Method for resonant tuning and energy efficiency optimization of wireless power supply for magnetic bearing

Abstract

The application relates to the technical field of magnetic suspension, and discloses a magnetic bearing wireless power supply resonance tuning and energy efficiency optimization method, which comprises the following steps: acquiring magnetic bearing parameters; dynamically predicting a model to calculate a coupling coefficient at a future time; obtaining a resonance frequency after feedforward tuning; solving an efficiency optimization function to obtain optimal transmission power and working frequency; calculating magnetic bearing current; solving optimal weight coefficients of a system stability function; generating and applying a control sequence to adjust a resonance element and a magnetic bearing; through the establishment of a dynamic prediction model, the application can accurately predict the change rule of the coupling coefficient in the future control period, the resonance element parameters are adjusted in advance through a coupling coefficient compensation mechanism, the resonance misadjustment problem caused by coupling changes in a high-speed rotating system is effectively solved, a multi-target coordinated decision mechanism is constructed, and the comprehensive balance of energy efficiency optimization, control precision and system stability is realized.

Description

Technical Field

[0001] This invention relates to the field of magnetic levitation technology, and more specifically, to a method for wireless power supply resonant tuning and energy efficiency optimization of magnetic bearings. Background Technology

[0002] With the development of magnetic levitation technology, active magnetic bearings have been widely used in high-speed rotating equipment due to their advantages such as contactless operation, frictionless operation, and high precision. In practical applications, to avoid mechanical interference from traditional wired power supply to high-speed rotating equipment, wireless power supply technology has gradually been introduced into magnetic bearing systems. Wireless power supply transmits energy through coil coupling, and its efficiency and stability are highly dependent on the resonant matching state between the transmitting and receiving coils.

[0003] Chinese Patent CN115395863B discloses an active magnetic bearing control method based on hybrid systems theory. The method establishes a hybrid logic dynamic model for the drive system, using this model as a predictive model to predict the current at the next moment. Minimizing the difference between the predicted current and the reference current is used as the control objective to establish a cost function for rolling optimization, effectively controlling the magnetic bearing coil current. This results in smaller displacement deviations when the magnetic bearing is disturbed, higher control accuracy, and enhanced robustness of the magnetic bearing control system. This invention introduces hybrid systems theory into the magnetic bearing control system, establishing a hybrid logic dynamic model as the predictive model. This integrates the system's continuous dynamics, logical rules, and operational constraints into a unified framework, avoiding complex computational loads and control algorithms. It reduces the rotor offset of the magnetic levitation flywheel, lowers the vibration of the magnetic levitation flywheel system, and effectively improves the control accuracy and stability of the magnetic levitation flywheel.

[0004] However, in high-speed rotation scenarios, the rotation of the device causes a high-frequency dynamic shift in the relative positions of the transmitting and receiving coils, leading to drastic fluctuations in the coupling coefficient and consequently, resonant frequency drift. Existing technologies primarily focus on closed-loop control of the magnetic bearing coil current, neglecting the impact of changes in the resonant state of the wireless power supply link on power efficiency and current stability. When the resonant frequency drifts, wireless power supply efficiency significantly decreases, resulting in unstable input energy to the magnetic bearing coil. The current fluctuation amplitude exceeds the accuracy threshold of the original control method, further increasing the displacement of the magnetic bearing under disturbances and potentially affecting system stability. Summary of the Invention

[0005] The purpose of this invention is to provide a method for wireless power supply resonant tuning and energy efficiency optimization of magnetic bearings in order to solve the above-mentioned problems.

[0006] This invention provides a method for wireless power supply resonant tuning and energy efficiency optimization of magnetic bearings, comprising the following steps:

[0007] Magnetic bearing parameters are obtained through a real-time monitoring system;

[0008] Based on the magnetic bearing parameters, a dynamic prediction model is established, and the dynamic prediction model calculates the coupling coefficient at future time points;

[0009] Based on the coupling coefficient at the future time, perform feedforward tuning of the resonant frequency to obtain the resonant frequency after feedforward tuning.

[0010] Based on the resonant frequency after feedforward tuning, an efficiency optimization function is constructed, and the optimal transmit power and operating frequency are obtained by solving the efficiency optimization function.

[0011] Calculate the magnetic bearing current based on the optimal transmission power and the coupling coefficient at future time.

[0012] Based on the coupling coefficient at the future moment, the resonant frequency after feedforward tuning, the optimal transmit power and operating frequency, and the magnetic bearing current, a system stability function is constructed, and the optimal weighting coefficient of the system stability function is solved.

[0013] Based on the optimal weights, rolling optimization control is performed to generate and apply control sequences to adjust the resonant elements and magnetic bearings.

[0014] Furthermore, the resonant frequency feedforward tuning includes:

[0015] The target value of the resonant frequency is calculated based on the coupling coefficient at a future time. The target value of the resonant frequency is the square root of the preset reference resonant frequency multiplied by the coupling coefficient compensation factor. The coupling coefficient compensation factor is the ratio of the coupling coefficient at a future time to the current coupling coefficient.

[0016] Based on the target resonant frequency, calculate the required inductance and capacitance adjustments;

[0017] Based on the inductance and capacitance adjustment, the adjustable inductance and adjustable capacitance values ​​after feedforward tuning are determined. The adjustable inductance value after feedforward tuning is the current adjustable inductance value plus the inductance adjustment, and the adjustable capacitance value after feedforward tuning is the current adjustable capacitance value plus the capacitance adjustment.

[0018] Calculate the resonant frequency after feedforward tuning based on the adjustable inductance and adjustable capacitance values. The resonant frequency after feedforward tuning is half of pi, divided by the square root of the product of the adjustable inductance and adjustable capacitance values ​​after feedforward tuning.

[0019] Furthermore, the calculation of the required inductance and capacitance adjustments includes:

[0020] The inductor adjustment is calculated using an inductor PID controller. The proportional term of the inductor PID controller is the preset inductor proportional gain coefficient multiplied by the resonant frequency offset; the integral term is the preset inductor integral gain coefficient multiplied by the cumulative integral value of the resonant frequency offset; and the derivative term is the preset inductor differential gain coefficient multiplied by the rate of change of the resonant frequency offset. The resonant frequency offset is the current resonant frequency minus the target resonant frequency value. The cumulative integral value of the resonant frequency offset is the sum of the resonant frequency offsets at each historical sampling time. The rate of change of the resonant frequency offset is the difference between the resonant frequency offset at the current time and the resonant frequency offset at the previous time divided by the preset sampling period.

[0021] The capacitor adjustment is calculated by a capacitor PID controller. The proportional term of the capacitor PID controller is the preset capacitor proportional gain coefficient multiplied by the resonant frequency offset, the integral term is the preset capacitor integral gain coefficient multiplied by the cumulative integral value of the resonant frequency offset, and the derivative term is the preset capacitor differential gain coefficient multiplied by the rate of change of the resonant frequency offset.

[0022] Furthermore, the coupling coefficient for future moments includes coupling coefficients for multiple predicted moments. The coupling coefficient for each predicted moment is a preset baseline coupling coefficient multiplied by a correction term. The correction term is the sum of a first constant term, a first period term, and a second period term. The first period term is a preset first coupling change amplitude coefficient multiplied by a cosine function. The independent variable of the cosine function is the product of the rotor angular velocity and the predicted moment, plus a preset first phase angle. The second period term is a preset second coupling change amplitude coefficient multiplied by a sine function. The independent variable of the sine function is twice the rotor angular velocity multiplied by the predicted moment, plus a preset second phase angle. The predicted moment is the current moment plus a predicted time step, and the predicted time step is an integer multiple of the preset sampling period.

