A dual-closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC

Abstract

This invention proposes a dual-closed-loop control method for the dynamics of a magnetically levitated energy storage flywheel rotor based on LADRC (Laser-Adjustable Dynamic Control) to achieve stable levitation and dynamic control of the flywheel rotor. First, mathematical models of each degree of freedom of the flywheel rotor and a linearized model of the power amplifier-electromagnet coil are established in the magnetic bearing coordinate system. Then, the electromagnetic coupling terms, gyroscopic coupling terms, and imbalance terms in the flywheel rotor mathematical model are defined as external disturbances. Mathematical models of the flywheel rotor and power amplifier-electromagnet coil used for controller design are derived, and a second-order LADRC controller for the position loop and a first-order LADRC controller for the current loop are designed. Finally, the parameters of the position loop and current loop controllers are tuned using the pole placement method. Simulation results show that this dual-closed-loop control strategy can effectively decouple the degrees of freedom of the flywheel rotor under static and high-speed levitation conditions. Compared with PID control, it has better dynamic characteristics and stronger anti-disturbance capability. This is of great significance in ensuring the stable and reliable operation of the magnetically levitated energy storage flywheel rotor.

Description

Technical Field

[0001] This invention relates to the field of rotor dynamics control of magnetic levitation energy storage flywheels, and particularly to a dual closed-loop control method for rotor dynamics of magnetic levitation energy storage flywheels based on LADRC. Background Technology

[0002] The magnetic levitation energy storage flywheel rotor is a highly coupled mechatronic system. Its control system consists of a position loop controller and a current loop controller. The position loop controller achieves stable levitation and dynamic control of the flywheel rotor, while the current loop controller ensures rapid tracking of the current supplied by the power amplifier to the position loop controller. At high speeds and rapidly varying speeds, the system experiences intensified gyroscopic effects, time-varying parameters, significant uncertainties, diverse disturbances, and complex dynamic behavior, which can easily lead to system instability, causing the rotor to fall or even disintegrate. Therefore, designing a control strategy that is weakly dependent on the system's mathematical model and considers decoupling and strong disturbance rejection capabilities to ensure stable system operation is of great significance. Summary of the Invention

[0003] This invention designs a dual-closed-loop control method for the rotor dynamics of a magnetic levitation energy storage flywheel based on LADRC.

[0004] The technical solution adopted by this invention to solve its technical problem is: to provide a dual closed-loop control method for the rotor dynamics of a magnetic levitation energy storage flywheel based on LADRC, comprising the following steps:

[0005] Step 1: Construct a mathematical model of each radial degree of freedom of the flywheel rotor in the magnetic bearing coordinate system;

[0006] Step 2: Construct a linearized model of the power amplifier-electromagnet coil;

[0007] Step 3: Define the electromagnetic coupling term, gyro coupling term, and imbalance term in the mathematical model of each radial degree of freedom of the flywheel rotor as external disturbances, derive the second-order mathematical model of each degree of freedom, and design a second-order LADRC controller for the position loop.

[0008] Step 4: Derive the first-order mathematical model of the power amplifier-electromagnet coil and design a first-order LADRC controller for the current loop;

[0009] Step 5: Use the pole placement method to tune the position loop and current loop controller parameters.

[0010] Step 1, which involves constructing a mathematical model of each radial degree of freedom of the flywheel rotor in the magnetic bearing coordinate system, specifically includes:

[0011] Considering gyroscopic effects and unbalanced forces in the upper and lower electromagnetic bearing coordinate systems, x a x b y a y bThe mathematical model for four degrees of freedom is:

[0012]

[0013] In the formula, x a x b y a y b These represent the displacements of the rotor's geometric center along the x and y axes at the positions of the upper and lower electromagnetic bearings, respectively. xa i xb i ya i yb x a x b y a y b The control current with four degrees of freedom, f u1 ~f u4 These are the effects of rotor mass imbalance on each degree of freedom, k. 11 ~k 46 These are the coefficients for each item.

