Magnetic Levitation Molecular Pump Magnetic Bearing Stable Control System

Abstract

The present application discloses a magnetic bearing stable control system for a magnetic levitation molecular pump, including: a sensor, a control module, an actuator, and a bearing-rotor module; the sensor is used to measure the axial displacement and radial displacement of the bearing-rotor module to obtain a measurement signal; the control module is used to calculate a control signal based on the measurement signal; the actuator is used to generate an electromagnetic force based on the control signal; the bearing-rotor module is used to support an asymmetric large-inertia rotor based on the electromagnetic force to achieve stable suspension of the asymmetric large-inertia rotor. The present application solves the problem of the instability of the whirling mode of the magnetic bearing rotor system caused by the strong gyroscopic effect of the rotor, and avoids the problems of difficult parameter tuning of traditional algorithms, the need for multi-stage switching, and the need to introduce rotational speed information. The method proposed in the present application is simple and easy to implement, and does not require the introduction of rotor rotational speed information, and can achieve stable control of the whirling mode of the asymmetric large-inertia magnetic bearing rotor system under the strong gyroscopic effect.

Description

Technical Field

[0001] This application belongs to the field of stable control of magnetic bearings, and particularly relates to a stable control system for the magnetic bearings of a magnetic levitation molecular pump. Background Art

[0002] A magnetic levitation molecular pump generally uses a five-degree-of-freedom magnetic bearing to support a turbine rotor. Except for the axial rotation of the magnetic levitation rotor driven by an electric motor, the other three translational degrees of freedom and two radial rotational degrees of freedom of the rotor are controlled by the magnetic bearing, which is a typical asymmetric large-inertia magnetic levitation rotor system. To ensure the stable operation of the magnetic levitation molecular pump, the magnetic levitation rotor must always be stably levitated at the working center. However, according to rotor dynamics, the magnetic levitation rotor will have a gyroscopic effect during the speed-up process. Due to the asymmetric large-inertia rotor system of the magnetic levitation molecular pump, its gyroscopic effect will be more obvious. A severe gyroscopic effect will cause the high-speed rotating turbine rotor to have two kinds of whirling, namely nutation and precession. At present, in order to achieve stable control of nutation and precession and suppress the two whirling modes of nutation and precession, the more widely used control method is PID cross-feedback control. Although PID cross-feedback control has clear engineering significance and a simple algorithm and is widely used in the field of magnetic levitation bearing control, this control method has problems such as complex calculation of cross-feedback parameters, multi-stage switching of the controller, and the need to introduce a speed signal. Summary of the Invention

[0003] The purpose of this application is to propose a robust centralized control for the whirling modes of a high-speed rotating asymmetric large-inertia magnetic levitation rotor system to solve the problems existing in the above-mentioned prior art.

[0004] To achieve the above purpose, this application provides a stable control system for the magnetic bearings of a magnetic levitation molecular pump, including: a sensor, a control module, an actuator, and a bearing-rotor module;

[0005] The sensor is used to measure the axial displacement and radial displacement of the bearing-rotor module to obtain a measurement signal;

[0006] The control module is used to calculate a control signal based on the measurement signal;

[0007] The actuator is used to generate an electromagnetic force based on the control signal;

[0008] The bearing-rotor module is used to support the asymmetric large-inertia rotor based on the electromagnetic force to achieve stable levitation of the asymmetric large-inertia rotor.

[0009] Preferably, the bearing-rotor module includes: a magnetic bearing and a rotor;

[0010] The magnetic bearing includes: an axial magnetic bearing and a radial magnetic bearing;

[0011] The rotor includes: an asymmetric large-inertia magnetic levitation rotor with an impeller.

[0012] Preferably, the axial magnetic bearing is used to control the single-degree-of-freedom translation in the direction of the inertial axis of the rotor; the radial magnetic bearing is used to control the two-degree-of-freedom translation and the two-degree-of-freedom rotation in the radial direction of the rotor.

[0013] Preferably, the sensor includes an a-end sensor and a b-end sensor;

[0014] The a-end sensor is located above the center of mass of the asymmetric large-inertia magnetic levitation rotor;

[0015] The b-end sensor is located below the center of mass of the asymmetric large-inertia magnetic levitation rotor.

