A control method and system for a magnetic bearing

Abstract

This invention belongs to the field of magnetic levitation bearing technology, specifically relating to a control method and system for magnetic levitation bearings. By combining auxiliary fourth-order LESO with integral sliding mode control, the anti-disturbance capability is significantly improved, and the suppression effect on various disturbances is superior to traditional control. By employing a saturation function and an external integrator, the problems of control chattering and integral saturation are solved. With the help of piecewise fal function TD and other designs, dynamic and steady-state performance are balanced, achieving zero steady-state error levitation and greatly shortening the settling time. The control method proposed in this invention features core parameter correlation design, requires no complex tuning, is compatible with existing hardware, and can be directly embedded into the controller, making engineering implementation simpler.

Description

Technical Field

[0001] This invention belongs to the field of magnetic levitation bearing technology, specifically relating to a control method and system for magnetic levitation bearings. Background Technology

[0002] Magnetic levitation bearings enable rotors to levitate without contact using electromagnetic force, offering significant advantages such as frictionless operation, high speed, long lifespan, and active control. They have been widely used in high-end rotating machinery fields such as high-speed motors, flywheel energy storage, and centrifugal compressors.

[0003] However, when magnetic levitation bearing-rotor systems are applied to moving vehicles such as ships, vehicles, and aircraft, or installed in industrial sites with other vibrating equipment, their mounting foundations are subjected to continuous low-frequency vibrations of 0-10Hz from the external environment; this vibration is called foundation excitation. Foundation excitation is transmitted to the entire magnetic levitation system through the support structure, directly interfering with the rotor's levitation clearance and posing a serious threat to the system's stable operation. Compared to the ideal operating condition with a fixed foundation, foundation excitation not only introduces additional disturbance forces but may also alter the dynamic characteristics of the system model, drastically increasing the complexity of control design and reducing stability margin.

[0004] Currently, the mainstream technical approaches for controlling magnetic levitation bearings based on basic excitation can be divided into two categories.

[0005] The first category is based on classical proportional-integral-derivative (PID) control and its improvements. PID controllers have a simple structure and perform well in stable environments with a fixed foundation, such as... Figure 1 This is a schematic diagram of the PID control principle of a traditional magnetic levitation system. However, under the action of the basic excitation, it still has the following inherent defects: 1) Its integral element is extremely sensitive to continuous low-frequency disturbance signals, and is prone to integral saturation, leading to loss of control output, and then causing system instability or even rotor drop. 2) The PID controller has difficulty distinguishing between disturbances caused by the rotor itself and disturbances caused by the basic excitation. Parameter tuning often results in one aspect being neglected while the other is addressed. While suppressing the basic excitation, it may lead to a deterioration in the control performance of disturbances in other frequency bands, and cannot meet the high-performance control requirements under multi-frequency composite disturbances.

[0006] The second category is control strategies based on feedforward compensation. To overcome the shortcomings of PID control, existing technologies typically add an acceleration feedforward channel to the feedback control loop of PID control. This method measures the basic excitation information in real time by installing an acceleration sensor on the foundation and generates the compensation control force in advance accordingly. However, this approach also has limitations: 1) High dependence: Its compensation performance is highly dependent on the accuracy and real-time performance of the basic excitation measurement signal, requiring high precision, installation location, and anti-interference capability of the acceleration sensor; 2) Model fragility: The effectiveness of feedforward compensation is based on an accurate inverse model of the system. Once the actual system parameters drift or the model contains unmodeled dynamics, the feedforward signal not only cannot effectively compensate but may also become a new source of interference, inducing excitation phenomena and reducing system stability; 3) Cost and complexity: The additional high-precision sensor and its signal processing circuit increase system cost, complexity, and potential failure points.