[0014] Step 2 involves constructing a linearized model of the power amplifier-electromagnet coil, specifically as follows:

[0015] Linearization analysis of the small-signal model of the power amplifier was performed using the state-space averaging method, yielding the transfer function of the ideal power amplifier-electromagnet coil linearized model as follows:

[0016]

[0017] In the formula, U amp A is the DC bus voltage of the power amplifier. amp L represents the amplitude of the triangular carrier wave during pulse width modulation. m R is the equivalent inductance of the electromagnet coil. m This is the equivalent resistance of the electromagnet coil.

[0018] Step 3 defines the electromagnetic coupling term, gyroscopic coupling term, and imbalance term in the mathematical model of each radial degree of freedom of the flywheel rotor as external disturbances, derives the second-order mathematical model of each degree of freedom, and designs a second-order LADRC controller for the position loop. Specifically, it includes the following sub-steps:

[0019] Step 3.1: Set x a x b y a y b In the mathematical model for each degree of freedom, the electromagnetic coupling term, the gyroscopic coupling term, and the imbalance term are defined as external disturbances:

[0020]

[0021] In the formula, ω xa ω xb ω ya ω yb x are defined respectively a x b y a y b External disturbances to the degrees of freedom;

[0022] Step 3.2: After defining the external disturbances for each degree of freedom, the mathematical model for each degree of freedom is expressed as follows:

[0023]

[0024] From the above formula, we can see that x a x b y a y b The mathematical model of each degree of freedom is simplified into a second-order mathematical model that includes the term of this degree of freedom, the control input term, and the external disturbance term;

[0025] Step 3.3: Express the general form of the second-order mathematical model as follows:

[0026]

[0027] In the formula, u and y are the input and output of the second-order system, respectively, ω represents the external disturbance, a1 and a2 are the system parameters, and b is the control gain, which is partially known; the known part is denoted as b0. The total disturbance f, including internal and external disturbance terms, is defined as:

[0028]

[0029] Let the system state variable x1 = y, And define the total disturbance f as the extended state x3, and write the extended state equation of the system as follows:

[0030]

[0031] For the above system, a third-order linear extended state observer (LESO) is designed as follows:

[0032]

[0033] In the formula, z1, z2, and z3 are the state variables of the third-order LESO algorithm. By properly configuring the values ​​of the LESO error feedback gain β1, β2, and β3, z1→y can be made to... z3→f; To achieve real-time compensation for the total disturbance estimated by LESO, the linear state error feedback control law (LSEF) is designed as follows:

[0034]

[0035] In the formula, k p k d Let z be the position loop controller gain, and r be the position loop reference signal. When the estimation error of the position loop LESO state variable z3 with respect to the total disturbance f is ignored, i.e., z3≈f, the system can be simplified to a second-order integrator in series.

[0036]

[0037] The closed-loop transfer function of the system is derived as follows:

[0038]

[0039] Define ω c The bandwidth of the position loop controller can be obtained using a parameterized configuration method:

[0040]

[0041] Step 4, which derives the first-order mathematical model of the power amplifier-electromagnet coil and designs the first-order LADRC controller for the current loop, specifically includes the following sub-steps:

[0042] Step 4.1: Perform an inverse Laplace transform on the transfer function of the linearized power amplifier-electromagnet coil model to derive its time-domain mathematical model:

[0043]

[0044] In the formula, u amp y amp These are the input and output of the power amplifier-electromagnet coil, respectively.

[0045] Step 4.2: The controlled object of the current loop is the power amplifier-electromagnet coil, and its mathematical model is of order one. The general form of the mathematical model of a first-order system is:

[0046]

[0047] In the formula, u d y d These are the input and output of a first-order system, respectively, where ωd represents the external disturbance, and a d For system parameters, b d The current loop control gain is partially known; let the known portion be denoted as b. d0 Define the total disturbance f, which includes internal and external disturbance terms. d for:

[0048]

[0049] Let the system state variable xd1 =y d And define the total disturbance f d For the extended state x d2 Write the extended state equation of the system as follows:

[0050]

[0051] For the above system, the second-order LESO is designed as follows:

[0052]

[0053] In the formula, z d1 z d2 For the second-order LESO state variables, the LESO error feedback gain value β is configured appropriately. d1 β d2 The value of z can make z d1 →y d , z d2 →f d To achieve real-time compensation for the total disturbance estimated by LESO, the LSEF is designed as follows:

[0054]

[0055] In the formula, r d For the current loop reference signal, k dp Define ω as the gain of the current loop controller. dc To determine the bandwidth of the current loop controller, a parameterized configuration method is used, letting k... dp =ω dc .