[0023] Furthermore, solving the efficiency optimization function to obtain the optimal transmit power and operating frequency includes:

[0024] The goal of the efficiency optimization function is to maximize the comprehensive transmission efficiency index. The comprehensive transmission efficiency index is the predicted transmission efficiency minus the resonance offset term and then minus the power loss term. The resonance offset term is the square of the resonant frequency offset after feedforward tuning multiplied by a preset first weighting coefficient, and the power loss term is the absolute value of the system power loss multiplied by a preset second weighting coefficient. Among them, the resonant frequency offset after feedforward tuning is equal to the difference between the resonant frequency after feedforward tuning and the target resonant frequency value. The system power loss is the transmit power related loss plus the frequency related loss. The transmit power related loss is the square of the transmit power multiplied by a preset power loss coefficient, and the frequency related loss is the square of the difference between the operating frequency and the target resonant frequency value multiplied by a preset frequency loss coefficient.

[0025] The efficiency optimization function is solved using the gradient ascent method. The optimal transmit power is the sum of the previous optimal transmit power multiplied by the preset power learning rate parameter, and then multiplied by the partial derivatives of the efficiency optimization function with respect to the transmit power. The optimal operating frequency is the sum of the previous optimal operating frequency multiplied by the preset frequency learning rate parameter, and then multiplied by the partial derivatives of the efficiency optimization function with respect to the operating frequency.

[0026] Furthermore, the predicted transmission efficiency is equal to the product of the preset maximum transmission efficiency, the coupling coefficient influence factor, the frequency tuning influence factor, and the power transmission influence factor.

[0027] The coupling coefficient influence factor is the ratio of the coupling coefficient at a future time to the preset reference coupling coefficient. The frequency tuning influence factor is equal to 1 minus the feedforward tuning term. The feedforward tuning term is the square of the ratio of the resonant frequency offset after feedforward tuning to the preset frequency tuning range. The power transmission influence factor is the ratio of the transmit power to the preset optimal transmit power multiplied by the power efficiency correction term. The power efficiency correction term is 1 minus the power efficiency term. The power efficiency term is the square of the difference between the transmit power and the preset optimal transmit power divided by the square of the preset power adjustment range.

[0028] Furthermore, the calculation of the magnetic bearing current includes:

[0029] The magnetic bearing coil current at the next sampling moment is calculated by dividing the preset sampling period by the temperature-compensated coil inductance and then multiplying by the control input voltage; the negative temperature-compensated coil resistance is multiplied by the ratio of the preset sampling period to the temperature-compensated coil inductance and then multiplied by the current magnetic bearing coil current; the preset power supply efficiency influence coefficient is multiplied by the current optimal predicted transmission efficiency; and the difference between the future coupling coefficient and the current real-time coupling coefficient is multiplied by the preset coupling coefficient influence coefficient. The optimal predicted transmission efficiency is the predicted transmission efficiency calculated using the optimal transmit power. The temperature-compensated coil inductance is the coil inductance at the preset reference temperature multiplied by the inductance correction factor, which is the difference between the current coil temperature and the preset reference temperature multiplied by the preset inductance temperature coefficient plus 1. The temperature-compensated coil resistance is the coil resistance at the preset reference temperature multiplied by the resistance correction factor, which is the difference between the current coil temperature and the preset reference temperature multiplied by the preset resistance temperature coefficient plus 1.

[0030] Furthermore, the comprehensive cost function is the sum of the products obtained by multiplying the third weighting coefficient by the magnetic bearing control performance function, the fourth weighting coefficient by the negative value of the comprehensive transmission efficiency index, and the fifth weighting coefficient by the system stability function.

[0031] The optimal weight coefficients are solved using a quadratic programming method. The optimization objective is to minimize the comprehensive cost function. The constraints are that the sum of the third, fourth, and fifth weight coefficients is equal to 1 and the third, fourth, and fifth weight coefficients are greater than or equal to 0. The optimal weight coefficients are the third, fourth, and fifth weight coefficients that minimize the comprehensive cost function.

[0032] Furthermore, the magnetic bearing control performance function is equal to the sum of the magnetic shaft terms from the first prediction time to the Nth prediction time. The magnetic shaft terms are the square of the difference between the magnetic bearing current and the preset magnetic bearing current reference value multiplied by the preset first weight matrix, and the square of the rotor displacement offset multiplied by the preset second weight matrix.

[0033] The system stability function is the sum of system terms from the first prediction time to the Nth prediction time. The system terms are: the product of the square of the difference between the resonant frequency after feedforward tuning and the target resonant frequency value and the preset third weight matrix; the product of the square of the difference between the predicted future coupling coefficient and the preset benchmark coupling coefficient and the preset fourth weight matrix; and the sum of the two products.

[0034] Furthermore, the magnetic bearing parameters include real-time coupling coefficient, resonant frequency offset, transmission power, magnetic bearing coil current and voltage, rotor displacement offset, rotor angular velocity, and coil parameter variation. The transmission efficiency is the ratio of load power to input power. The rotor displacement offset includes horizontal and vertical displacement offset and rotor angular velocity. The coil parameter variation includes resistance variation, inductance variation, and coil temperature.

[0035] The beneficial effects of this invention are as follows: By establishing a dynamic prediction model based on rotor angular velocity and position information, this invention can accurately predict the variation law of the coupling coefficient within future control cycles. This prediction model employs periodic correction terms, including a first periodic term and a second periodic term, which can accurately describe the dynamic changes in the magnetic coupling strength between the transmitting and receiving coils in a high-speed rotating magnetic levitation flywheel system. Compared with traditional static coupling analysis methods, the dynamic prediction technology of this invention improves the prediction accuracy of the coupling coefficient, providing a reliable prediction basis for subsequent feedforward tuning control.

[0036] This invention employs a feedforward tuning control strategy based on future coupling states, adjusting the resonant element parameters in advance through a coupling coefficient compensation mechanism. This method combines an inductor-based PID controller and a capacitor-based PID controller, dynamically calculating the optimal adjustment amount based on the current value, historical cumulative value, and trend of the resonant frequency offset. Compared to traditional feedback control methods, feedforward tuning control improves resonant frequency tracking accuracy, shortens response time, and effectively solves the resonance misalignment problem caused by coupling changes in high-speed rotating systems.

[0037] This invention establishes an optimization function aimed at maximizing transmission efficiency. It describes the impact of three physical mechanisms on transmission efficiency through coupling coefficient influence factors, frequency tuning influence factors, and power transmission influence factors. The gradient ascent method is used to solve for the optimal transmit power and optimal operating frequency, achieving dynamic optimization of transmission efficiency. Compared to wireless power supply systems with fixed parameters, the energy efficiency optimization method of this invention improves transmission efficiency and reduces power loss.

[0038] This invention employs an active magnetic bearing control system based on hybrid systems theory, establishing a discrete-time state equation for the magnetic bearing current and fully considering the impact of variations in wireless power supply efficiency and coupling coefficient on the magnetic bearing control. Through a temperature compensation mechanism and an adaptive compensator, stable control performance of the magnetic bearing is ensured even when the wireless power supply status changes. Compared to traditional independent control methods, the adaptive compensation method of this invention improves the control accuracy of the magnetic bearing and reduces rotor displacement deviation.

[0039] This invention constructs a comprehensive cost function that holistically considers the control performance of magnetic bearings, the transmission efficiency of wireless power supply, and the overall stability of the system, achieving multi-objective coordinated optimization through dynamic weight coefficients. This method can adaptively adjust the performance weights of each subsystem under different operating conditions, ensuring optimal overall system performance in complex operating environments. Compared to single-objective optimization methods, multi-objective coordinated decision-making improves the overall system performance and stability indicators.

