the advantages of fast response speed, high energy storage density, long service life, etc. Therefore, it has broad application prospects in power grids with a relatively high proportion of renewable energy generation. Such as participating in power grid frequency regulation, smoothing the fluctuations of renewable energy generation, etc.

[0003] Hybrid magnetic bearings are considered an important part of flywheel energy storage systems because they can achieve non-contact operation and ensure that the system can maintain good performance without lubrication during high-speed operation.

[0004] However, the modeling and control of the hybrid magnetic bearing itself are still challenging problems. A typical flywheel energy storage system includes five key components: a flywheel motor, a flywheel rotor, bearings, a vacuum chamber, and a bi-directional converter, and the hybrid magnetic bearing is the core of them. There are interferences of low-frequency disturbing forces in the hybrid radial magnetic bearing system, and at the same time, the white noise in the system cannot be ignored due to the high requirement for the control accuracy of the active radial bearing. Therefore, to ensure the stable operation of the flywheel energy storage system, the anti-disturbance ability of the hybrid magnetic bearing under the flywheel energy storage system still cannot meet the requirements. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a self-disturbance rejection decoupling control method and device based on a Kalman filter for a flywheel energy storage system.

[0006] Since the control quantities of the hybrid radial magnetic bearing body model under the flywheel energy storage system are seriously coupled and the body is vulnerable to noise interference, traditional self-disturbance rejection control methods are difficult to effectively eliminate the white noise and low-frequency disturbances in the system. How to decouple the hybrid radial magnetic bearing body model and effectively eliminate the low-frequency disturbances and white noise in the system has important research significance. To explore the anti-disturbance problem of the hybrid magnetic bearing under the flywheel energy storage system, a self-disturbance rejection decoupling control method based on a Kalman filter for the flywheel energy storage system is provided, which can effectively improve the anti-disturbance ability of the hybrid magnetic bearing under the flywheel system.

[0007] The present invention provides a self-disturbance rejection decoupling control method based on a Kalman filter for a flywheel energy storage system, including the following steps:

[0008] (1) Establish the body dynamics model of the hybrid magnetic bearing;

[0009] (2) Based on the established body dynamics model of the hybrid magnetic bearing, design and analyze a self-disturbance rejection decoupling controller;

[0010] (3) Establish the state equation and observation equation required for the Kalman filter, collect the displacement signal output by the hybrid magnetic bearing body, input it into the Kalman filter for noise elimination, and then transmit the signal to the active disturbance rejection decoupling controller to eliminate low-frequency disturbances to obtain the control result.

[0011] The present invention also provides an active disturbance rejection decoupling control device based on a Kalman filter for a flywheel energy storage system, including the following modules:

[0012] A dynamic model establishment module for establishing the body dynamic model of the hybrid magnetic bearing;

[0013] A design and analysis module of the active disturbance rejection decoupling controller, based on the established body dynamic model of the hybrid magnetic bearing, to carry out the design and analysis of the active disturbance rejection decoupling controller;

[0014] A noise elimination module for establishing the state equation and observation equation required for the Kalman filter, collecting the displacement signal output by the hybrid magnetic bearing body, feeding it into the Kalman filter for noise elimination, and then transmitting the signal to the active disturbance rejection decoupling controller to eliminate low-frequency disturbances to obtain the control result.

[0015] The present invention also provides an electronic device, including: one or more processors; a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method described above.

[0016] The present invention also provides a computer-readable storage medium, on which executable instructions are stored, and when the instructions are executed by a processor, the processor implements the method described above.

[0017] The present invention also provides a computer program product, including a computer program, characterized in that when the computer program is executed by a processor, the method described above is implemented.

