A low-power variable bias current control method for high-speed magnetic levitation bearing

Abstract

The application discloses a low-power variable bias current control method of a high-speed magnetic suspension bearing and belongs to the field of low-power control of a high-speed magnetic suspension bearing-rotor system, and comprises the following steps: S1, providing bottom model support for PID control and current optimization control; S2, completing parameter setting of a PID controller; S3, constructing a collaborative control system composed of the PID controller and a bias current adjusting controller; the bias current adjusting controller dynamically sets bias currents in a speed-up stage and a stable rotation stage based on state signals of rotation speeds and vibration displacements in the speed-up stage and the stable rotation stage, and obtains optimal bias current parameters. The low-power variable bias current control method of the high-speed magnetic suspension bearing realizes power consumption optimization for different working states under the premise of ensuring system stability and dynamic stiffness.

Description

Technical Field

[0001] This invention relates to the field of low-power control technology for high-speed magnetic levitation bearing-rotor systems, and in particular to a low-power variable bias current control method for high-speed magnetic levitation bearings. Background Technology

[0002] In the field of high-speed rotating machinery, magnetic levitation bearings, while demonstrating great application potential due to their advantages such as non-contact, frictionless operation, high speed, and long lifespan, are limited in their large-scale industrial application by consideration of power consumption. The power consumption of magnetic levitation bearings mainly comes from the copper loss of the electromagnetic coil and the hysteresis and eddy current losses of the iron core. Among these, the copper loss caused by the bias current continuously supplied to the coil to generate the levitation magnetic field constitutes the main body of the system power consumption.

[0003] To overcome the bottleneck of high losses mentioned above, existing research mainly focuses on the following three aspects: The first is the use of permanent magnet bias hybrid magnetic levitation bearing technology, which utilizes high-performance permanent magnets to provide a static bias magnetic field, thereby significantly reducing the steady-state current in the coil. However, the permanent magnets introduced may demagnetize at high temperatures, and the complexity and cost of the system are increased. The second is the optimization of electromagnetic design, using low-loss soft magnetic materials to reduce iron losses and optimizing coil design to reduce resistance. However, this faces the problems of high cost and difficult processing. The third is the improvement of control strategies and power amplifiers, using high-efficiency switching power amplifiers based on PWM to replace linear power amplifiers and introducing advanced control algorithms to optimize energy distribution. The algorithms of advanced control strategies are complex and have high requirements for processor performance. The stability and universality of their energy-saving effects need to be further improved. Summary of the Invention

[0004] The purpose of this invention is to provide a low-power variable bias current control method for high-speed magnetic levitation bearings, thereby solving the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention provides a low-power variable bias current control method for high-speed magnetic levitation bearings, comprising the following steps: S1. The overall kinematic equation of the magnetic levitation bearing-rotor system is derived through mechanical analysis, and the kinematic equation is mathematically transformed and the state space equation is derived, providing a mathematical calculation model for PID control and bias current optimization control. S2. Based on the state-space equation in step S1, extract the characteristic parameters used to tune the PID controller parameters; simplify the magnetic bearing-rotor system into a mass-spring-damping system and obtain the differential equation, associate the characteristic parameters extracted from the state-space equation, and derive the proportional gain, derivative gain, and integral gain of the PID controller that meet the stability requirements of the magnetic bearing-rotor system, thus completing the parameter tuning. S3. Construct a collaborative control system consisting of a PID controller and a bias current regulating controller. The PID controller uses the PID controller parameters derived in step S2 to output the control current in real time to maintain the rotor suspended at the preset balance position. The bias current regulator dynamically sets the bias current based on the speed and vibration displacement status signals during the acceleration and stable rotation phases, obtaining the optimal bias current parameters to optimize power consumption while ensuring the stability of the magnetic levitation bearing-rotor system.

[0006] Preferably, step S1 specifically includes the following steps: S11. Based on the force and motion relationship of the rotor during translation and rotation, determine the unbalanced force on the rotor. , The algorithm formula is: ; in, This refers to the rotor speed; 0 represents unbalanced mass; It is the eccentricity; This is the initial phase; For time; S12. Combining the multi-degree-of-freedom dynamic model of the magnetic bearing-rotor system, the magnetic bearing-rotor system under unbalanced forces is obtained. The kinematic equations under excitation are given by the formula: ; in, This refers to the total weight of the rotor; For the rotor's center of mass in Acceleration in the direction of; For the rotor's center of mass in Acceleration in the direction of; For magnetic levitation bearing A in Electromagnetic force generated in the axial direction; For magnetic levitation bearing B in Electromagnetic force generated in the axial direction; For magnetic levitation bearing A in Electromagnetic force generated in the axial direction; For magnetic levitation bearing B in Electromagnetic force generated in the axial direction; For the unbalanced force acting on the rotor Components along the axial direction; For the unbalanced force acting on the rotor Components along the axial direction; For the rotor to wind around it Moment of inertia of the shaft; For the rotor to wind around it Moment of inertia of the shaft; For the rotor to wind around it Moment of inertia of the shaft; For rotor winding Angular acceleration of the axis; For rotor winding Angular acceleration of the axis; For rotor winding Angular velocity of the axis; Rotor winding Angular velocity of the axis; , Let be the distance from the center of magnetic bearings A and B to the rotor's center of mass; S13. Based on the parameters from step S12, the state vector is composed. Taking the control current at the magnetic bearing as the system input and the rotor displacement as the system output, the state-space expression of the magnetic bearing-rotor system under the influence of unbalanced force is obtained as follows: ; in, To fully describe the internal state of the system, the state vector includes the rotor's displacement, velocity, and angular velocity from step S12. Represents the state vector The first derivative of reflects the rate of change of the state vector with time; For the system matrix; The input matrix; This refers to the control current for the magnetic levitation bearing. This refers to the rotor displacement at the magnetic levitation bearing or sensor. This is the displacement output matrix for the magnetic levitation bearing. This is a direct transmission matrix.