[0040] This invention employs a distributed model predictive control strategy, achieving joint optimization of resonant tuning control and magnetic bearing control through recursive solution. The rolling optimization mechanism fully utilizes the latest system state information in each control cycle, forming a closed-loop rolling optimization control. Compared to open-loop control methods, rolling optimization improves system response speed and enhances control stability. Attached Figure Description

[0041] Figure 1 This is a module example diagram of the magnetic bearing wireless power supply resonant tuning and energy efficiency optimization method of the present invention;

[0042] Figure 2 This is an example diagram showing the resonant frequency obtained after feedforward tuning using the magnetic bearing wireless power supply resonant tuning and energy efficiency optimization method of the present invention.

[0043] Figure 3 This is an example diagram illustrating the optimal transmission power and operating frequency obtained by the magnetic bearing wireless power supply resonant tuning and energy efficiency optimization method of the present invention.

[0044] Figure 4 This is an example diagram illustrating the calculation of magnetic bearing current in the magnetic bearing wireless power supply resonant tuning and energy efficiency optimization method of the present invention. Detailed Implementation

[0045] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0046] Example 1:

[0047] Methods for resonant tuning and energy efficiency optimization of wireless power supply for magnetic bearings, such as Figure 1 As shown, it includes the following steps:

[0048] Step 100: Obtain magnetic bearing parameters through a real-time monitoring system.

[0049] During startup, the following magnetic bearing parameters are acquired through a real-time monitoring system. This system includes a coupling coefficient sensor, a resonant frequency detector, current and voltage sensors, a displacement sensor, and a temperature sensor. These sensors work together to provide accurate status information. The magnetic bearing parameters include real-time coupling coefficient, resonant frequency offset, transmission power, transmission efficiency, magnetic bearing coil current and voltage, rotor displacement offset, and coil parameter changes.

[0050] The real-time coupling coefficient and resonant frequency offset are obtained by a coupling coefficient sensor. The real-time coupling coefficient represents the change of magnetic coupling strength between the transmitting coil and the receiving coil over time, and the resonant frequency offset represents the difference between the current resonant frequency and the target resonant frequency value.

[0051] The transmission power and transmission efficiency of the wireless power supply link are obtained by a resonant frequency detector. The transmission efficiency is the ratio of load power to input power. The load power is the actual power transmitted to the load end, and the input power is the total power of the system input end.

[0052] The current and voltage of the magnetic bearing coil are obtained by current and voltage sensors. These parameters reflect the working status and control effect of the magnetic bearing.

[0053] The rotor displacement offset is obtained by displacement sensors, including horizontal and vertical displacement offset, as well as rotor angular velocity. These parameters reflect the rotor's motion state.

[0054] The coil parameters, including changes in resistance and inductance, as well as the coil temperature, are obtained by current, voltage, and temperature sensors. These parameters reflect the coil's operating status and environmental influences.

[0055] These parameters provide the foundational data for subsequent dynamic prediction and control optimization.

[0056] Step 200: Based on the magnetic bearing parameters, establish a dynamic prediction model, and calculate the coupling coefficient at future time points using the dynamic prediction model.

[0057] To achieve efficient energy optimization of the wireless power supply system, a dynamic prediction model of the coupling coefficient at future moments needs to be established based on the rotor angular velocity and position information obtained in step 100. Since the high-speed rotation of the rotor in the magnetic bearing system causes continuous changes in the relative position between the transmitting and receiving coils, resulting in periodic fluctuations in the magnetic coupling strength, it is essential to accurately predict the dynamic change pattern of the coupling coefficient within the next control cycle to provide a reliable predictive basis for subsequent resonant frequency feedforward tuning. The wireless power supply system consists of transmitting and receiving coils, achieving contactless energy transmission based on the principle of electromagnetic induction.

[0058] In a high-speed rotating magnetic levitation flywheel system, the change in the coupling coefficient at future moments is mainly influenced by the current rotor angular velocity and position offset. The coupling coefficient at future moments includes coupling coefficients for multiple predicted moments. The coupling coefficient at each predicted moment is equal to a preset baseline coupling coefficient multiplied by a correction term containing periodic variations. The correction term is the sum of a first constant term, a first periodic term, and a second periodic term. The default value of the first constant term is 1. The first periodic term is a preset first coupling change amplitude coefficient multiplied by a cosine function, where the independent variable of the cosine function is the product of the rotor angular velocity and the predicted moment plus a preset first phase angle. The second periodic term is a preset second coupling change amplitude coefficient multiplied by a sine function, where the independent variable of the sine function is twice the product of the rotor angular velocity and the predicted moment plus a preset second phase angle. The predicted moment is the current moment plus the predicted time step. The default value of the preset sampling period is 1 millisecond, and the predicted time step is an integer multiple of the preset sampling period, typically set to 3 to 5 sampling periods to ensure that the prediction results provide sufficient lead time for feedforward control.

[0059] To ensure the accuracy and practicality of the dynamic prediction model, key parameters need to be determined through system identification and historical data analysis. The default value for the preset baseline coupling coefficient is 0.25, obtained through system calibration, reflecting the magnetic coupling strength under ideal alignment. The default values ​​for the preset first coupling variation amplitude coefficient are 0.15 and 0.1, respectively. These coefficients are obtained through least-squares fitting of historical data, quantifying the influence of rotor rotation on the coupling coefficient. The default values ​​for the preset first phase angle are 0 radians and 0.5 radians, respectively. These phase angles reflect the temporal characteristics of coupling changes, demonstrating the influence of rotor position offset on the coupling change phase, and are determined through frequency domain analysis of system operating data. The prediction model also needs to consider the deviation between the real-time coupling coefficient and the predicted baseline value at the current moment, improving prediction accuracy through a deviation compensation mechanism.

[0060] By establishing a dynamic prediction model, the changing trend of the coupling coefficient within the next control cycle can be predicted in advance, thus providing accurate future coupling coefficient information for the resonant frequency feedforward tuning in step 300. The dynamic prediction model not only considers the periodic coupling changes caused by rotor rotation but also fully utilizes the real-time magnetic bearing parameters obtained in step 100. By predicting the coupling coefficient changes at future moments, it achieves an organic connection between obtaining the current state and predicting the future state, laying a solid foundation for feedforward coordinated optimization control.

[0061] Step 300: Perform feedforward tuning of the resonant frequency based on the coupling coefficient at the future time, to obtain the feedforward tuned resonant frequency, specifically as follows... Figure 2 As shown.

[0062] Based on the predicted changes in the coupling coefficient at future moments in step 200, the parameters of the resonant elements are adjusted in advance by the resonant tuning controller to achieve feedforward tuning control based on the future coupling state.

[0063] First, the target resonant frequency is calculated based on the predicted coupling coefficient at future moments. The calculation of the target resonant frequency needs to consider the impact of the future coupling coefficient on the system's resonant characteristics, and the optimal resonant operating point is determined through a coupling coefficient compensation mechanism. The coupling coefficient compensation factor is equal to the ratio of the predicted future coupling coefficient to the real-time coupling coefficient at the current moment; this ratio reflects the dynamic trend of the coupling strength. The target resonant frequency is equal to the preset reference resonant frequency multiplied by the square root of the coupling coefficient compensation factor, where the default value of the preset reference resonant frequency is 85 kHz. This value represents the optimal resonant frequency under ideal coupling conditions and is obtained through system calibration.

[0064] After determining the target resonant frequency, a PID controller calculates the inductor and capacitor adjustments required to achieve this target value. The PID controller employs a proportional-integral-derivative (PID) control strategy, which dynamically calculates the optimal adjustment based on the current, historical cumulative, and trending values ​​of the resonant frequency offset, thus achieving precise tracking control of the resonant frequency.

