Dynamic double-closed-loop control method for magnetic suspension energy storage flywheel rotor based on LADRC

Abstract

The invention provides a dynamic double-closed-loop control method for a magnetic suspension energy storage flywheel rotor based on LADRC. The dynamic double-closed-loop control method is used for realizing stable suspension and dynamic control of the magnetic suspension energy storage flywheel rotor. Firstly, a mathematical model of each degree of freedom of a flywheel rotor and a linearization model of a power amplifier-electromagnet coil under a magnetic bearing coordinate system are established; then, defining an electromagnetic coupling term, a gyroscope coupling term and an unbalance term in the flywheel rotor mathematical model as external disturbance, deducing a flywheel rotor and power amplifier-electromagnet coil mathematical model for controller design, and designing a position loop second-order LADRC controller and a current loop first-order LADRC controller; and finally, setting controller parameters of a position loop and a current loop by adopting a pole assignment method. Simulation results show that the double-closed-loop control strategy can realize effective decoupling among degrees of freedom under static and high-speed suspension working conditions of the flywheel rotor, and compared with PID control, the double-closed-loop control strategy is good in dynamic characteristic and strong in anti-interference capability. The method is of great significance in guaranteeing stable and reliable operation of the magnetic suspension energy storage flywheel rotor.

Description

Technical Field

[0001] The invention relates to the field of magnetic suspension energy storage flywheel rotor dynamics control, and in particular to a magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method based on LADRC. Background Art

[0002] The magnetically suspended energy storage flywheel rotor is a highly coupled mechatronic system. Its control system consists of a position loop and a current loop controller. The position loop controller realizes the stable suspension and dynamic control of the flywheel rotor, and the current loop controller ensures that the power amplifier quickly tracks the current given by the position loop controller. Under high speed and fast-changing speed, the system's gyroscopic effect intensifies, parameters are time-varying, uncertainty problems are prominent, disturbances are multivariate, and dynamic behavior is complex, which can easily cause system instability and cause the rotor to fall or even disintegrate. Therefore, it is of great significance to design a control strategy that is weakly dependent on the mathematical model of the system and considers decoupling and strong anti-disturbance capabilities to ensure stable operation of the system. Summary of the invention

[0003] The present invention designs a LADRC-based magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method.

[0004] The technical solution adopted by the present invention to solve the technical problem is: to provide a magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method 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, gyroscopic coupling term and unbalance 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 the second-order LADRC controller of the position loop;

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

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

[0010] The step 1 constructs a mathematical model of each radial degree of freedom of the flywheel rotor in the magnetic bearing coordinate system, specifically:

[0011] Considering the gyroscopic effect and unbalanced force, the upper and lower electromagnetic bearing coordinate systems are x a 、x b ,y a ,y bThe mathematical model of the four degrees of freedom is:

[0012]

[0013] In the formula, x a 、x b ,y a ,y b are the displacements of the rotor geometric center along the x-axis and y-axis at the upper and lower electromagnetic bearing positions, respectively, i xa 、i xb 、i ya 、i yb x a 、x b ,y a ,y b Control currents for the four degrees of freedom, f u1 ~f u4 are the influence of rotor mass imbalance on each degree of freedom, k 11 ~k 46 are the coefficients of each item.

[0014] The step 2 constructs a linearized model of a power amplifier-electromagnetic coil, specifically:

[0015] The state space averaging method is used to linearize the small signal model of the power amplifier, and the transfer function of the linearized model of the power amplifier-electromagnetic coil under ideal conditions is obtained:

[0016]

[0017] Where U amp is the DC bus voltage of the power amplifier, A amp is the amplitude of the triangular carrier in the pulse width modulation process, L m is the equivalent inductance of the electromagnet coil, R m is the equivalent resistance of the electromagnet coil.

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

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

[0020]

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

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

[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 including the term of the 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:

[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 system parameters, b is the control gain and is partially known, and the known part is recorded as b0; the total disturbance f including the internal disturbance term and the external disturbance term is defined as:

[0028]

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

[0030]

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

[0032]

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

[0034]

[0035] In the formula, k p , k d is the position loop controller gain, r is the position loop reference signal; when the estimation error of the state variable z3 of the position loop LESO to the total disturbance f is ignored, that is, z3≈f, the system can be simplified to a second-order integrator series type:

[0036]

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

[0038]

[0039] Definition c is the bandwidth of the position loop controller, and the parameterized configuration method can be used to obtain:

[0040]