[0007] Preferably, the characteristic parameters of the magnetic levitation bearing-rotor system in step S2 include the displacement stiffness coefficient. Current stiffness coefficient Equivalent quality and damping ratio .

[0008] Preferably, step S2 specifically includes the following steps: S21. Based on the state-space equations of step S1, extract the displacement stiffness coefficients. Current stiffness coefficient Equivalent quality and damping ratio ; S22. The magnetic bearing suspends the rotor via electromagnetic force, providing elastic support without mechanical contact. This simplifies the magnetic bearing-rotor system to a mass-spring-damping system, yielding the following differential equation: ; in, The mass of the rotor; This is the acceleration of the rotor's center of mass in a certain direction; The equivalent damping coefficient that hinders rotor motion; The velocity of the rotor's center of mass in a certain direction; This is the equivalent spring stiffness coefficient; It represents the displacement of the rotor's center of mass relative to its equilibrium position in a certain direction; The external force acting on the rotor; S23. Adjust the proportional gain of the PID controller. Integral gain Differential gain Incorporating the differential equation from step S22 and performing a Laplace transform, we obtain its frequency domain expression: ; S24. Based on the Routh criterion, the frequency domain expression of step S23 is derived to obtain the expression for the range of values ​​of the PID control parameters as follows: ; in, The proportional gain of the PID controller; For adjustment coefficients; This is the displacement stiffness coefficient; This is the current stiffness coefficient; ; in, The derivative gain of the PID controller; The damping ratio; This is the equivalent stiffness coefficient; For equivalent quality; ; in, The integral gain of the PID controller; S25. Based on the parameter range of the Routh criterion in step S24, and combined with the dynamic performance requirements of the magnetic levitation bearing-rotor system, determine the proportional gain. Differential gain and integral gain This completes the parameter tuning of the PID controller.

[0009] Preferably, in step S3, during the acceleration phase, the rotational speed data of the magnetic bearing-rotor system is collected, and the optimal bias current value corresponding to multiple rotational speed ranges is preset to achieve the initial allocation of bias current based on rotational speed; during the stable rotation phase, when the magnetic bearing-rotor system stabilizes at the target rotational speed based on the acceleration phase, the bias current is adaptively adjusted by monitoring the unbalanced force and displacement caused by disturbances on the rotor through sensors.

[0010] Preferably, in step S3, when the rotor speed is in the dynamic range from standstill to rated operating speed, it is determined to be the speed-up stage; when the speed is stable at the target operating speed and the vibration displacement is not greater than the maximum allowable radial displacement of the rotor, it is determined to be the stable rotation stage.

[0011] Preferably, based on the acceleration phase in step S3, under the conditions of minimum current requirement for safe displacement and maximum current limit for power consumption optimization, the expression for the bias current setting value is derived as follows: ; in, The proportional gain of the PID controller; This represents the maximum permissible radial displacement of the rotor. The bias current is based on different speed ranges; This is the maximum bias current; The speed range division rules and corresponding bias current values ​​are written into the collaborative control system. The monitoring module provides real-time feedback of speed data, generates a matching signal between the monitored speed data and the speed range, and transmits the matching signal to the collaborative control system, enabling the collaborative control system to switch the bias current value and complete the initial allocation of bias current across the entire speed range.

[0012] Preferably, during the stable rotation stage in step S3, the bias current value is determined by the operating stability conditions and operating power consumption of the magnetic levitation bearing-rotor system. Based on the operational stability constraints of the magnetic levitation bearing-rotor system, and taking into account the linear characteristic of electromagnetic force changing with bias current, the formula for calculating the minimum bias current is derived: ; in, Equivalent stiffness; This represents the real-time vibration displacement of the rotor after it is disturbed. The minimum bias current under stable operating conditions; This is the maximum allowable bias current of the system; , The structural parameters are expressed as follows: ; in, The permeability of free space is approximately 4π × 10⁻⁶. -7 H / m; This is the effective cross-sectional area of ​​the magnetic core; This refers to the number of coil turns. θ is the angular coefficient of the magnetic field distribution; g is the clearance distance between the rotor and the stator. Based on the power consumption characteristics of the magnetic bearing-rotor system, copper loss is a core component of the system's operating power consumption. The bias current is determined based on the copper loss value. The copper loss calculation formula is as follows: ; in, For copper loss; The coil resistance; Given the coil current and the differential control used in the magnetic levitation bearing, the upper magnetic pole coil current is... The current in the lower magnetic pole coil is , To control the current, control the current To counteract displacement disturbances, the control current is derived based on the electromagnetic force formula. Substituting into the copper loss calculation formula, we get: ; Based on the copper loss calculation formula, copper loss Regarding bias current The function, for Find the first derivative and set it to 0. Then, find the extreme values ​​to obtain the formula for the minimum bias current at which the copper loss is minimal: ; Obtain the minimum bias current under stable operating conditions. Minimum bias current under operating power consumption constraints intersection To simultaneously satisfy both operational stability and power consumption constraints within a given current range, the equation for the minimum bias current range is obtained as follows: ; in, This is the final bias current; This is the bias current when the rotational speed is stable. The displacement of the rotor after it is disturbed; The threshold value for vibration displacement; Minimum bias current based on system power consumption constraints and minimum bias current at minimum copper loss The minimum value of the intersection of the two; The vibration displacement of the rotor is collected in real time by sensors, and the data is substituted into the adaptive allocation method formula to dynamically calculate the current bias current value that needs to be adjusted.