[0056] Step 5 uses the pole placement method to tune the position loop and current loop controller parameters, specifically including the following sub-steps:

[0057] Step 5.1: Define ω o To determine the LESO bandwidth of the position loop, a pole placement method is used to place all the poles of the LESO characteristic equation at the same location -ω. o At this point, the solution is:

[0058]

[0059] Mathematical model of the controlled object based on the position loop, i.e., x a x b y a y b From the second-order mathematical model of degrees of freedom, we can see that the control gains of the position loop are as follows:

[0060]

[0061] In the formula, b0xa b 0xb b 0ya b 0yb x a x b y a y b The position loop control gain for the degrees of freedom;

[0062] Step 5.2: Define ω do To determine the LESO bandwidth of the current loop, a pole placement method is used to place all the poles of the LESO characteristic equation at the same location -ω. do At this point, the solution is:

[0063]

[0064] Based on the mathematical model of the controlled object in the current loop, namely the first-order mathematical model of the power amplifier-electromagnet coil, the control gains of the current loop are as follows:

[0065]

[0066] In the formula, b d0xa～yb Represents x a x b y a y b The position loop controls the gain for degrees of freedom.

[0067] The beneficial effects of this invention are:

[0068] This invention proposes a dual-closed-loop control method for the dynamics of a magnetically levitated energy storage flywheel rotor based on LADRC (Laser-Adjustable Dynamic Control) to achieve stable levitation and dynamic control of the flywheel rotor. First, mathematical models of each degree of freedom of the flywheel rotor and a linearized model of the power amplifier-electromagnet coil are established in the magnetic bearing coordinate system. Then, the electromagnetic coupling terms, gyroscopic coupling terms, and imbalance terms in the flywheel rotor mathematical model are defined as external disturbances. Mathematical models of the flywheel rotor and power amplifier-electromagnet coil used for controller design are derived, and a second-order LADRC controller for the position loop and a first-order LADRC controller for the current loop are designed. Finally, the parameters of the position loop and current loop controllers are tuned using the pole placement method. Simulation results show that this dual-closed-loop control strategy can effectively decouple the degrees of freedom of the flywheel rotor under static and high-speed levitation conditions. Compared with PID control, it has better dynamic characteristics and stronger anti-disturbance capability. This is of great significance in ensuring the stable and reliable operation of the magnetically levitated energy storage flywheel rotor. Attached Figure Description

[0069] Figure 1 This is a flowchart of a dual-closed-loop control method for the rotor dynamics of a magnetic levitation energy storage flywheel based on LADRC, according to the present invention.

[0070] Figure 2 This invention presents a dual-closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC, specifically an embodiment 1, comparing the setpoint tracking performance curve of a PID control strategy under static levitation conditions.

[0071] Figure 3 This is a comparison of the decoupling performance curves of the PID control strategy under static levitation conditions in Embodiment 1 of the LADRC-based dual closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics of the present invention.

[0072] Figure 4 This invention presents a dual-closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC, specifically an embodiment 1, comparing the setpoint tracking performance curve of a PID control strategy under high-speed levitation conditions.

[0073] Figure 5 This is a comparison of the decoupling performance curves of the PID control strategy under high-speed levitation conditions in Example 1 of the dual closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC of the present invention.

[0074] Figure 6 The disturbance suppression performance curves of the comparative PID control strategy in Example 1 of the dual closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC of the present invention are shown. Detailed Implementation

[0075] The technical solution of the present invention will be further described below with reference to the accompanying drawings and Embodiment 1.