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

[0042] Step 4.1: Perform inverse Laplace transform on the transfer function of the power amplifier-electromagnet coil linearization model and derive its time domain mathematical model as follows:

[0043]

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

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

[0046]

[0047] In the formula, u d ,y d are the input and output of the first-order system, ωd represents the external disturbance, a d is the system parameter, b d is the current loop control gain and is partially known, and the known part is recorded as b d0 ; Define the total disturbance f including internal disturbance terms and external disturbance terms d for:

[0048]

[0049] Let the system state variable xd1 =y d , and define the total disturbance f d is the expansion state x d2 , the expanded state equation of the system is written as:

[0050]

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

[0052]

[0053] In the formula, z d1 、z d2 is the state variable of the second-order LESO. By properly configuring the LESO error feedback gain value β d1 , β d2 The value of z d1 →y d , z d2 →f d ; In order to achieve real-time compensation for the total disturbance estimated by LESO, the LSEF is designed as:

[0054]

[0055] In the formula, r d is the current loop reference signal, k dp is the current loop controller gain, define ω dc is the bandwidth of the current loop controller, and a parameterized configuration method is used, where k dp =ω dc .

[0056] The step 5 uses the pole configuration method to adjust the position loop and current loop controller parameters, which specifically includes the following sub-steps:

[0057] Step 5.1: Define ω o The position loop LESO bandwidth is calculated by using the pole configuration method to configure the poles of the LESO characteristic equation at the same position -ω o At, solve for:

[0058]

[0059] Based on the mathematical model of the position loop controlled object, that is, x a 、x b ,y a ,y b From the second-order mathematical model of the degrees of freedom, it can be seen that the position loop control gains are:

[0060]

[0061] Where b0xa 、b 0xb 、b 0ya 、b 0yb x a 、x b ,y a ,y b Position loop control gain of degrees of freedom;

[0062] Step 5.2: Define ω do The LESO bandwidth is the current loop. The poles of the LESO characteristic equation are configured at the same position using the pole configuration method. do At, solve for:

[0063]

[0064] Based on the mathematical model of the current loop controlled object, that is, the first-order mathematical model of the power amplifier-electromagnetic coil, it can be known that the current loop control gains are:

[0065]

[0066] Where b d0xa～yb Represents x a 、x b ,y a ,y b Position loop control gains for each degree of freedom.

[0067] The beneficial effects of the present invention are:

[0068] The present invention proposes a LADRC-based dual closed-loop control method for the dynamics of a magnetically suspended energy storage flywheel rotor to achieve stable suspension and dynamic control of a magnetically suspended energy storage flywheel rotor. First, a mathematical model of each degree of freedom of the flywheel rotor and a linearized model of a power amplifier-electromagnet coil are established in a magnetic bearing coordinate system. Then, the electromagnetic coupling term, gyroscopic coupling term and unbalance term in the mathematical model of the flywheel rotor are defined as external disturbances, and the mathematical models of the flywheel rotor and the 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 pole configuration method is used to adjust the position loop and current loop controller parameters. Simulation results show that the dual closed-loop control strategy can achieve effective decoupling between the degrees of freedom of the flywheel rotor under static and high-speed suspension conditions. Compared with PID control, it has good dynamic characteristics and strong anti-interference ability. It is of great significance in ensuring the stable and reliable operation of the magnetically suspended energy storage flywheel rotor. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 The present invention is a flow chart of a LADRC-based double closed-loop control method for magnetic suspension energy storage flywheel rotor dynamics.

[0070] Figure 2 It is a set value tracking performance curve of the PID control strategy under the static suspension condition in Example 1 of the magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method based on LADRC of the present invention.

[0071] Figure 3 It is a decoupling performance curve of the PID control strategy under the static suspension condition in Example 1 of the magnetic suspension energy storage flywheel rotor dynamics dual closed-loop control method based on LADRC of the present invention.

[0072] Figure 4 It is a set value tracking performance curve of the comparative PID control strategy under high-speed suspension conditions in Example 1 of a magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method based on LADRC of the present invention.

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

[0074] Figure 6 It is a disturbance suppression performance curve of the comparative PID control strategy in Example 1 of a magnetic levitation energy storage flywheel rotor dynamics double closed-loop control method based on LADRC of the present invention. DETAILED DESCRIPTION

[0075] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and Example 1.