[0013] Preferably, step S3 is followed by step S4: Using the theoretical copper loss formula for magnetic levitation bearing coils, the theoretical copper loss of the segmented variable bias strategy and the adaptive variable bias strategy used in step S3 is first calculated and verified. Then, this theoretical copper loss is compared with the theoretical copper loss obtained using the fixed bias current strategy. The theoretical copper loss calculation formula is as follows: ; in, This indicates the copper loss power of the magnetic levitation bearing coil; It is the resistance of the coil; , This represents the time interval for calculating copper loss.

[0014] Therefore, the present invention employs the above-mentioned low-power variable bias current control method for high-speed magnetic levitation bearings, which has the following beneficial effects: 1. By identifying the speed in real time, the optimal bias current is switched between different speed ranges to achieve initial current distribution across the entire speed range, taking into account both stability and low power consumption during dynamic stages. On the one hand, the high current at low speeds improves the equivalent stiffness of the system and pushes up the resonant speed, avoiding excessive rotor amplitude during speed increase. On the other hand, switching to low current at high speeds can significantly reduce copper losses during start-up, shutdown, and speed change stages. Compared with the fixed high bias current strategy, this solves the contradiction between the traditional fixed current strategy of instability at low speeds and high power consumption at high speeds.

[0015] 2. After the system stabilizes at the target speed, the minimum bias current formula is derived based on real-time disturbances. The intersection of the minimum power consumption constraint current and the minimum copper loss current is taken, and the bias current is dynamically adjusted. This achieves the optimal balance between stability and energy saving under steady-state conditions. It can accurately match the real-time disturbance state of the system. That is, when the rotor experiences vibration displacement exceeding the threshold due to unbalanced disturbances, the bias current is dynamically increased to expand the linear control range of electromagnetic force, quickly suppressing displacement fluctuations and ensuring system stability. When the disturbance subsides, it can automatically return to low bias current operation, avoiding the power waste caused by fixed high bias current. Compared with the fixed bias current strategy, it achieves precise optimization of operating point power consumption, breaking through the bottleneck of the traditional fixed bias current strategy of high power consumption for stability and instability for energy saving.

[0016] 3. By constructing a collaborative control system and jointly controlling the magnetic levitation bearing system with the active controller and the bias current regulating controller, a seamless connection between dynamic acceleration and steady-state operation throughout the entire cycle is achieved. The active controller strengthens the stability foundation, while the bias current regulating controller precisely optimizes power consumption, ultimately significantly reducing copper losses under all operating conditions of the system. At the same time, it also meets the stability, disturbance rejection and low power consumption requirements of the high-speed magnetic levitation bearing system.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is the overall control block diagram of a low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 2 This is a block diagram of the bias current distribution control based on rotational speed for a low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 3 This is an adaptive variable bias current distribution control block diagram of a low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 4 This is a schematic diagram comparing the rotor amplitude variation based on rotational speed in a low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 5 This is a schematic diagram comparing the control current changes based on rotational speed in a low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 6 This is a schematic diagram illustrating the change of rotor axial displacement over time when a fixed bias current (2A) strategy is adopted in the low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 7 This is a schematic diagram illustrating the change of rotor axial displacement over time when a fixed bias current (4A) strategy is used in the low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 8 This is a schematic diagram illustrating the change of rotor axial displacement over time when an adaptive variable bias current distribution strategy is adopted in the low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 9 This is a schematic diagram illustrating the change of system control current over time when a fixed bias current (2A) strategy is adopted in the low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 10 This is a schematic diagram illustrating the change of system control current over time when a fixed bias current (4A) strategy is adopted in the low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 11 This is a schematic diagram illustrating the change of system control current over time when an adaptive variable bias current allocation strategy is adopted in the low-power variable bias current control method for a high-speed magnetic levitation bearing according to the present invention. Figure 12 This is a schematic diagram of the current distribution strategy of a high-speed magnetic levitation bearing during its entire operating cycle, based on the low-power variable bias current control method for a high-speed magnetic levitation bearing of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0020] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0021] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0022] like Figure 1 The figure shown is the overall control block diagram of a low-power variable bias current control method for a high-speed magnetic levitation bearing. , , and This is an external input to the system, representing the given suspension position at the rotor bearing. , , and This is the external output of the system, representing the four vibration displacements at the rotor sensor. , , and Four current inputs for the magnetic levitation bearing; For use in controlling the bias current of the magnetic levitation bearing system; For unbalanced excitation; PID is a proportional-integral-derivative controller; A is an adaptive variable bias current distribution strategy; B is a speed-based current distribution strategy. like Figures 2-12 As shown, a low-power variable bias current control method for a high-speed magnetic levitation bearing includes the following steps: S1. The overall kinematic equation of the magnetic levitation bearing-rotor system is derived through mechanical analysis, and the state-space equation is extracted from the mathematical transformation of the kinematic equation, providing a mathematical calculation model for PID control and bias current optimization control. Step S1 specifically includes the following steps: S11. Based on the force and motion relationship of the rotor during translation and rotation, determine the unbalanced force on the rotor. , The algorithm formula is: ; in, This refers to the rotor speed; Unbalanced mass; It is the eccentricity; This is the initial phase; For time; S12. Based on the multi-degree-of-freedom dynamic model of the magnetic bearing-rotor system, the kinematic equations of the magnetic bearing-rotor system under unbalanced force excitation, including translation and rotation, are as follows: ; The translation equation is: ; The equation of rotation is: ; in, This refers to the total weight of the rotor; For the rotor's center of mass in Acceleration in the direction of; For the rotor's center of mass in Acceleration in the direction of; For magnetic levitation bearing A in Electromagnetic force generated in the axial direction; For magnetic levitation bearing B in Electromagnetic force generated in the axial direction; For magnetic levitation bearing A in Electromagnetic force generated in the axial direction; For magnetic levitation bearing B in Electromagnetic force generated in the axial direction; For the unbalanced force acting on the rotor Components along the axial direction; For the unbalanced force acting on the rotor Components along the axial direction; For the rotor to wind around it Moment of inertia of the shaft; For the rotor to wind around it Moment of inertia of the shaft; For the rotor to wind around it Moment of inertia of the shaft; For rotor winding Angular acceleration of the axis; For rotor winding Angular acceleration of the axis; For rotor winding Angular velocity of the axis; Rotor winding Angular velocity of the axis; , Let be the distance from the center of magnetic bearings A and B to the rotor's center of mass; S13. Based on the parameters from step S12, the state vector is composed. Taking the control current at the magnetic bearing as the system input and the rotor displacement as the system output, the state-space expression of the magnetic bearing-rotor system under the influence of unbalanced force is obtained as follows: ; in, To fully describe the internal state of the system, the state vector includes the rotor's displacement, velocity, and angular velocity from step S12. The first derivative of the state vector represents the rate of change of the state vector over time. For the system matrix; The input matrix; This refers to the control current for the magnetic levitation bearing. This refers to the rotor displacement at the magnetic levitation bearing or sensor. This is the displacement output matrix for the magnetic levitation bearing. For direct transmission matrix; Specifically, the state-space expression above can be transformed to obtain the following matrix expression: ; in, State vector The first derivative; This represents the displacement state of the magnetic levitation bearing rotor. The first derivative of the displacement, i.e., the velocity state, is used to fully describe the dynamic state of the system; ; The above equation is the system matrix, where, It is a 4×4 zero matrix. It is a 4×4 identity matrix. and The coefficient matrix, which describes the internal state evolution of the system, determines the state vector. Its own dynamic change characteristics; ; The above formula is the input matrix. It is a 4×4 zero matrix. The coefficient matrix represents the relationship between inputs and states, used to characterize external inputs, such as control current, on the system state vector. The relationship of action; ; The above formula is the output matrix. It is a 4×4 identity matrix. It is a 4×4 zero matrix used to represent the internal state vector of the system. The mapping is represented by an output signal, reflecting the transition relationship from state to output; ; The above formula is the direct transmission matrix, which is A zero matrix indicates that the input has no direct transmission effect on the output, and the output is only indirectly affected by the input through the state.