[0007] In summary, under the specific condition of low-frequency fundamental excitation, existing technologies face a dilemma: traditional PID control, while simple in structure, suffers from poor stability and insufficient performance; while feedforward-based solutions, though effective to some extent, suffer from low reliability, complex engineering implementation, and high cost due to their stringent reliance on sensors and models. Therefore, there is an urgent need for a novel control method that does not rely on additional precision sensors, is insensitive to model errors, and fundamentally avoids integral saturation, in order to achieve a synergistic improvement in the stability and control accuracy of the magnetic levitation bearing-rotor system under low-frequency fundamental excitation conditions. Summary of the Invention

[0008] Based on the above background, the present invention proposes a control method for a magnetic levitation bearing, which includes the following steps: Step S1: Establish a four-degree-of-freedom dynamic model of the magnetic levitation bearing-rotor system, and reduce, linearize and decouple the individual radial control degrees of freedom to obtain a single-degree-of-freedom equivalent model.

[0009] Step S2: Construct the sliding mode enhanced active disturbance rejection control (SM-ADRC) main loop, which includes a piecewise fal function tracking differentiator (TD), a model-assisted fourth-order linear extended state observer (LESO), and an integral sliding mode controller (SMC).

[0010] Step S3: Connect an external integral compensator with leakage and frequency limiting characteristics in parallel on the SM-ADRC main circuit. The output of the integral compensator satisfies: ,in, , The integrator output rate of change, Here, r is the integral coefficient, and r is the reference signal. These are displacement observations. This represents the leakage coefficient.

[0011] Step S4, the output control quantity of the SM-ADRC main circuit is... With the output of the external integral compensator Superimposed, the final control command is obtained. The output is then sent to a power amplifier to drive the electromagnet coil to generate electromagnetic force.

[0012] The present invention also proposes a control system for a magnetic levitation bearing, the control system comprising: The sensor module is used to acquire the radial displacement signal and rotor speed of the rotor; The model building module is used to build a four-degree-of-freedom dynamic model and a single-degree-of-freedom equivalent model. The SM-ADRC main control module includes a piecewise fal function TD unit, a model-aided fourth-order LESO unit, and an integral sliding mode SMC unit, used to generate the main control variables. ; An external integral compensation module is used to generate low-frequency compensation current. ; Signal fusion module, used to combine and The data is superimposed and then limited to obtain the final control command. ; The execution driver module is used to... It is converted into the driving current of the electromagnet.

[0013] Compared with the prior art, the present invention has the following advantages: 1. Significantly improved anti-disturbance capability. This invention achieves accurate estimation of displacement, velocity, total disturbance, and disturbance derivative through assisted fourth-order LESO, and predicts the changing trend of low-frequency basic excitation in advance. Combined with the strong robustness of integral sliding mode control, the suppression effect on low-frequency basic excitation, coupled interference, and model error is better than that of traditional control.

[0014] 2. Solving the problems of chattering and integral saturation. In the solution of this invention, the integral sliding mode controller uses a saturation function instead of a sign function, eliminating high-frequency chattering of the control current; the leakage characteristics of the external integrator ensure that the output does not accumulate indefinitely, fundamentally avoiding the problem of integral saturation.

[0015] 3. Balancing dynamic and steady-state performance. The piecewise fal function TD effectively reduces overshoot during startup and command switching. The combined effect of the integral sliding surface and the external integrator achieves zero steady-state error levitation. The proposed solution reduces the adjustment time by more than 30% compared to traditional solutions.

[0016] 4. Easier engineering implementation: The core parameters are designed based on the frequency correlation of the first bending mode of the system, which does not require complex tuning. It is compatible with existing magnetic levitation bearing hardware such as sensors and power amplifiers, and can be directly embedded into DSP / FPGA controllers. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the PID control principle of a traditional magnetic levitation system. Figure 2 The present invention provides a flowchart of a control method for a magnetic levitation bearing; Figure 3 The present invention provides a control system framework diagram for a magnetic levitation bearing. Detailed Implementation

[0019] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0020] like Figure 2 As shown, this invention proposes a control method for a magnetic levitation bearing, which includes the following steps: Step S1: Establish a four-degree-of-freedom dynamic model of the magnetic levitation bearing-rotor system, and reduce, linearize and decouple the individual radial control degrees of freedom to obtain a single-degree-of-freedom equivalent model.