[0016] Preferably, the a-end sensor is used to measure the displacement of the asymmetric large-inertia magnetic levitation rotor at the a-end; the b-end sensor is used to measure the displacement of the asymmetric large-inertia magnetic levitation rotor at the b-end.

[0017] Preferably, the core of the control module is a DSP, and the DSP includes: an AD unit, an ECAP unit, an EPWM unit, and a CAN unit.

[0018] Preferably, the AD unit converts the analog quantity of current displacement into a digital quantity that can be processed by the DSP; the ECAP unit is used to capture the square wave signal transmitted by the Hall sensor and convert the square wave signal into a corresponding rotational speed value; the EPWM unit is used to convert the digital control quantity generated by the DSP into a PWM signal with a variable duty cycle; the CAN unit is used to ensure the communication between the magnetic levitation molecular pump magnetic bearing stable control system and the upper computer.

[0019] Preferably, the actuator includes: an optocoupler unit and an H-bridge circuit;

[0020] The optocoupler unit is used to electrically isolate the control part and the high-power part in the magnetic levitation molecular pump magnetic bearing stable control system;

[0021] The H-bridge circuit is used to convert the power energy into a PWM voltage with a variable duty cycle under the action of the drive circuit.

[0022] Compared with the prior art, the beneficial effects of the present application are as follows:

[0023] This application proposes to regard the gyroscopic effect term as a bounded parameter perturbation that varies with the rotational speed, solves the problem of the whirling mode instability of the magnetic bearing rotor system caused by the strong gyroscopic effect of the rotor, and avoids the problems of difficult parameter tuning of traditional algorithms, the need for multi-level switching, and the need to introduce rotational speed information. The method proposed in this application is simple and easy to implement, and does not require the introduction of rotor rotational speed information, and can achieve the stable control of the whirling mode of the asymmetric large-inertia magnetic bearing rotor system under strong gyroscopic effects. Brief Description of the Drawings

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0025] Figure 1 It is a schematic structural diagram of the magnetic levitation bearing control system according to an embodiment of the present application;

[0026] Figure 2 It is a schematic diagram showing the change of poles caused by parameter perturbation due to the change of rotational speed according to an embodiment of the present application

[0027] Figure 3 It is a schematic diagram for describing the expected pole region according to an embodiment of the present application;

[0028] Figure 4 It is a schematic diagram of the poles when the closed-loop system is statically suspended under the cross-feedback PID controller according to an embodiment of the present application. Detailed Embodiments

[0029] The following will clearly and completely describe the technical solutions in the embodiments of the present application in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, rather than all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.

[0030] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the drawings and specific embodiments.

[0031] As Figure 1As shown in the figure, in this embodiment, an asymmetric large-inertia magnetic levitation magnetic bearing stable control system is provided, including: a sensor, a control module, an actuator, and a bearing-rotor module; the sensor is used to measure the axial displacement and radial displacement of the bearing-rotor module to obtain a measurement signal; the control module is used to calculate a control signal based on the measurement signal; the actuator is used to generate an electromagnetic force based on the control signal; the bearing-rotor module is used to support the asymmetric large-inertia rotor based on the electromagnetic force to achieve the stable suspension of the asymmetric large-inertia rotor.

[0032] Among them, the bearing-rotor module includes: a magnetic bearing and a rotor; the magnetic bearing includes: an axial magnetic bearing and a radial magnetic bearing; the rotor includes: an asymmetric large-inertia magnetic levitation rotor with an impeller. The axial magnetic bearing is used to control the single-degree-of-freedom translation in the direction of the rotor's inertia axis; the radial magnetic bearing is used to control the two-degree-of-freedom translation and two-degree-of-freedom rotation in the radial direction of the rotor.

[0033] In addition, the sensor includes an a-end sensor and a b-end sensor; the a-end sensor is located above the centroid of the asymmetric large-inertia magnetic levitation rotor; the b-end sensor is located below the centroid of the asymmetric large-inertia magnetic levitation rotor. The a-end sensor is used to measure the displacement of the asymmetric large-inertia magnetic levitation rotor at the a-end; the b-end sensor is used to measure the displacement of the asymmetric large-inertia magnetic levitation rotor at the b-end.