[0076] like Figure 1 FIG. 1 is a flow chart of a LADRC-based magnetic levitation energy storage flywheel rotor dynamics double closed-loop control method, which specifically includes the following steps:

[0077] The step 1 constructs a mathematical model of each radial degree of freedom of the flywheel rotor in the magnetic bearing coordinate system, specifically:

[0078] Considering the gyroscopic effect and unbalanced force, the upper and lower electromagnetic bearing coordinate systems are x a 、x b ,y a ,y b The mathematical model of the four degrees of freedom is:

[0079]

[0080] In the formula, x a 、x b ,y a ,y b are the displacements of the rotor geometric center along the x-axis and y-axis at the upper and lower electromagnetic bearing positions, respectively, ixa 、i xb 、i ya 、i yb x a 、x b ,y a ,y b Control currents for the four degrees of freedom, f u1 ~f u4 are the influence of rotor mass imbalance on each degree of freedom, k 11 ~k 46 are the coefficients of each item.

[0081] The step 2 constructs a linearized model of a power amplifier-electromagnet coil, specifically:

[0082] The state space averaging method is used to linearize the small signal model of the power amplifier, and the transfer function of the linearized model of the power amplifier-electromagnetic coil under ideal conditions is obtained:

[0083]

[0084] Where U amp is the DC bus voltage of the power amplifier, A amp is the amplitude of the triangular carrier in the pulse width modulation process, L m is the equivalent inductance of the electromagnet coil, R m is the equivalent resistance of the electromagnet coil.

[0085] The step 3 defines the electromagnetic coupling term, gyroscopic coupling term and unbalance 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 the second-order LADRC controller of the position loop, which specifically includes the following sub-steps:

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

[0087]

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

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

[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 including the term of the 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:

[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 system parameters, b is the control gain and is partially known, and the known part is recorded as b0; the total disturbance f including the internal disturbance term and the external disturbance term is defined as:

[0095]

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

[0097]

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

[0099]

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

[0101]

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

[0103]

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

[0105]

[0106] Definition c is the bandwidth of the position loop controller, and the parameterized configuration method can be used to obtain:

[0107]

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

[0109] Step 4.1: Perform inverse Laplace transform on the transfer function of the power amplifier-electromagnet coil linearization model and derive its time domain mathematical model as follows:

[0110]

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

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

[0113]

[0114] In the formula, u d ,y d are the input and output of the first-order system, ω d represents external disturbance, a d is the system parameter, b d is the current loop control gain and is partially known, and the known part is recorded as b d0 ; Define the total disturbance f including internal disturbance terms and external disturbance terms d for:

[0115]

[0116] Let the system state variable x d1 =y d , and define the total disturbance f d is the expansion state x d2 , the expanded state equation of the system is written as:

[0117]

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

[0119]

[0120] In the formula, z d1 、z d2 is the state variable of the second-order LESO. By properly configuring the LESO error feedback gain value β d1 , β d2 The value of z d1 →y d , z d2 →f d ; In order to achieve real-time compensation for the total disturbance estimated by LESO, the LSEF is designed as:

[0121]

[0122] In the formula, r d is the current loop reference signal, k dp is the current loop controller gain, define ω dc is the bandwidth of the current loop controller, and a parameterized configuration method is used, where k dp =ω dc .

[0123] The step 5 uses the pole configuration method to adjust the position loop and current loop controller parameters, which specifically includes the following sub-steps:

[0124] Step 5.1: Define ω o The position loop LESO bandwidth is calculated by using the pole configuration method to configure the poles of the LESO characteristic equation at the same position -ω o At, solve for:

[0125]

[0126] Based on the mathematical model of the position loop controlled object, that is, x a 、x b ,y a ,y b From the second-order mathematical model of the degrees of freedom, it can be seen that the position loop control gains are:

[0127]

[0128] Where b 0xa 、b 0xb 、b 0ya 、b 0yb x a 、x b ,y a ,y b Position loop control gain of degrees of freedom;

[0129] Step 5.2: Define ω do The LESO bandwidth is the current loop. The poles of the LESO characteristic equation are configured at the same position using the pole configuration method. do At, solve for:

[0130]

[0131] Based on the mathematical model of the current loop controlled object, that is, the first-order mathematical model of the power amplifier-electromagnetic coil, it can be known that the current loop control gains are:

[0132]

[0133] Where b d0xa～yb Represents x a 、x b ,y a ,y b Position loop control gains for each degree of freedom.