[0021] Specifically, a four-degree-of-freedom dynamic model of the magnetic levitation bearing-rotor system in the radial (X,Y directions) direction is established, and its equations of motion are as follows:

[0022] Where M is the mass matrix, D contains the damping term caused by the basic excitation, Ω is the rotor speed, G is the gyroscopic effect matrix, K contains the stiffness matrix caused by the basic excitation, KB is the bending and shear stiffness matrix, Q represents the outward force, including gravity, bearing force, basic excitation force, etc., and q represents the generalized displacement, including two translational degrees of freedom and two rotational degrees of freedom in the radial direction. This four-degree-of-freedom motion equation is used to describe the rotor's radial motion and is used for subsequent control parameter design.

[0023] When a single degree of freedom, such as a radial translation, needs to be controlled, it needs to be reduced in order, linearized, and decoupled to obtain an approximate second-order single-degree-of-freedom model, the general form of which is:

[0024] in , and Equivalent mass, damping, and stiffness can be extracted or identified from complex models; For current stiffness, To control the current, The total disturbance includes basic excitation, gravity, coupling, etc.; at this time, q is represented by the displacement y of the rotor in that degree of freedom read by the displacement sensor.

[0025] Step S2: Construct the sliding mode enhanced active disturbance rejection control (SM-ADRC) main loop, which includes a piecewise fal function tracking differentiator (TD), a model-assisted fourth-order linear extended state observer (LESO), and an integral sliding mode controller (SMC).

[0026] Specifically, the piecewise fal function tracks the differentiator TD by preprocessing the reference signal r to generate a smooth tracking signal. and approximate differential signals This helps avoid system oscillations caused by sudden changes in instructions.

[0027]

[0028] In the formula, h is the system sampling period.

[0029] The piecewise fal function is defined as:

[0030] In the formula, d is an intermediate variable used for calculating function property switching; d is a boundary layer parameter with a value of Sa is used to divide the linear and nonlinear regions of the function, and Sa is an intermediate variable used to smooth the function switching. a , is an intermediate variable, calculated based on the tracking signal and the differential signal, and r is the tracking speed factor.

[0031] The parameter is set to the tracking speed factor. , The controller bandwidth is given, the sampling period h is taken as the sensor sampling period, and the boundary layer parameters are given. This ensures smooth tracking in the low-frequency band.

[0032] The single-degree-of-freedom model is rewritten in a LESO-adapted form as follows:

[0033] In the formula, is the second derivative of the displacement sensor output, i.e., the actual acceleration; b0 is the compensation coefficient; u is the control current. This is the derivative of the total disturbance.

[0034] In LESO, equivalent damping and equivalent stiffness are introduced for auxiliary estimation to reduce observation burden, as detailed below:

[0035] In the formula, e is the observation error, which represents the difference between the displacement sensor output and the observed displacement; These are, respectively, displacement observations, velocity observations, total disturbance observations, and disturbance differential observations; The observer feedback gain, and the observer bandwidth. Related, respectively 4 6 4 , ; , , These are equivalent damping, equivalent mass, and equivalent stiffness, respectively.

[0036] Integral sliding mode controllers (SMCs) are used to improve the robustness of the system to low-frequency disturbances and define the tracking error. The error differential is The integral sliding surface is:

[0037] In the formula, s is the sliding surface variable, which is used to describe the deviation between the system state and the ideal trajectory; Here are the parameters for the sliding surface, with a value of 2. , used to adjust error weights; The integral term for tracking error is used to eliminate steady-state error; t is the current time.

[0038] The control law of the integral sliding mode controller is:

[0039] In the formula, To switch the gain, Let be the boundary layer thickness, k be the approach rate, and sat() be the saturation function; This is the SM-ADRC main control signal. This is the second derivative of the TD tracking signal.

[0040] Step S3: Connect an external integral compensator with leakage and frequency limiting characteristics in parallel on the SM-ADRC main circuit. The output of the integral compensator satisfies: ,in, , The integrator output rate of change, Here, r is the integral coefficient, and r is the reference signal. These are displacement observations. This represents the leakage coefficient.

[0041] Step S4, the output control quantity of the SM-ADRC main circuit is... With the output of the external integral compensator Superimposed, the final control command is obtained. The output is then sent to a power amplifier to drive the electromagnet coil to generate electromagnetic force.