[0018] The present invention has the following beneficial effects: The active disturbance rejection decoupling control strategy of the hybrid magnetic bearing based on the Kalman filter of the present invention establishes the mathematical models of the decoupled LADRC active disturbance rejection controller and the Kalman filter for the mathematical model of the radial bearing of the flywheel system. It effectively solves the problems of low-frequency disturbances and white noise in the flywheel system. Finally, through simulation, it can be found that the control strategy of the decoupled LADRC active disturbance rejection controller + Kalman filter can eliminate 98.5% of the white noise and low-frequency disturbance amount compared with the traditional PID control strategy, which is of great significance for the stable operation of the flywheel energy storage system. Description of the Drawings

[0019] Figure 1 It is a schematic diagram for modeling the dynamic model of the hybrid radial magnetic bearing;

[0020] Figure 2 Schematic diagram of the forces on the flywheel;

[0021] Figure 3 Frame diagram of the self-disturbance rejection decoupling control method for a hybrid magnetic bearing based on a Kalman filter;

[0022] Figure 4 Schematic diagram of white noise during the output displacement measurement process;

[0023] Figure 5 Schematic diagram of low-frequency disturbances during the output displacement measurement process;

[0024] Figure 6 Schematic diagram for comparing the decoupled LADRC with the traditional PID control;

[0025] Figure 7 Schematic diagram for comparing the decoupled LADRC with the LADRC control with a Kalman filter added. Specific implementation manners

[0026] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, the present invention adopts the following technical solutions.

[0027] The present invention provides a self-disturbance rejection decoupling control method based on a Kalman filter for a flywheel energy storage system, including the following steps:

[0028] (1) Establish the body dynamics model of the hybrid magnetic bearing;

[0029] (2) Based on the established body dynamics model of the hybrid magnetic bearing, design and analyze the self-disturbance rejection decoupling controller;

[0030] (3) Establish the state equation and observation equation required by the Kalman filter to provide an optimal estimate for the system, collect the displacement signal output by the hybrid magnetic bearing body, input it into the Kalman filter for noise elimination, and then transmit the signal to the self-disturbance rejection decoupling controller to eliminate the low-frequency disturbances in the system.

[0031] Step (1) of establishing the body dynamics model of the hybrid magnetic bearing includes:

[0032] As Figure 1As shown in the figure, in the schematic diagram of the radial magnetic bearing system of the magnetic levitation flywheel system, the radial magnetic bearing system of the magnetic levitation flywheel system includes: upper radial hybrid magnetic bearing, upper position sensor, lower radial hybrid magnetic bearing, lower position sensor, flywheel rotor. O represents the centroid of the flywheel. and respectively represent the distances from the upper and lower radial hybrid magnetic bearings to the centroid plane. and respectively represent the distances from the upper and lower position sensors to the centroid plane. L represents the total interval that the flywheel can move. m is the mass of the rotor, J Z is the polar moment of inertia, J is the equatorial moment of inertia, k i is the current stiffness of the magnetic bearing, k x is the displacement stiffness of the magnetic bearing.

[0033] Assume that the position of the flywheel at any moment is as shown in the vertical position of the black rectangle. This motion can be equivalently decomposed into first translating a distance x from the geometric center (vertical dotted line) and then rotating by an angle φ at this position. The tilt offset of the upper bearing is R u , and the tilt offset of the lower bearing is R d . At this time, at the position sensor, the distances by which the upper and lower ends of the flywheel deviate from the geometric center are respectively:

[0034] (1)

[0035] What the position sensor measures is the distance from the probe to the end face;

[0036] Among them, and respectively represent the distances from the upper and lower radial hybrid magnetic bearings to the centroid plane. and respectively represent the distances from the upper and lower position sensors to the centroid plane. What the position sensor measures is the distance from the probe to the end face. The distances measured by the two upper position sensors on the left and right of the upper end are:

[0037] (2-1)

[0038] Similarly, the distances measured by the two lower position sensors on the left and right of the lower end are:

[0039] (2-2)

[0040] The signals of the upper, lower, left, and right sensors are sent to the controller for differencing to obtain the differential signal. After solving the differential signal and then dividing by two, the deviations of the upper and lower ends of the flywheel rotor from the geometric center are obtained , , . The above deviations are used to generate the current commands for the magnetic bearing coils through operations.