[0076] like Figure 1 The diagram shows a flowchart of a dual-closed-loop control method for the rotor dynamics of a magnetic levitation energy storage flywheel based on LADRC, which specifically includes the following steps:

[0077] Step 1, which involves constructing a mathematical model of each radial degree of freedom of the flywheel rotor in the magnetic bearing coordinate system, specifically includes:

[0078] Considering gyroscopic effects and unbalanced forces in the upper and lower electromagnetic bearing coordinate systems, x a x b y a y b The mathematical model for four degrees of freedom is:

[0079]

[0080] In the formula, x a x b y a y b These represent the displacements of the rotor's geometric center along the x and y axes at the positions of the upper and lower electromagnetic bearings, respectively.xa i xb i ya i yb x a x b y a y b The control current with four degrees of freedom, f u1 ~f u4 These are the effects of rotor mass imbalance on each degree of freedom, k. 11 ~k 46 These are the coefficients for each item.

[0081] Step 2 involves constructing a linearized model of the power amplifier-electromagnet coil, specifically as follows:

[0082] Linearization analysis of the small-signal model of the power amplifier was performed using the state-space averaging method, yielding the transfer function of the ideal power amplifier-electromagnet coil linearized model as follows:

[0083]

[0084] In the formula, U amp A is the DC bus voltage of the power amplifier. amp L represents the amplitude of the triangular carrier wave during pulse width modulation. m R is the equivalent inductance of the electromagnet coil. m This is the equivalent resistance of the electromagnet coil.

[0085] Step 3 defines the electromagnetic coupling term, gyroscopic coupling term, and imbalance term in the mathematical model of each radial degree of freedom of the flywheel rotor as external disturbances, derives the second-order mathematical model of each degree of freedom, and designs a second-order LADRC controller for the position loop. Specifically, this includes the following sub-steps:

[0086] Step 3.1: Set x a x b y a y b In the mathematical model for each degree of freedom, the electromagnetic coupling term, the gyroscopic coupling term, and the imbalance term are defined as external disturbances:

[0087]

[0088] In the formula, ω xa ω xb ω ya ω yb x are defined respectively a x b y a y b External disturbances to the degrees of freedom;

[0089] Step 3.2: After defining the external disturbances for each degree of freedom, the mathematical model for each degree of freedom is expressed as follows:

[0090]

[0091] From the above formula, we can see that x a x b y a y b The mathematical model of each degree of freedom is simplified into a second-order mathematical model that includes the term of this degree of freedom, the control input term, and the external disturbance term;

[0092] Step 3.3: Express the general form of the second-order mathematical model as follows:

[0093]

[0094] In the formula, u and y are the input and output of the second-order system, respectively, ω represents the external disturbance, a1 and a2 are the system parameters, and b is the control gain, which is partially known; the known part is denoted as b0. The total disturbance f, including internal and external disturbance terms, is defined as:

[0095]

[0096] Let the system state variable x1 = y, And define the total disturbance f as the extended state x3, and write the extended state equation of the system as follows:

[0097]

[0098] For the above system, a third-order linear extended state observer (LESO) is designed as follows:

[0099]

[0100] In the formula, z1, z2, and z3 are the state variables of the third-order LESO algorithm. By properly configuring the values ​​of the LESO error feedback gain β1, β2, and β3, z1→y can be made to... z3→f; To achieve real-time compensation for the total disturbance estimated by LESO, the linear state error feedback control law (LSEF) is designed as follows:

[0101]

[0102] In the formula, k p k d Let z be the position loop controller gain, and r be the position loop reference signal. When the estimation error of the position loop LESO state variable z3 with respect to the total disturbance f is ignored, i.e., z3≈f, the system can be simplified to a second-order integrator in series:

[0103]

[0104] The closed-loop transfer function of the system is derived as follows:

[0105]

[0106] Define ω c The bandwidth of the position loop controller can be obtained using a parameterized configuration method:

[0107]

[0108] Step 4, which derives the first-order mathematical model of the power amplifier-electromagnet coil and designs the first-order LADRC controller for the current loop, specifically includes the following sub-steps:

[0109] Step 4.1: Perform an inverse Laplace transform on the transfer function of the linearized power amplifier-electromagnet coil model to derive its time-domain mathematical model:

[0110]

[0111] In the formula, u amp y amp These are the input and output of the power amplifier-electromagnet coil, respectively.