[0023] S2. Based on the state-space equation in step S1, extract the characteristic parameters used to tune the PID controller parameters; simplify the magnetic bearing-rotor system into a mass-spring-damping system and obtain the differential equation, associate the characteristic parameters extracted from the state-space equation, and derive the proportional gain, derivative gain, and integral gain of the PID controller that meet the stability requirements of the magnetic bearing-rotor system, thus completing the parameter tuning. The characteristic parameters of the magnetic levitation bearing-rotor system in step S2 include the displacement stiffness coefficient. Current stiffness coefficient Equivalent quality and damping ratio ; Step S2 specifically includes the following steps: S21. Based on the state-space equations of step S1, extract the displacement stiffness coefficients. Current stiffness coefficient Equivalent quality and damping ratio ; S22. The magnetic bearing suspends the rotor via electromagnetic force, providing elastic support without mechanical contact. This simplifies the magnetic bearing-rotor system to a mass-spring-damping system, yielding the following differential equation: ; in, The mass of the rotor; This is the acceleration of the rotor's center of mass in a certain direction; The equivalent damping coefficient that hinders rotor motion; The velocity of the rotor's center of mass in a certain direction; This is the equivalent spring stiffness coefficient; It represents the displacement of the rotor's center of mass relative to its equilibrium position in a certain direction; The external force acting on the rotor; S23. Adjust the proportional gain of the PID controller. Integral gain Differential gain Incorporating the differential equation from step S22 and performing a Laplace transform, we obtain its frequency domain expression: ; S24. Based on the Routh criterion, the frequency domain expression of step S23 is further derived to obtain the expression for the range of values ​​of the PID control parameters: ; in, The proportional gain of the PID controller is used to adjust the speed and magnitude of the system's response to deviations. For adjustment coefficients; This is the displacement stiffness coefficient; This is the current stiffness coefficient; ; in, The derivative gain of the PID controller is used to predict the changing trend of system deviation and correct the deviation in advance. The damping ratio; This is the equivalent stiffness coefficient; For equivalent quality; ; in, The integral gain of the PID controller is used to eliminate the steady-state error of the system. S25. Based on the parameter range of the Routh criterion in step S24, and combined with the dynamic performance requirements of the magnetic levitation bearing-rotor system, determine the proportional gain. Differential gain and integral gain This completes the parameter tuning of the PID controller; S3, such as Figure 1 As shown, a collaborative control system consisting of a PID controller and a bias current regulating controller is constructed. The PID controller outputs the control current in real time using the PID controller parameters derived in step S2 to maintain the rotor's suspension at the preset equilibrium position. The bias current regulating controller dynamically sets the bias current in the acceleration phase and the stable rotation phase based on the state signals of the rotation speed and vibration displacement during the acceleration phase and the stable rotation phase, thereby obtaining the optimal bias current parameters to optimize power consumption while ensuring the stability of the magnetic levitation bearing-rotor system.

[0024] In step S3, as Figure 2 As shown, during the acceleration phase, the rotational speed data of the magnetic levitation bearing-rotor system is collected, and optimal bias current values ​​corresponding to multiple rotational speed ranges are preset to achieve preliminary allocation of bias current based on rotational speed; as shown... Figure 3As shown, during the stable rotation phase, when the magnetic levitation bearing-rotor system based on the acceleration phase stabilizes at the target speed, the bias current is adaptively adjusted by monitoring the unbalanced force and displacement caused by disturbances on the rotor through sensors.

[0025] In step S3, when the rotor speed is in the dynamic range from standstill to rated operating speed, it is determined to be the speed-up stage; when the speed is stable at the target operating speed and the vibration displacement is not greater than the maximum allowable radial displacement of the rotor, it is determined to be the stable rotation stage.