[0041] Let \(L\) denote the total interval within which the flywheel rotor can move. and respectively represent the distances from the upper and lower radial hybrid magnetic bearings to the centroid plane. In dynamics, the vector is defined as the positive direction, the torque and the deflection angle vector are defined as positive in the counterclockwise direction, and the forces acting on the flywheel rotor are all defined as the positive direction. In the force analysis of the flywheel rotor, a cross-section facing the X-axis is taken, that is, rotation around the X-axis and translation along the Y-axis. Assume that the electromagnetic force of the upper radial hybrid magnetic bearing is \(F_{u}\) uy , the electromagnetic force of the lower radial hybrid magnetic bearing is \(F_{l}\) dy , the resultant force in the positive Y-axis direction is \(F_{y}\) y , the positive torque generated around the X-axis is \(T_{x}\) x , and the positive rotation deflection angle in the X-direction is \(\varphi_{x}\) x . Similarly, take a cross-section facing the Y-axis, that is, rotation around the Y-axis and translation along the X-axis. Assume that the electromagnetic force of the upper radial hybrid magnetic bearing is \(F_{u}'\) ux , the electromagnetic force of the lower radial hybrid magnetic bearing is \(F_{l}'\) dx , the resultant force in the positive X-axis direction is \(F_{x}\) x , the positive torque generated around the Y-axis is \(T_{y}\) y , and the positive rotation deflection angle in the Y-direction is \(\varphi_{y}\) y . The force analysis is as follows:

[0042] (a) The resultant force in the positive Y-axis direction is: , and its scalar form is ;

[0043] (b) The positive torque applied counterclockwise around the X-axis is , generating a positive rotation deflection angle . The torque vector is:

[0044] (3)

[0045] According to the right-hand rule, its scalar form is:

[0046] (4)

[0047] Similarly, for the cross-section facing the Y-axis, the force analysis is as follows:

[0048] (5)

[0049] In step (2), based on the established body dynamics model of the hybrid magnetic bearing, the design and analysis of the active disturbance rejection decoupling controller are carried out, including:

[0050] Let \(m\) be the mass of the rotor, the current motor speed be \(w\), and the displacement stiffness of the hybrid magnetic bearing be , be the polar moment of inertia, \(J\) be the equatorial moment of inertia, and the positive rotation deflection angle in the X-direction be , a positive rotational deflection angle is generated in the Y direction , displacement in the X direction is x, displacement in the Y direction is y, and the resultant force in the positive direction of the X-axis is F x， The resultant force in the positive direction of the Y-axis is F y , a positive torque of T is generated about the X-axis x , a positive torque of T is generated about the Y-axis y , H is the angular momentum J of the flywheel z w. The linear dynamic model in the flywheel coordinate system is:

[0051] (6)

[0052] Then, the two angles can be resolved through the displacements in the x and y directions to obtain the final state equation:

[0053] (7)

[0054] For the displacements in the X and Y directions at the equilibrium position . For the four-way control currents in the X and Y directions at the equilibrium position 、 、 、 .

[0055] The system variables selected in formula (7) At the same time, A in the state equation 1 、A 2 The matrix is:

[0056] (8)

[0057] Thus, the A, B, C, and D matrices in the state equation can be obtained:

[0058] (9)

[0059] Considering the coupling of the four-way displacements with the displacements of other branches as all disturbances, compensated by the observer, and regarding the body equation completely as a double-integral system, the body equation is rewritten as follows:

[0060] (10)

[0061] Thus, a decoupled active disturbance rejection decoupled LADRC controller and a linear extended state observer LESO are designed, where 、 、 are the observed quantities of the LESO, is the bandwidth of the observer, u is the input quantity of the hybrid magnetic bearing body, y is the output quantity of the hybrid magnetic bearing body through the Kalman filter, b is the estimated coefficient of the input quantity, and the state equation of the LESO is as follows:

[0062] (11)

[0063] The decoupled LADRC auto-disturbance rejection controller is finally established through the state equations of (10)-(11).