[0034] In this embodiment, the core of the control module is a DSP, and the DSP F28335 is selected as the digital controller chip. The DSP includes: an AD unit, an ECAP unit, an EPWM unit, and a CAN unit. The AD unit is used to convert the current displacement analog quantity into a digital quantity that the DSP can process; the ECAP unit is used to capture the square wave signal transmitted by the Hall sensor and convert the square wave signal into the corresponding rotational speed value; the EPWM unit is used to convert the digital control quantity generated by the DSP into a PWM signal with a variable duty cycle; the CAN unit is used to ensure the communication between the magnetic levitation molecular pump magnetic bearing stable control system and the upper computer.

[0035] Finally, the actuator includes: an optocoupler unit and an H-bridge circuit; the optocoupler unit is used to electrically isolate the control part and the high-power part in the magnetic levitation molecular pump magnetic bearing stable control system; the H-bridge circuit is used to convert the power energy into a PWM voltage with a variable duty cycle under the action of the drive circuit.

[0036] In this embodiment, the distance from the a-end radial drive coil to the centroid of the asymmetric large-inertia rotor is l am , and the distance from the b-end radial drive coil to the centroid of the asymmetric large-inertia rotor is l bm Taking the center of the magnetic bearing as the origin and establishing a magnetic bearing coordinate system parallel to the stator coordinate system X and Y directions, then the relationship between the generalized force received by the rotor and the magnetic bearing force is:

[0037]

[0038] Among them, F x and F y are the resultant forces of the radial magnetic bearings at the a and b ends of the magnetic levitation rotor in the x and y directions. f ax is the force of the radial magnetic bearing at the a end on the magnetic levitation rotor in the x direction, and f bx is the force of the radial magnetic bearing at the b end on the magnetic levitation rotor in the x direction, and f ay is the force of the radial magnetic bearing at the a end on the magnetic levitation rotor in the y direction, and f by is the force of the radial magnetic bearing at the b end on the magnetic levitation rotor in the y direction. M x and M y are the torque values of the magnetic levitation rotor in the x and y directions along the rotor's inertia axis.

[0039] In the sensor coordinate system, the rotor is described by h s =[x as x bs y as y bs T The distance from the a - end sensor to the centroid of the asymmetric large - inertia rotor is l as , and the distance from the b - end sensor to the centroid of the asymmetric large - inertia rotor is l bs . In the generalized stator coordinate system of the magnetic bearing, the relative position of the magnetic - bearing rotor is represented by [x, y, α, β] T . The relationship between the sensor coordinate system and the generalized stator coordinate system is:

[0040]

[0041] The dynamic equations of the magnetic - bearing - rotor module for translational and rotational motions in the radial direction are:

[0042]

[0043] Substituting into the simplified rotor dynamic equation gives:

[0044]

[0045] The mechanical model of the magnetic bearing can be obtained by taking the difference of the forces of the upper and lower magnetic bearings and performing Taylor expansion, omitting the high - order terms. Its linearized mechanical model is:

[0046] F m =k i i m +k h h pm (5) ​

[0047] Among them, k i represents the current stiffness of the magnetic bearing, and k h represents the displacement stiffness of the magnetic bearing. i m = [i ax i bx i ay i by T represents the coil current of the magnetic bearing, and h pm = [x am x bm y am y bm T represents the displacement of the rotor in the magnetic bearing coordinate system, and F m = [f ax f bx f ay f by T represents the magnetic bearing force received by the rotor.