[0026] Based on the acceleration phase in step S3, and under the conditions of minimum current requirement for safe displacement and maximum current limit for power consumption optimization, the expression for the bias current setpoint is derived: ; in, The proportional gain of the PID controller; This represents the maximum permissible radial displacement of the rotor. The bias current is based on different speed ranges; This is the maximum bias current; The speed range division rules and corresponding bias current values ​​are written into the control system. The monitoring module provides real-time feedback of speed data, generates a matching signal between the monitored speed data and the speed range, and transmits the matching signal to the control system, so that the control system switches the bias current value to complete the initial allocation of bias current across the entire speed range. See Figure 2 and Figure 4 As shown, the bias current is initially allocated based on the rotational speed. In the low-speed range, a high bias current is applied, such as... The system is configured with appropriate PID parameters to improve equivalent stiffness and damping, thereby increasing the system's resonant speed and providing sufficient safety margin for low-speed acceleration. When the speed approaches the resonance risk zone under this high stiffness, the bias current is strategically switched to a low level, i.e., as shown below. Figure 2 During the switching of bias current, when the rotor speed is below 2450 rpm / min, a high bias current of 4A is used to control the rotor speed increase. After the rotor speed smoothly transitions, a lower bias current is used. The low bias current controls the rotor speed to reach the operating speed; See Figure 4 and Figure 5 As shown, by comparing the rotor amplitude and control current changes with a fixed bias current and a speed-based bias current segmented allocation strategy, the technical effectiveness of the speed-based bias current segmented allocation strategy in terms of stability and control current optimization during the acceleration process is intuitively verified.

[0027] Figure 4 Rotor amplitude variation in: ① Fixed low bias current ( ,dotted line): When the speed is increased to about 20Hz, the amplitude rises sharply to nearly 3μm, posing a risk of low-speed resonance.

[0028] ② Fixed high bias current ( (dotted line) In the low-speed range (frequency less than 40Hz), the amplitude is lower than The amplitude is relatively high, but there is redundancy in the high-speed range above 40Hz, which is maintained at around 2μm, indicating that the bias current is excessive and there is a waste of power.

[0029] ③ Bias current segmentation strategy based on rotational speed (solid line): In the low-speed range (frequency less than 40Hz), the bias current is automatically increased, and the amplitude is... The amplitude is the same; after switching to low current in the high-speed segment (frequency greater than 40Hz), the amplitude is stably maintained at about 1.5μm, which not only solves the defect of instability at low speed with fixed low current, but also avoids the problem of power consumption at high speed with fixed high current.

[0030] Figure 5 Control current variation in: ① Fixed low bias current ( ,dotted line): The control current surges in the low-speed range (frequency less than 40Hz) because the bias current is insufficient, requiring a large control current to compensate for the electromagnetic force. Although the control current is low in the high-speed range, as shown in Figure (a), this low current comes at the cost of exceeding the amplitude limit, resulting in weak anti-interference and stability capabilities.

[0031] ② Fixed high bias current ( (dotted line) In the high-frequency range (frequency greater than 40Hz), the control current is higher than The control current remains above 0.15A and continues to rise, indicating that the bias current redundancy causes the control current to be unnecessarily high, resulting in large copper losses.

[0032] ③ Bias current segmentation strategy based on rotational speed (solid line): The control current in the low-speed range increases moderately with the amplitude demand, while it drops rapidly and remains at a low level in the high-speed range, demonstrating the characteristic of adjusting the current on demand. This ensures that there is no resonance during the speed-up process and significantly reduces the copper loss caused by the control current in the high-speed range, verifying the balance between stability and energy saving in step S3.

[0033] In conclusion, Figure 4 and Figure 5Both studies demonstrate, through a two-dimensional comparison of "amplitude-current", that the bias current segmentation strategy based on rotational speed can dynamically adapt to operating conditions during rotor speed-up, while simultaneously achieving the technical goals of improving stability and reducing power consumption.

[0034] See Figure 3 As shown, when the rotor enters the constant speed high-speed operating condition, it will maintain low current operation under the initial allocation of bias current based on the rotational speed. Given that the linear range of electromagnetic force corresponding to low bias current is narrow, the system may not be able to provide sufficient force to suppress rotor displacement when encountering sudden disturbances, causing it to deviate from the stable region. Therefore, an adaptive variable bias strategy is introduced. Its core objective is to increase the bias current in real time to expand the linear control range when the displacement caused by the disturbance force is detected to exceed the safety threshold, and adjust the PID parameters accordingly to form a synergistic optimization of current and control, thereby quickly curbing the deterioration of the state. Once the disturbance disappears, the system will automatically switch back to the low current high-efficiency operating mode.

[0035] When the system stabilizes at the target operating speed in step S3, the displacement change of the rotor caused by the unbalanced disturbance is monitored by the sensor, the magnitude of the disturbance force is accurately determined, and the bias current is dynamically and adaptively adjusted to obtain the optimal bias current magnitude, thereby achieving power consumption optimization while ensuring stability. Based on the operational stability constraints of the magnetic levitation bearing-rotor system, and taking into account the linear characteristic of electromagnetic force changing with bias current, the formula for calculating the minimum bias current is derived: The formula for electromagnetic force is: ; in, Since it is an electromagnetic force, the force generated by rotor disturbance needs to be balanced, that is... ,and Substituting and deriving the formula for calculating the minimum bias current, we obtain: ; in, Equivalent stiffness; This represents the real-time vibration displacement of the rotor after it is disturbed. The minimum bias current under stable operating conditions; This is the maximum allowable bias current of the system; , The structural parameters are expressed as follows: ; in, The permeability of free space is approximately 4π × 10⁻⁶. -7 H / m; This is the effective cross-sectional area of ​​the magnetic core; This refers to the number of coil turns. The angular coefficient of the magnetic field distribution; This refers to the clearance distance between the rotor and the stator. Based on the power consumption characteristics of the magnetic bearing-rotor system, copper loss is a core component of the system's operating power consumption. The bias current is determined based on the copper loss value. The copper loss calculation formula is as follows: ; in, For copper loss; The coil resistance; Given the coil current and the differential control used in the magnetic levitation bearing, the upper magnetic pole coil current is... The current in the lower magnetic pole coil is , To control the current, control the current To counteract displacement disturbances, the control current is derived based on the electromagnetic force formula. Substituting into the copper loss calculation formula, we get: ; Differentiating it yields the formula for the minimum bias current at which minimum copper loss is achieved: ; Minimum bias current under stable operating conditions Minimum bias current under low operating power consumption constraints intersection To simultaneously satisfy both operational stability and power consumption constraints within a given current range, the equation for the minimum bias current range is obtained as follows: ; in, This is the final bias current; The bias current obtained in step S3 when the rotational speed is stable; The displacement of the rotor after it is disturbed; The threshold value for vibration displacement; Minimum bias current based on system power consumption constraints And the minimum bias current at minimum copper loss in step S343 The minimum value of the intersection of the two; The vibration displacement of the rotor is collected in real time by sensors, and the data is substituted into the adaptive allocation method formula to dynamically calculate the current bias current value that needs to be adjusted.