[0134] like Figure 2 As shown in FIG. 1 , the set value tracking performance curve of the PID control strategy under the static suspension condition in the embodiment 1 of the magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method based on LADRC of the present invention is shown. The flywheel rotor speed is zero, and x is set at 0.2s. a The reference value of the degree of freedom displacement ref jumps from zero to 0.1mm. As can be seen from the figure, under PID control, the system response has overshoot, the maximum overshoot is about 28.5%, and the adjustment time is too long, about 2.2s. Under the method proposed in this patent, the system responds quickly and has no overshoot, and has good dynamic characteristics.

[0135] Figure 3 As shown, it is a decoupling performance curve of the PID control strategy under static suspension conditions in Example 1 of a magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method 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 of the degree of freedom displacement ref changes from zero to 0.1 mm. Figure 3 (a) and Figure 3 (b) It can be seen that when x a When the degree of freedom displacement changes step by step, y a and b The displacement of the degree of freedom is not affected, indicating that there is no coupling between them, which is consistent with the theoretical analysis. Under the PID control strategy, x b The degree of freedom displacement has obvious fluctuations, and the maximum displacement fluctuation is about 7.2um. Under the method proposed in this patent, xb The degree of freedom displacement has a slight fluctuation, and the maximum displacement fluctuation is about 0.26um. Therefore, the decoupling effect of the method proposed in this patent is good.

[0136] Figure 4 As shown in FIG. 1 , the set value tracking performance curve of the PID control strategy under high-speed suspension conditions in Example 1 of the magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method based on LADRC of the present invention is shown. The flywheel rotor speed is 4800rpm, and x is set at 0.15s. a The reference value of the degree of freedom displacement ref changes from zero to 0.1mm. As can be seen from the figure, under the PID control strategy, the system has a maximum overshoot of about 34%, and the adjustment time is about 2.4s. Under the method proposed in this patent, the system responds quickly and without overshoot.

[0137] Figure 5 As shown, it is a decoupling performance curve of the PID control strategy under high-speed suspension conditions in Example 1 of a magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method 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 4800rpm, and x is a The reference value of the degree of freedom displacement ref changes from zero to 0.1 mm. Figure 5 (a) and Figure 5 (b) It can be seen that when x a When the degree of freedom displacement changes step by step, x b ,y a ,y b The displacements of the three degrees of freedom are all affected and fluctuate to a certain extent, indicating that there is coupling between the four degrees of freedom under high-speed suspension conditions, which is consistent with theoretical analysis. b The maximum displacement fluctuation of the degree of freedom is about 9.5um, y a The maximum displacement fluctuation of the degree of freedom is about 10.3um, y b The maximum displacement fluctuation of the degree of freedom is about 11.8um. ​​Under the method proposed in this patent, x b The maximum displacement fluctuation of the degree of freedom is about 0.14um, y a The maximum displacement fluctuation of the degree of freedom is about 1.1um, y b The maximum displacement fluctuation of the degree of freedom is about 1.06um. Therefore, the decoupling effect of the method proposed in this patent is good.

[0138] Figure 6As shown in FIG. 1 , the disturbance suppression performance curve of the comparative PID control strategy in Example 1 of the LADRC-based magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method of the present invention is shown. The flywheel rotor speed is 4800 rpm, and x is given in the time period of 0.1 to 0.2 s. a Degree 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 speed) is applied to the input. As can be seen from the figure, under the PID control strategy, x a The maximum displacement fluctuation of the degree of freedom is about 5.1um. Under the method proposed in this patent, x a The degree of freedom displacement fluctuation is about 1.5um. Therefore, the method proposed in this patent has better disturbance suppression ability.

Claims

1. A LADRC-based magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method, characterized in that: The following steps are involved: 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 unbalance 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 the second-order LADRC controller of the position loop; Step 4: Derive the first-order mathematical model of the power amplifier-electromagnet coil and design the first-order LADRC controller of the current loop; Step 5: Use the pole configuration method to adjust the position loop and current loop controller parameters.

2. According to claim 1, a LADRC-based magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method is characterized in that: The step 1 is specifically as follows: Considering the gyroscopic effect and unbalanced force, the upper and lower electromagnetic bearing coordinate systems are x a 、x b ,y a ,y b The mathematical model of the four degrees of freedom is: In the formula, x a 、x b ,y a ,y b are the displacements of the rotor geometric center along the x-axis and y-axis at the upper and lower electromagnetic bearing positions, respectively, i xa 、i xb 、i ya 、i yb x a 、x b ,y a ,y b Control currents for the four degrees of freedom, f u1 ~f u4 are the influence of rotor mass imbalance on each degree of freedom, k 11 ~k 46 are the coefficients of each item.