[0112] Step 4.2: The controlled object of the current loop is the power amplifier-electromagnet coil, and its mathematical model is of order one. The general form of the mathematical model of a first-order system is:

[0113]

[0114] In the formula, u d y d These are the input and output of a first-order system, ω and ω', respectively. d Representing external disturbances, a d For system parameters, b d The current loop control gain is partially known; let the known portion be denoted as b. d0 Define the total disturbance f, which includes internal and external disturbance terms. d for:

[0115]

[0116] Let the system state variable x d1 =y d And define the total disturbance f d For the extended state x d2 Write the extended state equation of the system as follows:

[0117]

[0118] For the above system, the second-order LESO is designed as follows:

[0119]

[0120] In the formula, z d1 z d2 For the second-order LESO state variables, the LESO error feedback gain value β is configured appropriately. d1 β d2 The value of z can make z d1 →y d , z d2 →f d To achieve real-time compensation for the total disturbance estimated by LESO, the LSEF is designed as follows:

[0121]

[0122] In the formula, r d For the current loop reference signal, k dp Define ω as the gain of the current loop controller. dc To determine the bandwidth of the current loop controller, a parameterized configuration method is used, letting k... dp =ω dc .

[0123] Step 5 uses the pole placement method to tune the position loop and current loop controller parameters, specifically including the following sub-steps:

[0124] Step 5.1: Define ω o To determine the LESO bandwidth of the position loop, a pole placement method is used to place all the poles of the LESO characteristic equation at the same location -ω. o At this point, the solution is:

[0125]

[0126] Mathematical model of the controlled object based on the position loop, i.e., x a x b y a y b From the second-order mathematical model of degrees of freedom, we can see that the control gains of the position loop are as follows:

[0127]

[0128] In the formula, b 0xa b 0xb b 0ya b 0yb x a x b y a y b The position loop control gain for the degrees of freedom;

[0129] Step 5.2: Define ω do To determine the LESO bandwidth of the current loop, a pole placement method is used to place all the poles of the LESO characteristic equation at the same location -ω. do At this point, the solution is:

[0130]

[0131] Based on the mathematical model of the controlled object in the current loop, namely the first-order mathematical model of the power amplifier-electromagnet coil, the control gains of the current loop are as follows:

[0132]

[0133] In the formula, b d0xa～yb Represents x a x b y a y b The position loop controls the gain for degrees of freedom.

[0134] like Figure 2 The figure shows the setpoint tracking performance curves of a PID control strategy under static levitation conditions in Embodiment 1 of the LADRC-based dual-closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics. The flywheel rotor speed is zero, and at 0.2s, x... a The displacement reference value ref jumps from zero to 0.1 mm. As can be seen from the figure, under PID control, the system response exhibits overshoot, with a maximum overshoot of approximately 28.5%, and the settling time is excessively long, around 2.2 seconds. In contrast, the method proposed in this patent provides a fast system response without overshoot, demonstrating excellent dynamic characteristics.

[0135] Figure 3 The figure shows the decoupling performance curves of the PID control strategy under static levitation conditions in Embodiment 1 of the dual closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC of the present invention. Figure 3 (a) is PID control. Figure 3 (b) is the method proposed in this patent. The flywheel rotor speed is zero, and x is... a The reference value for displacement of the degree of freedom, ref, jumps from zero to 0.1 mm. Figure 3 (a) and Figure 3 (b) It can be seen that when x a When the displacement of the degree of freedom undergoes a step change, y a and y b The displacements of the degrees of freedom are unaffected, indicating that there is no coupling between them, consistent with the theoretical analysis. Under the PID control strategy, x b The displacement of the degrees of freedom fluctuates significantly, with the maximum displacement fluctuation being approximately 7.2 μm. Under the method proposed in this patent, xb The displacement of the degrees of freedom exhibits slight fluctuations, with the maximum displacement fluctuation being approximately 0.26 μm. Therefore, the method proposed in this patent achieves good decoupling results.

[0136] Figure 4 The figure shows the setpoint tracking performance curves of a PID control strategy under high-speed levitation conditions in Embodiment 1 of the LADRC-based dual-closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics. The flywheel rotor speed is 4800 rpm, and x is... a The displacement reference value ref jumps from zero to 0.1 mm. As shown in the figure, under the PID control strategy, the system exhibits a maximum overshoot of approximately 34%, with a settling time of about 2.4 seconds. The method proposed in this patent provides a fast system response with no overshoot.