[0036] Experimental Example 1: Figure 6-8 A comparative experiment on system stability and power consumption based on adaptive variable bias current distribution strategy and fixed bias current strategy.

[0037] Experimental objective: To verify whether the adaptive variable bias current distribution strategy, compared to the fixed bias current strategy, can effectively reduce power consumption during system operation in a high-speed magnetic levitation bearing-rotor system while ensuring system stability.

[0038] Comparative Model: When the system adopts a fixed bias current strategy and the current value is set to 2A, due to the limited linear control range of the electromagnetic bearing, the rotor displacement response exhibits significant overshoot after being subjected to external disturbances, with a maximum offset approaching ±70μm. When the fixed bias current value is increased to 4A, the system's anti-interference capability and dynamic stiffness are enhanced, its maximum displacement offset is suppressed to around ±20μm, and the recovery speed is faster with reduced oscillation amplitude; however, maintaining a high constant bias current will directly lead to a significant increase in the system's steady-state power consumption.

[0039] Experimental Model: Employing an adaptive variable bias current distribution strategy, the system can dynamically optimize based on real-time operating conditions. When rotor displacement exceeds a preset safety threshold, the control module increases the bias current in real time and simultaneously adjusts the parameters of the PID controller, achieving coordinated optimization of current distribution and control law. Under this strategy, displacement fluctuations are effectively suppressed within ±30μm, overcoming the instability issues associated with low bias currents and avoiding the high power consumption problems caused by fixed high bias currents. The adaptive strategy significantly improves energy efficiency while ensuring system robustness, achieving an optimal balance between dynamic performance and power consumption.

[0040] Experimental Methods: An adaptive variable bias current distribution strategy was deployed in the experimental model, controlling the bias current according to the logic of segmented current control based on speed and adaptive current adjustment under disturbance. A fixed bias current value was set in the comparative model. The rotor was controlled to accelerate from rest, passing through a low-speed segment, an acceleration segment, and finally stabilizing at the target high speed. The current, vibration displacement, and power consumption data of the two models at different speeds were recorded. During the high-speed steady-state stage, unbalanced disturbances were artificially introduced or monitored by the system, and the current adjustment, vibration displacement suppression, and power consumption changes of the two models under the disturbances were recorded. The current, vibration displacement, and power consumption data of the experimental model and the comparative model under various operating conditions were compared to analyze the performance of the adaptive variable bias current distribution strategy in terms of stability and power consumption optimization, and to verify its technical advantages.

[0041] Experimental Example 2: Figure 9-11 A comparative experiment on the control current waveforms and dynamic performance of adaptive variable bias current distribution strategy and fixed bias current strategy.

[0042] Experimental objective: By comparing the control current waveforms under different strategies, the advantages of this invention in terms of control efficiency and dynamic performance can be verified.

[0043] Comparative Model: When using a strategy with a fixed bias current of 2A, the control current exhibits significant transient pulse fluctuations with large amplitudes when responding to disturbances due to the low bias current. Although the control current quickly converges to near-zero after the disturbance subsides, this reflects insufficient system control margin, limiting its ability to combat continuous or sudden disturbances. When the fixed bias current is increased to 4A, the system obtains a more ample linear operating range, and the fluctuation amplitude of the control current can be effectively suppressed, exhibiting smoother dynamic characteristics and maintaining rotor stability within a smaller current regulation range. However, a consistently high current exists in the bias winding, leading to a significant increase in the system's base power consumption.

[0044] Experimental Model: The adaptive variable bias current strategy adopted in this invention can be automatically adjusted. When the system is subjected to disturbance, its control current response exhibits a more active dynamic adjustment process: by increasing the bias current in real time and simultaneously optimizing the control parameters, the instantaneous linear operating range is expanded, thereby effectively suppressing disturbances in a wider control domain. The current fluctuation characteristics under this strategy are essentially the system's dynamic optimal energy allocation to suppress disturbances, which considers superior robustness and response while avoiding the high power consumption caused by a fixed high bias current.

[0045] Experimental Example 3: Calculation and comparison of theoretical copper loss for different strategy systems.

[0046] The theoretical formula for calculating copper loss is: ; in, This indicates the copper loss power of the magnetic levitation bearing coil; It is the resistance of the coil; , This represents the time interval for calculating copper loss; For the upper magnetic pole current, For the lower magnetic pole current, the formulas are as follows: ; ; in, For bias current, To control the current.