[0065] The inductance adjustment is calculated using an inductor-based PID controller. The output of the inductor-based PID controller is equal to the weighted sum of the proportional, integral, and derivative terms. The proportional term equals the preset inductor proportional gain coefficient multiplied by the resonant frequency offset; the integral term equals the preset inductor integral gain coefficient multiplied by the cumulative integral value of the resonant frequency offset; and the derivative term equals the preset inductor derivative gain coefficient multiplied by the rate of change of the resonant frequency offset. The default values ​​for the preset inductor proportional gain coefficient are 0.8, the preset inductor integral gain coefficient is 0.2, and the preset inductor derivative gain coefficient is 0.1. These parameters are determined through system identification and optimization to ensure the stability and response speed of the control system. The resonant frequency offset equals the current resonant frequency minus the target resonant frequency value. The cumulative integral value of the resonant frequency offset is the sum of the resonant frequency offsets at all historical sampling times. The rate of change of the resonant frequency offset is the difference between the current and previous resonant frequency offsets divided by the preset sampling period.

[0066] The capacitance adjustment is calculated using a capacitor PID controller. The output of the capacitor PID controller is equal to the weighted sum of the proportional, integral, and derivative terms. The proportional term equals the preset capacitor proportional gain coefficient multiplied by the resonant frequency offset; the integral term equals the preset capacitor integral gain coefficient multiplied by the cumulative integral value of the resonant frequency offset; and the derivative term equals the preset capacitor derivative gain coefficient multiplied by the rate of change of the resonant frequency offset. The default values ​​for the preset capacitor proportional gain coefficient, integral gain coefficient, and derivative gain coefficient are 0.7, 0.15, and 0.08, respectively. These parameters are determined through system simulation analysis and experimental debugging to ensure the accuracy and stability of the capacitance adjustment. The capacitor PID controller uses the same resonant frequency offset, cumulative integral value, and rate of change as the inductor PID controller as its input signals.

[0067] Based on the calculated inductance and capacitance adjustments, the parameter values ​​of the resonant elements after feedforward tuning are determined. The adjustable inductance value after feedforward tuning equals the current adjustable inductance value plus the inductance adjustment, and the adjustable capacitance value after feedforward tuning equals the current adjustable capacitance value plus the capacitance adjustment. To ensure that the adjusted inductance and capacitance values ​​are within a reasonable range, boundary constraint checks are performed on the adjusted parameters. When the adjustable inductance value after feedforward tuning exceeds the preset inductance adjustment range, it is limited to between the preset maximum and minimum inductance values. When the adjustable capacitance value after feedforward tuning exceeds the preset capacitance adjustment range, it is limited to between the preset maximum and minimum capacitance values.

[0068] The resonant frequency after feedforward tuning is calculated based on the adjustable inductance and capacitor values. The resonant frequency after feedforward tuning is equal to half of pi divided by the square root of the product of the adjustable inductance and capacitor values. This calculation is based on the fundamental frequency characteristics of the resonant circuit, achieving precise control of the resonant frequency by adjusting the inductor and capacitor parameters. The resonant frequency after feedforward tuning reflects the optimal operating frequency under the coupling state at a future time, providing an accurate frequency reference for subsequent energy efficiency optimization.

[0069] The resonant frequency after feedforward tuning is used as the input parameter for step 400.

[0070] Step 400: Based on the resonant frequency after feedforward tuning, construct an efficiency optimization function, and solve the efficiency optimization function to obtain the optimal transmit power and operating frequency, as detailed below. Figure 3 As shown.

[0071] Based on the resonant frequency after feedforward tuning in step 300 and the coupling coefficient for future moments predicted in step 200, an optimization function aimed at maximizing transmission efficiency is established through a power transmission optimization controller.

[0072] The goal of the efficiency optimization function is to maximize the comprehensive transmission efficiency index. This index uses transmit power and operating frequency as optimization variables, and describes the impact of three physical mechanisms on transmission efficiency through coupling coefficient influence factors, frequency tuning influence factors, and power transmission influence factors, respectively. The comprehensive transmission efficiency index equals the predicted transmission efficiency minus the resonance offset term and the power loss term. The resonance offset term is calculated by multiplying a preset first weighting coefficient by the square of the resonant frequency offset after feedforward tuning, and the power loss term is calculated by multiplying a preset second weighting coefficient by the absolute value of the system power loss. The predicted transmission efficiency is calculated based on the coupling coefficient, the resonant frequency after feedforward tuning, and the transmit power at future time points, reflecting the expected operating performance at those future time points. The resonant frequency offset after feedforward tuning equals the difference between the resonant frequency after feedforward tuning and the target resonant frequency value; this offset reflects the degree of deviation between the feedforward tuning effect and the ideal state.

[0073] The predicted transmission efficiency is calculated using a multi-factor coupling effect method, comprehensively considering the influence of coupling coefficient, frequency tuning, and transmit power on transmission efficiency. The predicted transmission efficiency equals the preset maximum transmission efficiency multiplied by the coupling coefficient influence factor, then by the frequency tuning influence factor, and finally by the power transmission influence factor. The default value for the preset maximum transmission efficiency is 0.92, determined through theoretical analysis and experimental testing, representing the highest transmission efficiency achievable under ideal conditions. The coupling coefficient influence factor is the ratio of the predicted future coupling coefficient to the preset baseline coupling coefficient, reflecting the degree of influence of changes in magnetic coupling strength on transmission efficiency. The frequency tuning influence factor equals 1 minus the feedforward tuning term, which is the square of the ratio of the resonant frequency offset after feedforward tuning to the preset frequency tuning range; this factor reflects the degree of influence of frequency deviation from the optimal resonant point on transmission efficiency. The power transmission impact factor equals the ratio of the transmit power to the preset optimal transmit power multiplied by a power efficiency correction term. The power efficiency correction term equals 1 minus the power efficiency term, which is the square of the difference between the transmit power and the preset optimal transmit power divided by the square of the preset power adjustment range. This factor reflects the degree to which the transmit power deviates from the optimal operating point affects transmission efficiency. The default value for the preset frequency tuning range is 5000 Hz, representing the maximum allowable frequency deviation range, determined through system stability analysis. The default value for the preset optimal transmit power is 50 watts, obtained through system calibration, representing the optimal transmit power under standard operating conditions. The default value for the preset power adjustment range is 20 watts, representing the maximum allowable power deviation range, determined by the characteristics of the power devices.

[0074] The calculation of system power loss considers the direct impact of transmit power on the loss. System power loss equals transmit power-related loss plus frequency-related loss. Transmit power-related loss equals the square of the transmit power multiplied by a preset power loss coefficient, and frequency-related loss equals the square of the difference between the operating frequency and the target resonant frequency multiplied by a preset frequency loss coefficient. The default value of the preset power loss coefficient is 0.02, determined through system characteristic testing, reflecting the degree of influence of transmit power on system loss. The default value of the preset frequency loss coefficient is 0.01, determined through frequency characteristic analysis, reflecting the degree of influence of frequency offset on system loss.

[0075] The default value of the first weight coefficient is 0.3, and the default value of the second weight coefficient is 0.2. The first and second weight coefficients are determined by a multi-objective optimization algorithm to balance efficiency optimization and frequency stability.

[0076] The optimal transmit power and optimal operating frequency are determined using the gradient ascent method. The optimal transmit power is the sum of the previous optimal transmit power multiplied by a preset power learning rate parameter, and then multiplied by the partial derivatives of the efficiency optimization function with respect to the transmit power. The optimal operating frequency is the sum of the previous optimal operating frequency multiplied by a preset frequency learning rate parameter, and then multiplied by the partial derivatives of the efficiency optimization function with respect to the operating frequency. Simultaneously, the optimal transmit power should be greater than or equal to a preset minimum allowable transmit power, which defaults to 10 watts and is determined based on minimum operating requirements.