[0064] Step (3): Establish the state equation and observation equation required for the Kalman filter to provide an optimal estimate for the system. Collect the displacement signal output by the hybrid magnetic bearing body, input it into the Kalman filter for noise cancellation, and then transfer the signal to the auto-disturbance rejection decoupling controller to effectively eliminate the low-frequency disturbance in the system. It includes:

[0065] Generally speaking, the Kalman filter is divided into two major parts: prediction and update. The core problem of the Kalman filtering method is: how to establish the state equation and observation equation required for filtering. In the actual working process, the Kalman filtering method will provide an optimal estimate for the system, provided that the system should have a linear model. Using the Kalman filtering method can simplify the calculation amount and save data storage. Among them, T s is the sampling period, A' is the state transition matrix, 、 are the state matrices at time t and t-1, B' is the matrix that converts the input into the state, H is the matrix that converts the state quantity to the observed quantity, is the measured value which is the input of the filter, is the input at time t-1. Define the state equation and observation equation of the system as follows:

[0066] (12)

[0067] A', B', and H in the system equation are as follows:

[0068] (13)

[0069] are the noise in the state equation and the noise in the observation equation respectively;

[0070] Meanwhile, represents the prior state estimate value at time t, 、 represent the posterior state estimate values at time t-1 and t respectively, and represent the posterior estimate covariance at time t-1 and t respectively, is the prior estimate covariance at time t, Q is the process excitation noise covariance, R is the measurement noise covariance, is the filter gain matrix; is the measured value which is the input of the filter.

[0071] First, perform a priori estimation:

[0072] (14)

[0073] The predicted covariance is the previous error covariance:

[0074] (15)

[0075] The Kalman gain is:

[0076] (16)

[0077] The posteriori estimation is:

[0078] (17)

[0079] Update the error covariance as:

[0080] (18)

[0081] Among them, weighing the predicted state covariance and the covariance R of the observed quantity determines the degree of trust in the observation model of the prediction model. At the same time, the residual, which is the form of the observed value minus the filtered estimated observed value, is transformed from the observation domain to the state domain.

[0082] Compare and analyze the control results with those of traditional PID control. Specifically, it includes:

[0083] Finally, establish the overall control block diagram as Figure 3 shown: In the control process of the hybrid magnetic bearing, the reference displacement is first input to the LADRC controller of the displacement loop. After processing, it outputs the reference current. The reference current is further input to the P controller of the inner loop, and the actual current is output through the H-bridge drive circuit, finally driving the hybrid magnetic bearing body to generate a magnetic field to control the radial displacement of the rotor. At the same time, the actual displacement output by the hybrid magnetic bearing body is processed by the Kalman filter, and the filtered displacement is obtained after removing the noise. The filtered displacement is input to the LESO extended observer, which outputs the displacement, the first derivative of the displacement, and the disturbance information, and feeds back to the LADRC controller to complete the control closed-loop, thereby achieving precise control of the radial displacement of the rotor.

[0084] Make a certain comparison of the simulation results, and perform PID control, LADRC control, and LADRC + Kalman filter control respectively. Figure 4 、 Figure 5Respectively show the white noise and low-frequency disturbances suffered by the hybrid magnetic bearing in the flywheel energy storage system. White noise mainly comes from the electrical noise and electromagnetic interference of the system, which will affect the control accuracy of the magnetic bearing. The low-frequency disturbances are usually caused by the imbalance of the mechanical structure, load changes or external vibrations. Their frequencies are relatively low, but they may cause large displacement deviations. Both have an adverse impact on the stability of the flywheel energy storage system.