[0047] Based on the above model, the copper loss comparison of different control strategies is as follows: During the rotor speed-up stage, the copper loss generated by the speed-based segmented variable bias strategy increased by 73.47% compared to the fixed 2A low bias strategy, but decreased by 56.61% compared to the fixed 4A high bias strategy. After the system enters the speed stabilization stage, the effectiveness of the adaptive variable bias strategy becomes more prominent. Its copper loss only increased by 18.87% compared to the fixed 2A low bias strategy, but decreased significantly by 69.43% compared to the fixed 4A high bias strategy. The adaptive variable bias current distribution method proposed in this invention can significantly reduce copper loss compared to the fixed high bias strategy without affecting dynamic performance after the system enters steady-state operation, verifying its significant technical progress in improving system power consumption. Specific copper loss comparison results are shown in Tables 1 and 2.

[0048] Table 1 Comparison of copper losses between segmented variable bias and constant / zero bias

[0049] Table 2 Comparison of copper losses between adaptive variable bias and constant bias

[0050] As shown in Tables 1 and 2, compared with the 4A constant bias current distribution strategy, the copper loss of the system is reduced by more than 57.8% when this low-power variable bias current control method is adopted, and the energy saving effect is significant.

[0051] like Figure 12 As shown, a phased variable bias current optimization control architecture was constructed based on conventional PID control. Its specific implementation includes the following steps: establishing an accurate dynamic model of the magnetic bearing-rotor system under external disturbance and deriving its state-space expression; based on this model, completing the parameter tuning of the magnetic bearing PID controller; during the rotor acceleration phase, a speed-based variable bias current distribution strategy is adopted; this strategy avoids resonance peaks and suppresses rotor amplitude by switching between high and low bias currents in different speed zones, maximizing the use of the low bias current range to achieve initial power consumption reduction; when the rotor crosses the resonance zone and enters the target operating speed range, the system automatically switches to an adaptive variable bias current distribution strategy. The strategy uses the real-time vibration state of the system as a feedback signal to dynamically and smoothly adjust the set value of the bias current, thereby optimizing the power consumption at the operating point while ensuring system stability and dynamic stiffness.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A low-power variable bias current control method for a high-speed magnetic levitation bearing, characterized in that: Includes the following steps: S1. The overall kinematic equation of the magnetic levitation bearing-rotor system is derived through mechanical analysis, and the kinematic equation is mathematically transformed and the state space equation is derived, providing a mathematical calculation model for PID control and bias current optimization control. S2. Based on the state-space equation in step S1, extract the characteristic parameters used to tune the PID controller parameters; simplify the magnetic bearing-rotor system into a mass-spring-damping system and obtain the differential equation, associate the characteristic parameters extracted from the state-space equation, and derive the proportional gain, derivative gain, and integral gain of the PID controller that meet the stability requirements of the magnetic bearing-rotor system, thus completing the parameter tuning. S3. Construct a collaborative control system consisting of a PID controller and a bias current regulating controller. The PID controller uses the PID controller parameters derived in step S2 to output the control current in real time to maintain the rotor suspended at the preset balance position. The bias current regulation controller dynamically sets the bias current in the acceleration phase and the stable rotation phase based on the state signals of the rotation speed and vibration displacement during the acceleration phase and the stable rotation phase, so as to obtain the optimal bias current parameters and achieve power consumption optimization while ensuring the stability of the magnetic levitation bearing-rotor system. The characteristic parameters of the magnetic levitation bearing-rotor system in step S2 include the displacement stiffness coefficient. Current stiffness coefficient Equivalent quality and damping ratio ; In step S3, during the speed-up phase, the rotational speed data of the magnetic levitation bearing-rotor system is collected, and the optimal bias current values ​​corresponding to multiple rotational speed ranges are preset to achieve preliminary allocation of bias current based on rotational speed. During the stable rotation phase, when the magnetic levitation bearing-rotor system based on the acceleration phase stabilizes at the target speed, the bias current is adaptively adjusted by monitoring the unbalanced force and displacement caused by disturbances on the rotor through sensors.

2. The low-power variable bias current control method for a high-speed magnetic levitation bearing according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Based on the force and motion relationship of the rotor during translation and rotation, determine the unbalanced force on the rotor. , The algorithm formula is: ； in, This refers to the rotor speed; Unbalanced mass; It is the eccentricity; This is the initial phase; For time; S12. Combining the multi-degree-of-freedom dynamic model of the magnetic bearing-rotor system, the magnetic bearing-rotor system under unbalanced forces is obtained. The kinematic equations under excitation are given by: ； in, This refers to the total weight of the rotor; For the rotor's center of mass in Acceleration in the direction of; For the rotor's center of mass in Acceleration in the direction of; For magnetic levitation bearing A in Electromagnetic force generated in the axial direction; For magnetic levitation bearing B in Electromagnetic force generated in the axial direction; For magnetic levitation bearing A in Electromagnetic force generated in the axial direction; For magnetic levitation bearing B in Electromagnetic force generated in the axial direction; For the unbalanced force acting on the rotor Components along the axial direction; For the unbalanced force acting on the rotor Components along the axial direction; For the rotor to wind around it Moment of inertia of the shaft; For the rotor to wind around it Moment of inertia of the shaft; For the rotor to wind around it Moment of inertia of the shaft; For rotor winding Angular acceleration of the axis; For rotor winding Angular acceleration of the axis; For rotor winding Angular velocity of the axis; Rotor winding Angular velocity of the axis; , Let be the distance from the center of magnetic bearings A and B to the rotor's center of mass; S13. Based on the parameters from step S12, form a state vector, take the control current at the magnetic bearing as the system input, and the rotor displacement as the system output, and obtain the state-space expression of the magnetic bearing-rotor system under the influence of unbalanced forces: ； in, To fully describe the internal state of the system, the state vector includes the rotor's displacement, velocity, and angular velocity from step S12. The first derivative of the state vector represents the rate of change of the state vector over time. For the system matrix; The input matrix; This refers to the control current for the magnetic levitation bearing. This refers to the rotor displacement at the magnetic levitation bearing or sensor. This is the displacement output matrix for the magnetic levitation bearing. This is a direct transmission matrix.