[0077] The partial derivative of the comprehensive transmission efficiency index with respect to transmit power is calculated by subtracting the partial derivative of system power loss with respect to transmit power from the partial derivative of predicted transmission efficiency with respect to transmit power. The partial derivative of predicted transmission efficiency with respect to transmit power is calculated using the partial derivative of the power transmission impact factor with respect to transmit power; this partial derivative reflects the direct impact of transmit power variations on transmission efficiency. The partial derivative of the comprehensive transmission efficiency index with respect to operating frequency is calculated by subtracting the partial derivative of system power loss with respect to operating frequency from the partial derivative of predicted transmission efficiency with respect to operating frequency, as well as the partial derivative of the resonant frequency offset penalty term after feedforward tuning with respect to operating frequency.

[0078] The default values ​​for the preset power learning rate parameter are 0.01 and the default value for the preset frequency learning rate parameter are 0.005. These two learning rate parameters were determined through experimentation and debugging to ensure the convergence speed and stability of the algorithm. The optimized optimal transmit power and optimal operating frequency parameters, along with the corresponding predicted transmission efficiency, are then passed to step 500.

[0079] Step 500: Based on the optimal transmission power and the coupling coefficient at future times, calculate the magnetic bearing current, specifically as follows: Figure 4 As shown.

[0080] Based on the optimal transmit power, optimal operating frequency, and predicted transmission efficiency obtained in step 400, and the coupling coefficient predicted in step 200 for future moments, adaptive compensation is required for the magnetic bearing control system to ensure that the energy efficiency optimization of the wireless power supply system does not adversely affect the stable control of the magnetic bearing. Since changes in the operating state of the wireless power supply system directly affect the electromagnetic environment of the magnetic bearing coil, thereby affecting the control accuracy and stability of the magnetic bearing, an adaptive compensation mechanism for the magnetic bearing control parameters that considers changes in the wireless power supply state must be established.

[0081] To achieve coordinated optimization between wireless power supply and magnetic bearing control, an active magnetic bearing control system based on hybrid systems theory is adopted. This active magnetic bearing control system employs a hybrid logic dynamic model, a mathematical framework for describing hybrid systems that can uniformly handle continuous dynamics and discrete events. Hybrid systems are systems that simultaneously include continuous dynamics and discrete events, effectively handling the complex nonlinear characteristics in magnetic bearing control. The system achieves dynamic adjustment of the magnetic bearing control parameters through the collaborative operation of a hybrid system magnetic bearing controller and a parameter adaptive compensator, ensuring stable control performance of the magnetic bearing even when the wireless power supply status changes.

[0082] The adaptive compensation mechanism for the magnetic bearing control parameters is achieved by establishing a discrete-time state equation for the magnetic bearing current. This state equation fully considers the influence of the wireless power supply parameters optimized in step 400 on the magnetic bearing control. The discrete-time state equation for the magnetic bearing current describes the relationship between the magnetic bearing coil current at the next sampling moment and the current state. By using changes in wireless power supply efficiency and coupling coefficient as external disturbance inputs, dynamic compensation for the magnetic bearing control is achieved. The magnetic bearing coil current at the next sampling moment is equal to the sum of four terms. The first term is the preset sampling period divided by the temperature-compensated coil inductance and then multiplied by the control input voltage. This term reflects the direct effect of the control input on the magnetic bearing current. The second term is the negative temperature-compensated coil resistance multiplied by the ratio of the preset sampling period to the temperature-compensated coil inductance and then multiplied by the current magnetic bearing coil current. This term describes the influence of the coil resistance on the current attenuation. The third term is the preset power supply efficiency influence coefficient multiplied by the optimal predicted transmission efficiency at the current moment. This term reflects the influence of the predicted transmission efficiency obtained in step 400 on the magnetic bearing current. The optimal predicted transmission efficiency is the predicted transmission efficiency calculated through the optimal transmission power. The fourth term is the difference between the predicted future coupling coefficient and the real-time coupling coefficient at the current moment multiplied by the preset coupling coefficient influence coefficient. This term reflects the influence of the predicted coupling coefficient change in step 200 on the magnetic bearing control.

[0083] In the parameter settings of the magnetic bearing current state equation, the current magnetic bearing coil current is the magnetic bearing coil current at the k-th sampling time. The default value of the preset sampling period is 1 millisecond, which is determined according to the system control accuracy requirements. The control input voltage is the control input voltage at the k-th sampling time. The default value of the preset power supply efficiency influence coefficient is 0.1. This coefficient is obtained through the system identification method and reflects the influence of changes in wireless power supply efficiency on the magnetic bearing current. The default value of the preset coupling coefficient influence coefficient is 0.05. This coefficient quantifies the degree of influence of changes in the coupling coefficient on the magnetic bearing control. The setting of these influence coefficients ensures that the state changes of the wireless power supply system can be accurately reflected in the magnetic bearing control system, realizing effective coupling between the two subsystems.

[0084] To improve the accuracy and stability of magnetic bearing control, the coil parameters in the state equation require temperature compensation. The temperature compensation mechanism is based on the coil temperature information obtained in step 100, and adjusts the coil resistance and inductance in real time using a temperature correction factor. The temperature-compensated coil resistance is equal to the coil resistance at the preset reference temperature multiplied by one resistance correction factor. The resistance correction factor is equal to the difference between the current coil temperature and the preset reference temperature multiplied by a preset resistance temperature coefficient plus one. The temperature-compensated coil inductance is equal to the coil inductance at the preset reference temperature multiplied by one inductance correction factor. The inductance correction factor is the difference between the current coil temperature and the preset reference temperature multiplied by a preset inductance temperature coefficient plus one. The default value for the preset reference temperature is 25 degrees Celsius, which is the standard ambient temperature. The default value for the coil resistance at the preset reference temperature is 0.5 ohms, and the default value for the coil inductance at the preset reference temperature is 10 millihenries. These parameters are obtained through coil characteristic testing at the preset reference temperature. The default value for the preset temperature coefficient of resistance is 0.0039 degrees Celsius, and the default value for the preset temperature coefficient of inductance is 0.002 degrees Celsius. These two temperature coefficients are obtained through coil material characteristic testing. The temperature compensation mechanism ensures that the magnetic bearing control system maintains stable control performance under different operating temperatures.

[0085] The compensated magnetic bearing current calculated through the aforementioned adaptive compensation mechanism not only considers the basic requirements of traditional magnetic bearing control but also fully integrates the results of wireless power supply efficiency optimization in step 400 and the information from coupling coefficient prediction in step 200, achieving deep coupling and coordinated optimization between wireless power supply and magnetic bearing control. The compensated magnetic bearing current, as an important state variable, will, together with the efficiency optimization results from step 400 and the coupling coefficient prediction information from step 200, provide comprehensive system state information for the multi-objective coordinated decision-making in step 600.

[0086] Step 600: Based on the coupling coefficient at the future time, the resonant frequency after feedforward tuning, the optimal transmission power and operating frequency, and the magnetic bearing current, construct the system stability function and solve for the optimal weighting coefficient of the system stability function.

[0087] After completing the adaptive compensation of the magnetic bearing control parameters in step 500, the compensated magnetic bearing current, taking into account changes in the wireless power supply state, has been obtained. It also possesses the optimal transmit power and optimal operating frequency optimized in step 400, as well as the coupling coefficient predicted in step 200 for future moments. To achieve global coordination between wireless power supply energy efficiency optimization and magnetic bearing stable control, a unified multi-objective coordination decision-making mechanism needs to be established. This mechanism determines the optimal system operation strategy by comprehensively balancing three key objectives: magnetic bearing control performance, wireless power supply transmission efficiency, and overall system stability.