[0042] This invention also proposes a control system for a magnetic levitation bearing, such as... Figure 3 As shown, the control system includes: The sensor module is used to acquire the radial displacement signal and rotor speed of the rotor; The model building module is used to build a four-degree-of-freedom dynamic model and a single-degree-of-freedom equivalent model. The SM-ADRC main control module includes a piecewise fal function TD unit, a model-aided fourth-order LESO unit, and an integral sliding mode SMC unit, used to generate the main control variables. ; An external integral compensation module is used to generate low-frequency compensation current. ; Signal fusion module, used to combine and The data is superimposed and then limited to obtain the final control command. ; The execution driver module is used to... It is converted into the driving current of the electromagnet.

[0043] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0044] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0045] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0046] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A control method for a magnetic levitation bearing, characterized in that, The control method includes the following steps: Step S1: Establish a four-degree-of-freedom dynamic model of the magnetic levitation bearing-rotor system, and reduce, linearize and decouple the individual radial control degrees of freedom to obtain a single-degree-of-freedom equivalent model. Step S2: Construct the sliding mode enhanced active disturbance rejection control (SM-ADRC) main loop, which includes a piecewise fal function tracking differentiator (TD), a model-assisted fourth-order linear extended state observer (LESO), and an integral sliding mode controller (SMC). Step S3: Connect an external integral compensator with leakage and frequency limiting characteristics in parallel on the SM-ADRC main circuit. The output of the integral compensator satisfies: ,in, , The integrator output rate of change, Here, r is the integral coefficient, and r is the reference signal. These are displacement observations. Leakage coefficient; Step S4, the output control quantity of the SM-ADRC main circuit is... With the output of the external integral compensator Superimposed, the final control command is obtained. The output is then sent to a power amplifier to drive the electromagnet coil to generate electromagnetic force.

2. The control method for a magnetic levitation bearing according to claim 1, wherein in step S1, the single-degree-of-freedom model is: ； in , and Equivalent mass, damping, and stiffness are extracted or identified from complex models; For current stiffness, To control the current, For the total disturbance, at this time This is reflected in the displacement y of the rotor in that degree of freedom, as read by the displacement sensor.

3. The control method for a magnetic levitation bearing according to claim 1, in step S2, the piecewise fal function tracking differentiator TD preprocesses the reference signal r to generate a smooth tracking signal. and approximate differential signals The details are as follows: ； In the formula, h is the system sampling period.

4. The control method for a magnetic levitation bearing according to claim 1, in step S2, The piecewise fal function is defined as: ； In the formula, d is an intermediate variable used for calculating function property switching; d is a boundary layer parameter with a value of Sa is used to divide the linear and nonlinear regions of the function, and Sa is an intermediate variable used to smooth the function switching. a , is an intermediate variable, calculated based on the tracking signal and the differential signal, and r is the tracking speed factor.

5. The control method for a magnetic levitation bearing according to claim 1, wherein in step S2, the integral sliding surface in the integral sliding mode controller SMC is: ； In the formula, s is the sliding surface variable, which is used to describe the deviation between the system state and the ideal trajectory; Here are the parameters for the sliding surface, with a value of 2. , used to adjust error weights; The integral term for tracking error is used to eliminate steady-state error; t is the current time.

6. In the control method for magnetic levitation bearings according to claim 4, the control law of the integral sliding mode controller (SMC) is: ； In the formula, To switch gain, Let be the boundary layer thickness, k be the approach rate, and sat() be the saturation function; This is the SM-ADRC main control signal. This is the second derivative of the TD tracking signal.

7. A control system based on the control method according to any one of claims 1-6, characterized in that, The control system includes: The sensor module is used to acquire the radial displacement signal and rotor speed of the rotor; The model building module is used to build a four-degree-of-freedom dynamic model and a single-degree-of-freedom equivalent model. The SM-ADRC main control module includes a piecewise fal function TD unit, a model-aided fourth-order LESO unit, and an integral sliding mode SMC unit, used to generate the main control variables. ; An external integral compensation module is used to generate low-frequency compensation current. ; Signal fusion module, used to combine and The data is superimposed and then limited to obtain the final control command. ; The execution driver module is used to... It is converted into the driving current of the electromagnet.

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