3. The low-power variable bias current control method for a high-speed magnetic levitation bearing according to claim 2, characterized in that: Step S2 specifically includes the following steps: S21. Based on the state-space equations of step S1, extract the displacement stiffness coefficients. Current stiffness coefficient Equivalent quality and damping ratio ; S22. The magnetic bearing suspends the rotor via electromagnetic force, providing elastic support without mechanical contact. This simplifies the magnetic bearing-rotor system to a mass-spring-damping system, yielding the following differential equation: ； in, The mass of the rotor; This is the acceleration of the rotor's center of mass in a certain direction; The equivalent damping coefficient that hinders rotor motion; The velocity of the rotor's center of mass in a certain direction; This is the equivalent spring stiffness coefficient; It represents the displacement of the rotor's center of mass relative to its equilibrium position in a certain direction; The external force acting on the rotor; S23. Adjust the proportional gain of the PID controller. Integral gain Differential gain Incorporating the differential equation from step S22 and performing a Laplace transform, we obtain its frequency domain expression: ； S24. Based on the Routh criterion, the frequency domain expression of step S23 is derived to obtain the expression for the range of values ​​of the PID control parameters as follows: ； in, The proportional gain of the PID controller; For adjustment coefficients; This is the displacement stiffness coefficient; This is the current stiffness coefficient; ； in, The derivative gain of the PID controller; The damping ratio; This is the equivalent stiffness coefficient; For equivalent quality; ； in, The integral gain of the PID controller; S25. Based on the parameter range of the Routh criterion in step S24, and combined with the dynamic performance requirements of the magnetic levitation bearing-rotor system, determine the proportional gain. Differential gain and integral gain This completes the parameter tuning of the PID controller.

4. The low-power variable bias current control method for a high-speed magnetic levitation bearing according to claim 3, characterized in that: In step S3, the rotor speed is within the dynamic range from rest to rated operating speed, which is determined to be the speed-up stage; when the speed is stable at the target operating speed and the vibration displacement is not greater than the maximum allowable radial displacement of the rotor, it is determined to be the stable rotation stage.

5. The low-power variable bias current control method for a high-speed magnetic levitation bearing according to claim 4, characterized in that: Based on the acceleration phase in step S3, and under the conditions of minimum current requirement for safe displacement and maximum current limit for power consumption optimization, the expression for the bias current setpoint is derived: ； in, The proportional gain of the PID controller; This represents the maximum permissible radial displacement of the rotor. The bias current is based on different speed ranges; This is the maximum bias current; The speed range division rules and corresponding bias current values ​​are written into the collaborative control system. The monitoring module provides real-time feedback of speed data, generates a matching signal between the monitored speed data and the speed range, and transmits the matching signal to the collaborative control system, enabling the collaborative control system to switch the bias current value and complete the initial allocation of bias current across the entire speed range.

6. The low-power variable bias current control method for a high-speed magnetic levitation bearing according to claim 5, characterized in that: During the stable rotation phase in step S3, the bias current value is determined by the stable operating conditions and power consumption of the magnetic levitation bearing-rotor system. Based on the operational stability constraints of the magnetic levitation bearing-rotor system, and taking into account the linear characteristic of electromagnetic force changing with bias current, the formula for calculating the minimum bias current is derived: ； in, Equivalent stiffness; This represents the real-time vibration displacement of the rotor after it is disturbed. The minimum bias current under stable operating conditions; This is the maximum allowable bias current of the system; , The structural parameters are expressed as follows: ； in, The permeability of free space is approximately 4π × 10⁻⁶. -7 H / m; This is the effective cross-sectional area of ​​the magnetic core; This refers to the number of coil turns. The angular coefficient of the magnetic field distribution; This refers to the clearance distance between the rotor and the stator. Based on the power consumption characteristics of the magnetic bearing-rotor system, copper loss is a core component of the system's operating power consumption. The bias current is determined based on the copper loss value. The copper loss calculation formula is as follows: ； in, For copper loss; The coil resistance; Given the coil current and the differential control used in the magnetic levitation bearing, the upper magnetic pole coil current is... The current in the lower magnetic pole coil is , To control the current, control the current To counteract displacement disturbances, the control current is derived based on the electromagnetic force formula. Substituting into the copper loss calculation formula, we get: ； Based on the copper loss calculation formula, copper loss Regarding bias current The function, for Find the first derivative and set it to 0. Then, find the extreme values ​​to obtain the formula for the minimum bias current at which the copper loss is minimal: ； Obtain the minimum bias current under stable operating conditions. Minimum bias current under operating power consumption constraints intersection To simultaneously satisfy both operational stability and power consumption constraints within a given current range, the equation for the minimum bias current range is obtained as follows: ； in, This is the final bias current; This is the bias current when the rotational speed is stable. The displacement of the rotor after it is disturbed; The threshold value for vibration displacement; Minimum bias current based on system power consumption constraints and minimum bias current at minimum copper loss The minimum value of the intersection of the two; The vibration displacement of the rotor is collected in real time by sensors, and the data is substituted into the adaptive allocation method formula to dynamically calculate the current bias current value that needs to be adjusted.

7. The low-power variable bias current control method for a high-speed magnetic levitation bearing according to claim 6, characterized in that: Step S3 is followed by step S4: Using the theoretical copper loss formula for magnetic levitation bearing coils, the theoretical copper loss of the segmented variable bias strategy and the adaptive variable bias strategy used in step S3 is first calculated and verified. Then, this theoretical copper loss is compared with the theoretical copper loss obtained using the fixed bias current strategy. The theoretical copper loss calculation formula is as follows: ； in, This indicates the copper loss power of the magnetic levitation bearing coil; It is the resistance of the coil; , This represents the time interval for calculating copper loss.

Images