[0088] The core of multi-objective coordinated decision-making lies in constructing a comprehensive cost function that can comprehensively consider the performance requirements of each subsystem. This comprehensive cost function organically integrates the magnetic bearing current state information obtained in step 500, the energy efficiency optimization results in step 400, and the coupling coefficient prediction information in step 200, forming a unified optimization objective. The comprehensive cost function is equal to the sum of three products: the third weighting coefficient multiplied by the magnetic bearing control performance function, the fourth weighting coefficient multiplied by the negative value of the comprehensive transmission efficiency index, and the fifth weighting coefficient multiplied by the system stability function. This multi-objective weighted combination method ensures that the performance requirements of each subsystem are fully reflected in the global optimization.

[0089] The magnetic bearing control performance function directly utilizes the compensated magnetic bearing current calculated in step 500. It quantifies the control performance of the magnetic bearing system by evaluating the magnetic bearing current tracking accuracy and rotor displacement control effect. The magnetic bearing control performance function is equal to the sum of the magnetic shaft terms from the first prediction time to the Nth prediction time. Each magnetic shaft term includes the sum of two parts. The first part is the square of the difference between the preset first weight matrix and the preset magnetic bearing current reference value. This term directly reflects the control effect of the adaptive compensation mechanism in step 500, ensuring stable levitation control of the magnetic bearing under the influence of changes in wireless power supply status by minimizing the current tracking error. The second part is the square of the rotor displacement offset multiplied by the preset second weight matrix. This term reflects the ultimate goal of magnetic bearing control, namely, maintaining stable levitation of the rotor in the ideal position. The control of the rotor displacement offset is directly related to the operational safety and stability of the entire magnetic levitation flywheel system.

[0090] The comprehensive transmission efficiency index directly adopts the one defined in step 400. This index fully considers the impact of the coupling coefficient predicted in step 200 on the transmission efficiency, as well as the effect of the resonant frequency after feedforward tuning in step 300 on the system energy efficiency. By incorporating the energy efficiency optimization results of step 400 into the multi-objective coordinated decision-making framework, it ensures that the transmission efficiency optimization objective of the wireless power supply system is coordinated and unified with the magnetic bearing control requirements, avoiding the problem of simply pursuing energy efficiency optimization while neglecting the stability of the magnetic bearing. Since the optimization objective of the comprehensive cost function is minimization, while the optimization objective of the comprehensive transmission efficiency index is maximization, a negative value of the comprehensive transmission efficiency index is used in the comprehensive cost function to ensure consistency in the optimization direction.

[0091] The system stability function comprehensively considers the impact of resonant frequency stability and coupling coefficient changes on the overall system stability. The system stability function is equal to the sum of system terms from the first prediction time to the Nth prediction time, where each system term is the sum of two key stability indices. The first index is the square of the difference between the feedforward tuned resonant frequency and the target resonant frequency value multiplied by a preset third weight matrix. This index ensures that the effect of feedforward tuning in step 300 is maintained in multi-objective optimization, preventing the system from deviating from the optimal resonant operating point when pursuing other performance objectives. The second index is the square of the difference between the predicted future coupling coefficient and the preset baseline coupling coefficient multiplied by a preset fourth weight matrix. This index directly utilizes the coupling coefficient prediction result from step 200, ensuring stable operation of the system amidst coupling changes caused by high-speed rotor rotation by minimizing the coupling coefficient deviation.

[0092] In the parameter settings of the comprehensive cost function, the default values ​​for the third weighting coefficient are 0.4, the fourth weighting coefficient is 0.35, and the fifth weighting coefficient is 0.25. The sum of the three weighting coefficients equals 1. These weighting coefficients were determined through expert experience and simulation optimization, reflecting the dominant role of the magnetic bearing control performance in the entire system while also considering the importance of energy efficiency optimization and system stability. The prediction time domain length is typically set to 10 to 20 preset sampling periods. This time domain length matches the time range of the coupling coefficient prediction in step 200, ensuring that multi-objective coordinated decision-making can fully utilize future state prediction information. The default values ​​for the preset first weighting matrix are 10 times the identity matrix, the preset second weighting matrix is ​​5 times the identity matrix, the preset third weighting matrix is ​​3 times the identity matrix, and the preset fourth weighting matrix is ​​2 times the identity matrix. These weighting matrices are determined based on control performance requirements and are used to adjust the importance of each performance index. The magnetic bearing current reference value is provided by the rotor position controller.

[0093] To achieve adaptive matching of system performance requirements under different operating conditions, a dynamic determination mechanism for optimal weighting coefficients is needed. Optimal weighting coefficients refer to the best combination of the third, fourth, and fifth weighting coefficients that minimizes the overall cost function under the current system operating conditions. Determining the optimal weighting coefficients requires comprehensive consideration of current magnetic bearing control performance requirements, wireless power supply transmission efficiency requirements, and overall system stability constraints. By dynamically adjusting the allocation ratio of weighting coefficients through real-time evaluation of the performance status and operating condition changes of each subsystem, the system can achieve optimal overall performance under various operating conditions.

[0094] To determine the optimal combination of weight coefficients, a quadratic programming method is used to solve for the optimal weight coefficients. The optimization objective is to minimize the comprehensive cost function, with the constraint that the sum of the third, fourth, and fifth weight coefficients equals 1 and that the third, fourth, and fifth weight coefficients are greater than or equal to 0. This constrained optimization method ensures the rationality and feasibility of the weight coefficients, and simultaneously achieves adaptive matching to the system performance requirements under different operating conditions by dynamically adjusting the weight coefficients.

[0095] The optimal weight coefficients obtained from the solution will serve as important input parameters for the rolling optimization execution in step 700, providing accurate objective function weight configuration for subsequent distributed model predictive control, thereby achieving deep coordinated optimization of wireless power supply resonant tuning and magnetic bearing control.

[0096] Step 700 performs rolling optimization control based on the optimal weights, generating and applying control sequences to adjust the resonant element and the magnetic bearing. The control sequences include a resonant tuning control sequence and a magnetic bearing control sequence.

[0097] Based on the optimal weight coefficient combination obtained from the multi-objective coordinated decision-making in step 600, the system needs to transform the optimization results of the preceding steps into specific real-time control actions. To fully utilize the future coupling coefficients predicted in step 200, the resonant frequency after feedforward tuning in step 300, the optimal transmit power and optimal operating frequency optimized in step 400, and the compensated magnetic bearing current calculated in step 500, a distributed model predictive control strategy is adopted to achieve rolling optimization execution. Distributed model predictive control is a multi-agent coordinated control method that can simultaneously handle the two coupled subsystems of resonant tuning control and magnetic bearing control within a unified optimization framework, ensuring that the control actions of each subsystem not only meet their respective performance requirements but also achieve global coordinated optimization.

[0098] The core of the rolling optimization execution lies in constructing a joint optimization problem including a resonant tuning control sequence and a magnetic bearing control sequence. The resonant tuning control sequence directly addresses the resonant frequency adjustment requirement after feedforward tuning in step 300. Through precise control of the adjustable inductance and capacitor values, it achieves accurate tracking of the optimal operating frequency in step 400. The resonant tuning control sequence includes inductance and capacitor adjustments at various times within the predicted time domain from the current moment. Each adjustment is dynamically adjusted based on the output results of the inductor PID controller and capacitor PID controller in step 300. The magnetic bearing control sequence directly uses the compensated magnetic bearing current calculated in step 500 as a reference trajectory. Through precise control of the magnetic bearing coil voltage, it effectively suppresses rotor displacement deviation. The magnetic bearing control sequence fully considers the coil resistance and inductance parameters after temperature compensation in step 500, as well as the impact of changes in wireless power supply efficiency and coupling coefficient on magnetic bearing control, ensuring that the magnetic bearing maintains stable levitation control performance even under dynamically changing wireless power supply conditions.