[0137] Figure 5 The figure shows the decoupling performance curves of the PID control strategy under high-speed levitation conditions in Embodiment 1 of the dual closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC of the present invention. Figure 5 (a) is PID control. Figure 5 (b) is the method proposed in this patent. The flywheel rotor speed is 4800 rpm, and x is transferred in 0.15 s. a The reference value for displacement of the degree of freedom, ref, jumps from zero to 0.1 mm. Figure 5 (a) and Figure 5 (b) It can be seen that when x a When the displacement of the degrees of freedom undergoes a step change, x b y a y b All three degrees of freedom displacements were affected, exhibiting fluctuations to some extent, indicating that coupling exists between the four degrees of freedom under high-speed levitation conditions, consistent with theoretical analysis. Under the PID control strategy, x b The maximum displacement fluctuation of the degree of freedom is approximately 9.5 μm, y a The maximum displacement fluctuation of the degree of freedom is approximately 10.3 μm, y b The maximum displacement fluctuation in the degree of freedom is approximately 11.8 μm. However, under the method proposed in this patent, x... b The maximum displacement fluctuation of the degree of freedom is approximately 0.14 μm, y a The maximum displacement fluctuation of the degree of freedom is approximately 1.1 μm, y b The maximum displacement fluctuation of the degree of freedom is approximately 1.06 μm. Therefore, the method proposed in this patent has a good decoupling effect.

[0138] Figure 6The figure shows the disturbance suppression performance curves of the comparative PID control strategy in Example 1 of the dual closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC of the present invention. The flywheel rotor speed is 4800 rpm, and x is applied during the time period of 0.1 to 0.2 s. a Degrees of freedom control current i xa A sinusoidal disturbance with an amplitude of 0.05A and a frequency of 80Hz (the same frequency as the rotational speed) is applied to the input. As shown in the figure, under the PID control strategy, x... a The maximum displacement fluctuation of the degree of freedom is approximately 5.1 μm. Under the method proposed in this patent, x a The displacement fluctuation of the degree of freedom is approximately 1.5 μm. Therefore, the method proposed in this patent has better disturbance suppression capability.

Claims

1. A dual-closed-loop control method for the rotor dynamics of a magnetic levitation energy storage flywheel based on LADRC, characterized in that, Includes the following steps: Step 1: Construct a mathematical model of each radial degree of freedom of the flywheel rotor in the magnetic bearing coordinate system; Step 2: Construct a linearized model of the power amplifier-electromagnet coil; Step 3: Define the electromagnetic coupling term, gyroscopic coupling term, and imbalance term in the mathematical model of each radial degree of freedom of the flywheel rotor as external disturbances, derive the second-order mathematical model of each degree of freedom, and design a second-order LADRC controller for the position loop; where: Step 3.1: Set x a x b y a y b In the mathematical model for each degree of freedom, the electromagnetic coupling term, the gyroscopic coupling term, and the imbalance term are defined as external disturbances: In the formula, ω xa ω xb ω ya ω yb x are defined respectively a x b y a y b External disturbances to the degrees of freedom; Step 3.2: After defining the external disturbances for each degree of freedom, the mathematical model for each degree of freedom is expressed as follows: From the above formula, we can see that x a x b y a y b The mathematical model of each degree of freedom is simplified into a second-order mathematical model that includes the term of this degree of freedom, the control input term, and the external disturbance term; Step 3.3: Express the general form of the second-order mathematical model as follows: In the formula, u and y are the input and output of the second-order system, respectively, ω represents the external disturbance, a1 and a2 are the system parameters, and b is the control gain, which is partially known; the known part is denoted as b0. The total disturbance f, including internal and external disturbance terms, is defined as: Let the system state variable x1 = y, And define the total disturbance f as the extended state x3, and write the extended state equation of the system as follows: For the above system, a third-order linear extended state observer (LESO) is designed as follows: In the formula, z1, z2, and z3 are the state variables of the third-order LESO algorithm. By properly configuring the values ​​of the LESO error feedback gain β1, β2, and β3, z1→y can be made to... z3→f; To achieve real-time compensation for the total disturbance estimated by LESO, the linear state error feedback control law (LSEF) is designed as follows: In the formula, k p k d Let z be the position loop controller gain, and r be the position loop reference signal. When the estimation error of the position loop LESO state variable z3 with respect to the total disturbance f is ignored, i.e., z3≈f, the system can be simplified to a second-order integrator in series. The closed-loop transfer function of the system is derived as follows: Define ω c The bandwidth of the position loop controller can be obtained using a parameterized configuration method: Step 4: Derive the first-order mathematical model of the power amplifier-electromagnet coil and design a first-order LADRC controller for the current loop; where: Step 4.1: Perform an inverse Laplace transform on the transfer function of the linearized power amplifier-electromagnet coil model to derive its time-domain mathematical model: In the formula, u amp y amp These are the input and output of the power amplifier-electromagnet coil, respectively. Step 4.2: The controlled object of the current loop is the power amplifier-electromagnet coil, and its mathematical model is of order one. The general form of the mathematical model of a first-order system is: In the formula, u d y d These are the input and output of a first-order system, ω and ω', respectively. d Representing external disturbances, a d For system parameters, b d The current loop control gain is partially known; let the known portion be denoted as b. d0 Define the total disturbance f, which includes internal and external disturbance terms. d for: Let the system state variable x d1 =y d And define the total disturbance f d For the extended state x d2 Write the extended state equation of the system as follows: For the above system, the second-order LESO is designed as follows: In the formula, z d1 z d2 For the second-order LESO state variables, the LESO error feedback gain value β is configured appropriately. d1 β d2 The value of z can make z d1 →y d , z d2 →f d To achieve real-time compensation for the total disturbance estimated by LESO, the LSEF is designed as follows: In the formula, r d For the current loop reference signal, k dp Define ω as the gain of the current loop controller. dc To determine the bandwidth of the current loop controller, a parameterized configuration method is used, letting k... dp =ω dc ; Step 5: Use the pole placement method to tune the position loop and current loop controller parameters.