[0085] Figure 6 Show the four-way displacements from top to bottom The comparison between the decoupled LADRC control and the traditional PID control. The results show that the decoupled LADRC control can significantly suppress the disturbances, and the total disturbance elimination amount of its system is about 95%. This shows that the decoupled LADRC is significantly superior to the traditional PID control in terms of disturbance rejection performance and can more effectively maintain the stability of the flywheel energy storage system. Continue to improve the design of the Kalman filter for low-frequency disturbances and white noise disturbances. According to Equations (12) to (17), the simulation is as Figure 7 shown. Figure 7 Show the four-way displacements from top to bottom The comparison between the decoupled LADRC control and the LADRC control with the Kalman filter added.

[0086] The control method of LADRC + Kalman filter effectively reduces the disturbances of the system. Compared with the traditional LADRC control strategy, the total disturbance reduction amount reaches 70%, effectively suppressing the system noise disturbances.

Claims

1. A Kalman filter-based auto-disturbance rejection decoupling control method for a flywheel energy storage system, characterized in that: Includes steps: (1) Establish the bulk dynamics model of the hybrid magnetic bearing; (2) Based on the established dynamic model of the hybrid magnetic bearing, the self-disturbance rejection decoupling controller is designed and analyzed; (3) The state equation and observation equation required by the Kalman filter are established, the displacement signal output by the hybrid magnetic bearing body is collected, and the signal is fed into the Kalman filter for noise elimination. The signal is then passed to the anti-disturbance decoupling controller to eliminate low-frequency disturbances and obtain the control result.

2. The method for anti-disturbance decoupling control based on Kalman filter in a flywheel energy storage system according to claim 1, characterized in that: The flywheel energy storage system includes: an upper radial hybrid magnetic bearing, an upper position sensor, a lower radial hybrid magnetic bearing, a lower position sensor, and a flywheel rotor.

3. The method for anti-disturbance decoupling control based on Kalman filter in a flywheel energy storage system according to claim 1, characterized in that: Step (1) includes: The motion of the flywheel rotor at any time is equivalently decomposed into the translation distance from the geometric center , and then rotate the deflection angle φ at this position, the tilt offset of the upper radial hybrid magnetic bearing is , the tilt offset of the lower radial hybrid magnetic bearing is At this time, at the position sensor, the distances of the upper and lower ends of the flywheel rotor from the geometric center are: （1） in, , Respectively represent the distance from the upper and lower position sensors to the centroid plane. The position sensor measures the distance from the probe to the end face. The distance measured by the two upper position sensors on the left and right ends is: （2-1） Similarly, the distances measured by the two lower position sensors on the left and right sides of the lower end are: （2-2） The upper and lower left and right sensor signals are up and down The differential signal is sent to the controller for differentiation. After the differential signal is resolved and divided by two, the deviation of the upper and lower ends of the flywheel rotor from the geometric center is obtained. , , the above deviation is calculated to generate the current instruction of the magnetic bearing coil; L represents the total range in which the flywheel rotor can move, , Respectively represent the distance from the upper and lower radial hybrid magnetic bearings to the mass center plane. In dynamics, the vector is defined as the positive direction, the moment and deflection vector are defined as the counterclockwise direction is positive, and the flywheel rotor force is defined as the positive direction. In the flywheel rotor force analysis, the section facing the X axis is taken, that is, rotation around the X axis and translation along the Y axis. It is assumed that the electromagnetic force of the upper radial hybrid magnetic bearing is F uy , the electromagnetic force of the radial hybrid magnetic bearing is F dy , the resultant force in the positive direction of the Y axis is F y , the positive moment T is generated around the X axis x , the X direction produces a positive rotation angle φ x Similarly, take the section facing the Y axis, that is, rotate around the Y axis and translate along the X axis. Assume that the electromagnetic force of the upper radial hybrid magnetic bearing is F ux , the electromagnetic force of the radial hybrid magnetic bearing is F dx , the force in the positive direction of the X-axis is F x , the positive moment T is generated around the Y axis y , the Y direction produces a positive rotation angle φ y , the force analysis is as follows: (a) The resultant force in the positive direction of the Y axis is: , whose scalar form is ; (b) The positive moment applied counterclockwise around the X-axis is , generating a positive rotation angle , the moment vector is: （3） According to the right-hand rule, its scalar form is: （4） Similarly, the force analysis of the section facing the Y axis is as follows: （5）。 4. The method for anti-disturbance decoupling control based on Kalman filter in a flywheel energy storage system according to claim 3, characterized in that: Step (2) includes: m is the rotor mass, the current motor speed is w, J is the equatorial moment of inertia, the displacement in the X direction is x, the displacement in the Y direction is y, and H is the flywheel angular momentum J z w; the linear dynamic model in the flywheel coordinate system is: （6） Then, the two angles are analyzed through the displacement in the X and Y directions to obtain the final state equation: （7） The system variables selected in formula (7) At the same time, the A1 and A2 matrices in the state equation are: （8） This gives the A, B, C, and D matrices in the state equation: （9） m is the rotor mass, and the displacement stiffness of the hybrid magnetic bearing is , is the polar moment of inertia, and the displacements in the X and Y directions of the equilibrium position are , the four control currents in the X and Y directions of the equilibrium position are , , , , the coupling of the four-way displacement and the displacement of other branches is regarded as disturbance, which is observed and compensated by the observer. The main equation is completely regarded as a double integral system, and the main equation of the hybrid magnetic bearing is rewritten as follows: （10） Based on this, a decoupled auto-disturbance rejection decoupling controller and a linear expansion observer LESO are designed, where , , is the LESO observation quantity, is the bandwidth of the observer, u is the input of the hybrid magnetic bearing body, y is the output of the hybrid magnetic bearing body through the Kalman filter, b is the input coefficient estimation, and the LESO state equation is as follows: （11） The decoupled LADRC active disturbance rejection controller is finally established through the state equations of Eqs. (10)-(11).