[0099] The objective function of the joint optimization problem directly adopts the comprehensive cost function constructed in step 600. This objective function achieves a coordinated balance between the magnetic bearing control performance function, the comprehensive transmission efficiency index, and the system stability function through the optimal combination of the third, fourth, and fifth weighting coefficients. During the rolling optimization process, the magnetic bearing control performance function ensures that the compensated magnetic bearing current can accurately track the magnetic bearing current reference value, while controlling the rotor displacement offset within a safe range. The comprehensive transmission efficiency index ensures that the control action is always adjusted towards the optimal transmission power and optimal operating frequency determined in step 400, maximizing the realization of the predicted transmission efficiency. The system stability function, through constraints on the resonant frequency deviation and coupling coefficient deviation, ensures that it will not deviate from the target resonant frequency after feedforward tuning determined in step 300 during the rolling optimization process, while fully utilizing the coupling coefficient information predicted in step 200 for future moments to proactively address the impact of coupling changes on system stability.

[0100] To ensure the feasibility and safety of rolling optimization, the joint optimization problem needs to meet strict constraints. The resonant tuning control constraints are directly related to the boundary limits of the inductor and capacitor adjustments determined in step 300, ensuring that the adjustable inductor value after feedforward tuning is always between the preset maximum and minimum inductance values, and the adjustable capacitor value after feedforward tuning is always between the preset maximum and minimum capacitance values. These constraints guarantee that the resonant tuning control action will not exceed the physical limitations of the hardware, while maintaining the effectiveness of the feedforward tuning mechanism in step 300. The magnetic bearing control constraints are based on the physical limitations of the magnetic bearing current state equation in step 500, ensuring that the control input voltage will not exceed the rated operating range of the magnetic bearing coil, while ensuring that the rate of change of the compensated magnetic bearing current is within a reasonable range, avoiding system oscillations caused by overly aggressive control actions. The rotor displacement constraints directly serve the safe operation requirements of the magnetic bearing system, ensuring that the rotor remains within the safe range of the magnetic bearing air gap during high-speed rotation by strictly limiting the maximum allowable value of the rotor displacement offset.

[0101] The rolling optimization execution employs a recursive solution strategy. After obtaining the complete control sequence within each control cycle, only the control action at the current moment is executed, including the resonant tuning control input and the magnetic bearing control input at the current moment. The resonant tuning control input directly acts on the resonant tuning controller in step 300, driving the actual adjustment actions of the adjustable inductor and adjustable capacitor to achieve precise control of the resonant frequency after feedforward tuning. The magnetic bearing control input directly acts on the hybrid system magnetic bearing controller in step 500, achieving accurate tracking of the compensated magnetic bearing current through precise adjustment of the magnetic bearing coil voltage. After executing the current control action, the system rolls the time domain forward by one sampling cycle, re-executes the complete process from steps 100 to 700 using the latest acquired system state information, forming a closed-loop rolling optimization control mechanism.

[0102] Through this rolling optimization execution mechanism, the system can fully utilize the coupling coefficient information predicted in step 200 for future moments within each control cycle, ensuring that the resonant tuning control is always based on the latest coupling state prediction for feedforward adjustment. Simultaneously, the optimal transmit power and optimal operating frequency obtained in step 400 are continuously tracked and realized through rolling optimization, ensuring that the transmission efficiency of the wireless power supply system remains at an optimal level. The compensated magnetic bearing current calculated in step 500 is precisely controlled through rolling optimization, ensuring that the magnetic bearing system maintains stable levitation control performance under the influence of dynamic changes in the wireless power supply state. The multi-objective coordination weights determined in step 600 are dynamically applied through rolling optimization, ensuring that the optimal balance between magnetic bearing control performance, wireless power supply transmission efficiency, and overall system stability can be achieved under different operating conditions. The entire rolling optimization execution process realizes a complete closed loop from coupling state prediction to control action execution, effectively solving the deep coupling problem between wireless power supply and magnetic bearing control in a high-speed rotating magnetic levitation flywheel system, providing a reliable guarantee for the safe and stable operation of the system.

[0103] Example 2:

[0104] This embodiment further optimizes the accuracy and real-time performance of the dynamic coupling state prediction model based on Embodiment 1. For ultra-high-speed magnetic levitation flywheel systems with rotational speeds exceeding 50,000 revolutions per minute, an adaptive prediction algorithm based on machine learning is adopted to improve the accuracy of coupling coefficient prediction.

[0105] Building upon step 200, a learning mechanism based on historical data is added. By collecting long-term operational data, the system establishes a deep learning model of coupling coefficient changes, enabling more accurate prediction of coupling state changes under complex operating conditions. The prediction model employs a long short-term memory network structure, with inputs including historical coupling coefficient sequences, rotor angular velocity sequences, and displacement offset sequences, and outputs predicted coupling coefficient values ​​for multiple future time points.

[0106] The Long Short-Term Memory (LSTM) network structure consists of an input layer, hidden layers, and an output layer. The default number of neurons in the input layer is 20, corresponding to the length of the historical data time window. The default number of neurons in the hidden layer is 50, a value determined through network performance optimization. The default number of neurons in the output layer is 10, corresponding to the number of future prediction moments. Network training uses the backpropagation algorithm, with a default learning rate of 0.001 and a default number of training epochs of 1000. These parameters are determined using cross-validation.

[0107] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A method for magnetic bearing wireless power supply resonance tuning and energy efficiency optimization, characterized in that, The method comprises: obtaining a magnetic bearing parameter through a real-time monitoring system; based on the magnetic bearing parameter, a dynamic prediction model is established, which calculates a coupling coefficient at a future time; based on the coupling coefficient at the future time, a resonant frequency feedforward tuning is performed to obtain a resonant frequency after feedforward tuning; the resonant frequency feedforward tuning comprises: calculating a resonant frequency target value based on the coupling coefficient at the future time, the resonant frequency target value being a preset reference resonant frequency multiplied by the square root of a coupling coefficient compensation factor, the coupling coefficient compensation factor being the ratio of the coupling coefficient at the future time to a current coupling coefficient; based on the resonant frequency target value, calculating the required inductance and capacitance adjustment amount; based on the inductance and capacitance adjustment amount, determining the adjustable inductance value and the adjustable capacitance value after feedforward tuning, the adjustable inductance value after feedforward tuning being the current adjustable inductance value plus the inductance adjustment amount, and the adjustable capacitance value after feedforward tuning being the current adjustable capacitance value plus the capacitance adjustment amount; based on the adjustable inductance value and the adjustable capacitance value after feedforward tuning, calculating the resonant frequency after feedforward tuning, the resonant frequency after feedforward tuning being one-half divided by pi, and then divided by the square root of the product of the adjustable inductance value after feedforward tuning and the adjustable capacitance value after feedforward tuning; based on the resonant frequency after feedforward tuning, constructing an efficiency optimization function, and solving the efficiency optimization function to obtain an optimal transmit power and a working frequency; based on the optimal transmit power and the coupling coefficient at the future time, calculating a magnetic bearing current; based on the coupling coefficient at the future time, the resonant frequency after feedforward tuning, the optimal transmit power and the working frequency, and the magnetic bearing current, constructing a system stability function, and solving the optimal weight coefficient of the system stability function; based on the optimal weight, performing a rolling optimization control to generate and apply a control sequence to adjust the resonant element and the magnetic bearing.