2. The dual-closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC as described in claim 1, characterized in that, Step 1 specifically includes: Considering gyroscopic effects and unbalanced forces in the upper and lower electromagnetic bearing coordinate systems, x a x b y a y b The mathematical model for four degrees of freedom is: In the formula, x a x b y a y b These represent the displacements of the rotor's geometric center along the x and y axes at the positions of the upper and lower electromagnetic bearings, respectively. xa i xb i ya i yb x a x b y a y b The control current with four degrees of freedom, f u1 ~f u4 These are the effects of rotor mass imbalance on each degree of freedom, k. 11 ~k 46 These are the coefficients for each item.

3. The dual-closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC as described in claim 1, characterized in that, Step 2 specifically includes: Linearization analysis of the small-signal model of the power amplifier was performed using the state-space averaging method, yielding the transfer function of the ideal power amplifier-electromagnet coil linearized model as follows: In the formula, U amp A is the DC bus voltage of the power amplifier. amp L represents the amplitude of the triangular carrier wave during pulse width modulation. m R is the equivalent inductance of the electromagnet coil. m This is the equivalent resistance of the electromagnet coil.

4. The dual-closed-loop control method for magnetic levitation energy storage flywheel rotor dynamics based on LADRC as described in claim 1, characterized in that, Step 5 specifically includes: Step 5.1: Define ω o To determine the LESO bandwidth of the position loop, a pole placement method is used to place all the poles of the LESO characteristic equation at the same location -ω. o At this point, the solution is: Mathematical model of the controlled object based on the position loop, i.e., x a x b y a y b From the second-order mathematical model of degrees of freedom, we can see that the control gains of the position loop are as follows: In the formula, b 0xa b 0xb b 0ya b 0yb x a x b y a y b The position loop control gain for the degrees of freedom; Step 5.2: Define ω do To determine the LESO bandwidth of the current loop, a pole placement method is used to place all the poles of the LESO characteristic equation at the same location -ω. do At this point, the solution is: Based on the mathematical model of the controlled object in the current loop, namely the first-order mathematical model of the power amplifier-electromagnet coil, the control gains of the current loop are as follows: In the formula, b d0xa～yb Represents x a x b y a y b The position loop controls the gain for degrees of freedom.

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