5. The method for anti-disturbance decoupling control based on Kalman filter in a flywheel energy storage system according to claim 4, characterized in that: Step (3) includes: The state equation and observation equation of the system are defined as follows: （12） A', B', and H in the system equation are as follows: （13） Among them, T s is the sampling period, A' is the state transfer matrix, , is the state matrix at time t and time t-1, B' is the matrix of input conversion to state, H is the conversion matrix from state quantity to observation quantity, The measured value is the input of the filter, is the input at time t-1, , are the noise in the state equation and the noise in the observation equation, respectively.

6. The method for anti-disturbance decoupling control based on Kalman filter in a flywheel energy storage system according to claim 5, characterized in that: Step (3) also includes: First, make a priori estimates: （14） The prior covariance is the previous error covariance: （15） The Kalman gain is: （16） The posterior estimate is: （17） The updated error covariance is: （18） in, represents the prior state estimate at time t, , They represent the posterior state estimates at time t-1 and time t respectively, and denote the posterior estimated covariance at time t-1 and time t, respectively. is the prior estimate covariance at time t, Q is the process excitation noise covariance, R is the measurement noise covariance, is the filter gain matrix.

7. A Kalman filter-based anti-disturbance decoupling control device for a flywheel energy storage system, characterized in that: Includes the following modules: A dynamic model building module is used to build a main body dynamic model of the hybrid magnetic bearing; The design and analysis module of the auto-disturbance rejection decoupling controller is used to design and analyze the auto-disturbance rejection decoupling controller based on the established body dynamics model of the hybrid magnetic bearing; The noise elimination module establishes the state equation and observation equation required by the Kalman filter, collects the displacement signal output by the hybrid magnetic bearing body, feeds it into the Kalman filter for noise elimination, and then passes the signal to the self-disturbance rejection decoupling controller to eliminate low-frequency disturbances and obtain the control result.

8. An electronic device, characterized in that: include: one or more processors; A memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: Executable instructions are stored thereon, and when the instructions are executed by a processor, the processor implements the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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