2. The magnetic bearing wireless power supply resonance tuning and energy efficiency optimization method of claim 1, wherein, The calculation of the required inductance and capacitance adjustment amount comprises: calculating the inductance adjustment amount through an inductance PID controller, the proportional term of the inductance PID controller being a preset inductance proportional gain coefficient multiplied by a resonant frequency offset, the integral term being a preset inductance integral gain coefficient multiplied by the cumulative integral value of the resonant frequency offset, and the differential term being a preset inductance differential gain coefficient multiplied by the rate of change of the resonant frequency offset; wherein the resonant frequency offset is the current resonant frequency minus the resonant frequency target value, the cumulative integral value of the resonant frequency offset is the sum of the resonant frequency offsets at each sampling time in history, and the rate of change of the resonant frequency offset is the difference between the resonant frequency offset at the current time and the resonant frequency offset at the previous time divided by a preset sampling period; calculating the capacitance adjustment amount through a capacitance PID controller, the proportional term of the capacitance PID controller being a preset capacitance proportional gain coefficient multiplied by the resonant frequency offset, the integral term being a preset capacitance integral gain coefficient multiplied by the cumulative integral value of the resonant frequency offset, and the differential term being a preset capacitance differential gain coefficient multiplied by the rate of change of the resonant frequency offset.

3. The magnetic bearing wireless power supply resonance tuning and energy efficiency optimization method of claim 1, wherein, The future time coupling coefficient comprises coupling coefficients of multiple prediction times, the coupling coefficient of a prediction time is a preset reference coupling coefficient multiplied by a correction term, the correction term is a sum of a first constant term, a first periodic term and a second periodic term, the first periodic term is a preset first coupling variation amplitude coefficient multiplied by a cosine function, an argument of the cosine function is a product of a rotor angular velocity and the prediction time, and then a preset first phase angle is added, the second periodic term is a preset second coupling variation amplitude coefficient multiplied by a sine function, an argument of the sine function is a product of twice the rotor angular velocity and the prediction time, and then a preset second phase angle is added; wherein the prediction time is a current time plus a prediction time step, the prediction time step is an integer multiple of a preset sampling period.

4. The magnetic bearing wireless power supply resonance tuning and energy efficiency optimization method of claim 1, wherein, Solving the efficiency optimization function to obtain the optimal transmission power and working frequency comprises: The efficiency optimization function aims to maximize a transmission efficiency comprehensive index; the transmission efficiency comprehensive index is a predicted transmission efficiency minus a resonance deviation term and then minus a power loss term, the resonance deviation term is a preset first weight coefficient multiplied by a square of a resonance frequency deviation after feedforward tuning, the power loss term is a preset second weight coefficient multiplied by an absolute value of a system power loss; wherein the resonance frequency deviation after feedforward tuning is equal to a difference between a resonance frequency after feedforward tuning and a resonance frequency target value; the system power loss is a transmission power related loss plus a frequency related loss, the transmission power related loss is a square of the transmission power multiplied by a preset power loss coefficient, the frequency related loss is a square of a difference between the working frequency and the resonance frequency target value multiplied by a preset frequency loss coefficient; The efficiency optimization function is solved by a gradient ascent method; wherein the optimal transmission power is the optimal transmission power at a previous time multiplied by a preset power learning rate parameter, and then multiplied by a sum of partial derivatives of the efficiency optimization function with respect to the transmission power, the optimal working frequency is the optimal working frequency at the previous time multiplied by a preset frequency learning rate parameter, and then multiplied by a sum of partial derivatives of the efficiency optimization function with respect to the working frequency.

5. The magnetic bearing wireless power supply resonance tuning and energy efficiency optimization method of claim 4, wherein, The predicted transmission efficiency is equal to a product of a preset maximum transmission efficiency, a coupling coefficient influence factor, a frequency tuning influence factor and a power transmission influence factor; The coupling coefficient influence factor is a ratio of the future time coupling coefficient to a preset reference coupling coefficient, the frequency tuning influence factor is equal to 1 minus a feedforward tuning term, the feedforward tuning term is a square of a ratio of the resonance frequency deviation after feedforward tuning to a preset frequency tuning range, the power transmission influence factor is a ratio of the transmission power to a preset optimal transmission power multiplied by a power efficiency correction term, the power efficiency correction term is 1 minus a power efficiency term, the power efficiency term is a square of a difference between the transmission power and the preset optimal transmission power divided by a square of a preset power adjustment range.

6. The magnetic bearing wireless power supply resonance tuning and energy efficiency optimization method of claim 1, wherein, The calculation of the magnetic bearing current comprises: The magnetic bearing coil current at the next sampling time is preset sampling period divided by the temperature-compensated coil inductance, multiplied by the control input voltage, multiplied by the negative temperature-compensated coil resistance, multiplied by the ratio of the preset sampling period to the temperature-compensated coil inductance, multiplied by the current magnetic bearing coil current, multiplied by the preset power supply efficiency influence coefficient, multiplied by the optimal predicted transmission efficiency at the current time, multiplied by the difference between the future time coupling coefficient and the current real-time coupling coefficient, multiplied by the preset coupling coefficient influence coefficient; wherein the optimal predicted transmission efficiency is the predicted transmission efficiency calculated by the optimal transmission power; the temperature-compensated coil inductance is the coil inductance at the preset reference temperature multiplied by the inductance correction factor, the inductance correction factor is the difference between the current coil temperature and the preset reference temperature multiplied by the preset inductance temperature coefficient plus 1, and the temperature-compensated coil resistance is the coil resistance at the preset reference temperature multiplied by the resistance correction factor, the resistance correction factor is the difference between the current coil temperature and the preset reference temperature multiplied by the preset resistance temperature coefficient plus 1.

7. The magnetic bearing wireless power supply resonance tuning and energy efficiency optimization method of claim 1, wherein, The comprehensive cost function is the sum of the product of the third weight coefficient multiplied by the magnetic bearing control performance function, the fourth weight coefficient multiplied by the negative value of the transmission efficiency comprehensive index, and the fifth weight coefficient multiplied by the system stability function; The optimal weight coefficient is solved by the quadratic programming method, the optimization objective is to minimize the comprehensive cost function, and the constraint condition is that the sum of the third weight coefficient, the fourth weight coefficient and the fifth weight coefficient is equal to 1 and the third weight coefficient, the fourth weight coefficient and the fifth weight coefficient are greater than or equal to 0; wherein the optimal weight coefficient is the third weight coefficient, the fourth weight coefficient and the fifth weight coefficient that make the comprehensive cost function reach the minimum value.

8. The magnetic bearing wireless power supply resonance tuning and energy efficiency optimization method of claim 7, wherein, The magnetic bearing control performance function is equal to the sum of the magnetic shaft terms from the 1st prediction time to the Nth prediction time, and the magnetic shaft term is the square of the difference between the magnetic bearing current and the preset magnetic bearing current reference value multiplied by the preset first weight matrix, the square of the rotor displacement offset multiplied by the preset second weight matrix; The system stability function is the sum of the system terms from the 1st prediction time to the Nth prediction time, and the system term is: the product of the square of the difference between the feedforward tuned resonance frequency and the resonance frequency target value and the preset third weight matrix, and the product of the square of the difference between the predicted future time coupling coefficient and the preset reference coupling coefficient and the preset fourth weight matrix, and the sum of the two products.

9. The magnetic bearing wireless power supply resonance tuning and energy efficiency optimization method of claim 1, wherein, The magnetic bearing parameters include real-time coupling coefficient, resonance frequency offset, transmission power, magnetic bearing coil current and voltage, rotor displacement offset, rotor angular velocity and coil parameter change amount, wherein the transmission efficiency is the ratio of the load power to the input power, the rotor displacement offset includes horizontal and vertical displacement offsets and rotor angular velocity, and the coil parameter change amount includes resistance change amount and inductance change amount, and coil temperature.

Images