3. The LADRC-based magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method according to claim 1 is characterized in that: The step 2 is specifically as follows: The state space averaging method is used to linearize the small signal model of the power amplifier, and the transfer function of the linearized model of the power amplifier-electromagnetic coil under ideal conditions is obtained: Where U amp is the DC bus voltage of the power amplifier, A amp is the amplitude of the triangular carrier in the pulse width modulation process, L m is the equivalent inductance of the electromagnet coil, R m is the equivalent resistance of the electromagnet coil.

4. The LADRC-based magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method according to claim 1 is characterized in that: The step 3 is specifically as follows: Step 3.1: Set x a 、x b ,y a ,y b The electromagnetic coupling term, gyroscopic coupling term and unbalance term in the mathematical model of each degree of freedom are defined as external disturbances: In the formula, ω xa ,ω xb ,ω ya ,ω yb The x defined respectively a 、x b ,y a ,y b External disturbances of the degrees of freedom; Step 3.2: After defining the external disturbance of each degree of freedom, the mathematical model of each degree of freedom is expressed as: 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 including the term of the 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: 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 system parameters, b is the control gain and is partially known, and the known part is recorded as b0; the total disturbance f including the internal disturbance term and the external disturbance term is defined as: Let the system state variable x1 = y, And define the total disturbance f as the expansion state x3, and write the expansion state equation of the system as: For the above system, the third-order linear extended state observer (LESO) is designed as: Where z1, z2, and z3 are the state variables of the third-order LESO. By properly configuring the values ​​of the LESO error feedback gain values ​​β1, β2, and β3, z1→y can be achieved. z3→f; In order to realize the real-time compensation of the total disturbance estimated by LESO, the linear state error feedback control law (LSEF) is designed as: In the formula, k p , k d is the position loop controller gain, r is the position loop reference signal; when the estimation error of the state variable z3 of the position loop LESO to the total disturbance f is ignored, that is, z3≈f, the system can be simplified to a second-order integrator series type: The closed-loop transfer function of the system is derived as: Definition c is the bandwidth of the position loop controller, and the parameterized configuration method can be used to obtain:

5. The LADRC-based magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method according to claim 1 is characterized in that: The step 4 is specifically as follows: Step 4.1: Perform inverse Laplace transform on the transfer function of the power amplifier-electromagnet coil linearization model and derive its time domain mathematical model as follows: In the formula, u amp ,y amp They are the input and output of the power amplifier-electromagnet coil respectively; Step 4.2: The control object of the current loop is the power amplifier-electromagnet coil, and the order of its mathematical model is first order. The general form of the first-order system mathematical model is: In the formula, u d ,y d are the input and output of the first-order system, ω d represents external disturbance, a d is the system parameter, b d is the current loop control gain and is partially known, and the known part is recorded as b d0 ; Define the total disturbance f including internal disturbance terms and external disturbance terms d for: Let the system state variable x d1 =y d , and define the total disturbance f d is the expansion state x d2 , the expanded state equation of the system is written as: For the above system, the second-order LESO is designed as: In the formula, z d1 、z d2 is the state variable of the second-order LESO. By properly configuring the LESO error feedback gain value β d1 , β d2 The value of z d1 →y d , z d2 →f d ; In order to achieve real-time compensation for the total disturbance estimated by LESO, the LSEF is designed as: In the formula, r d is the current loop reference signal, k dp is the current loop controller gain, define ω dc is the bandwidth of the current loop controller, and a parameterized configuration method is used, where k dp =ω dc .

6. The LADRC-based magnetic suspension energy storage flywheel rotor dynamics double closed-loop control method according to claim 1 is characterized in that: The step 5 is specifically as follows: Step 5.1: Define ω o The position loop LESO bandwidth is calculated by using the pole configuration method to configure the poles of the LESO characteristic equation at the same position -ω o At, solve: Based on the mathematical model of the position loop controlled object, that is, x a 、x b ,y a ,y b From the second-order mathematical model of the degrees of freedom, it can be seen that the position loop control gains are: Where b 0xa 、b 0xb 、b 0ya 、b 0yb x a 、x b ,y a ,y b Position loop control gain of degrees of freedom; Step 5.2: Define ω do The LESO bandwidth is the current loop. The poles of the LESO characteristic equation are configured at the same position using the pole configuration method. do At, solve: Based on the mathematical model of the current loop controlled object, that is, the first-order mathematical model of the power amplifier-electromagnetic coil, it can be known that the current loop control gains are: Where b d0xa～yb Represents x a 、x b ,y a ,y b Position loop control gains for each degree of freedom.

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