[0048] Replacing the displacement of the sensor in the magnetic bearing coordinate system with the displacement in the sensor coordinate system gives:

[0049]

[0050] Substituting Equation (6) into Equation (4) gives:

[0051]

[0052] For the above quantitative relationships between state variables and inputs / outputs, the state space variables of the asymmetric rotor magnetic bearing system are selected as Define the controller output and system output as u p = [u cax u cay u cbx u cby T , y p = [x as y as x bs y bs T . The controller output u p = [u cax u cay u cbx u cby T and the coil current i m = [i ax i ay i bx i by ​​​​​​​T The simplified form of the differential equation is as follows:

[0053]

[0054] Combining Equation (7) and (8), as well as the state variables of the system, the controller output, and the system output, this embodiment can obtain the state space model of the asymmetric rotor magnetic bearing system:

[0055]

[0056] The definitions of each matrix and parameter are as follows:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] It can be seen from the state space model of the above-mentioned asymmetric large-inertia magnetic levitation rotor system that the state matrix A of the system p in which K 11 and K 12 will increase with the increase of the rotational speed ω z , while the other parameters of the state matrix remain unchanged. In this embodiment, the terms that change with the rotational speed are called parameter perturbation terms. The fundamental reason for the instability of the two whirling modes of nutation and precession in the asymmetric large-inertia rotor system is that the state matrix of the system changes with the rotational speed, as Figure 2 shown. That is, the parameters that make the system stable under zero rotational speed conditions cannot ensure the stability of the system throughout the speed-up process without instability. Since all the state space variables of the system can be directly measured or indirectly measured, next, we will discuss how to set a state feedback matrix K to suppress the two whirling modes of precession and nutation throughout the speed-up process.

[0069] First, to make the asymmetric large-inertia rotor stable within all speed ranges, it is necessary to be familiar with the Lyapunov second method.

[0070] Definition 1:

[0071] It can be seen that for the study of a general linear system:

[0072]

[0073] In the formula, x represents an n-dimensional state column vector, and A represents the system's n×n-dimensional state matrix. Suppose A is non-singular. Then the necessary and sufficient condition for the system to be globally asymptotically stable at its equilibrium state x = 0 is: Given a positive definite real symmetric matrix Q, there exists a positive definite real symmetric matrix P, and they satisfy:

[0074] A T TP + PA = -Q (11)

[0075] That is, take the scalar function:

[0076] V(x) = x T TPx (12)

[0077] The p in the formula represents a positive definite real symmetric square matrix. According to the Lyapunov stability criterion, when V(x) > 0, the equilibrium state of the system is asymptotically stable. So here it is required that:

[0078]

[0079] When the state feedback matrix K u is introduced, to make the state of the system asymptotically stable, it is required that:

[0080]

[0081] As long as the controller Ku satisfies the above formula, it can theoretically keep the system stable within the speed range from zero to the maximum speed after the state feedback is introduced, that is, the controller Ku that satisfies the above formula can prevent the asymmetric large-inertia magnetic levitation rotor system from experiencing two types of whirling modes, namely nutation and precession, thus solving the strong gyroscopic effect to a certain extent.

[0082] The controller K that satisfies the above conditions uIn theory, it can keep the asymmetric large-inertia magnetic levitation rotor system stable within the speed range from zero to the highest speed. However, as the speed increases, the gyroscopic effect of the system enhances, the poles of the closed-loop system will gradually approach the imaginary axis, the damping of the two whirling modes of nutation and precession of the system will decrease, and the stability of the system will gradually decrease. The nutation and precession displacements of the system gradually increase, destroying the stability of the system. Seriously, it will touch the protection bearing and cause serious instability, thus damaging the protection bearing and greatly shortening the service life of the magnetic levitation system. In addition to the decrease in the damping of the two whirling modes of nutation and precession of the system, there are also certain errors between the theoretical analysis, modeling and simulation process and the actual magnetic levitation rotor system. As the speed increases, a series of related variables such as the switch power amplifier parameters and saturation current will also change. Therefore, the controller K that only satisfies the Lyapunov stability criterion u may not be able to keep the system stable within the full speed range. To ensure the stability of the system within the full speed range, more constraints need to be proposed to improve the stability margin of the system and increase the damping of the two whirling modes of nutation and precession of the system to improve the stability of the system.

[0083] As Figure 3 shown, design the corresponding feedback control law to configure the poles of the closed-loop system at the desired positions, rather than just in the negative half-plane. Initially, it was only required that the poles of the closed-loop system be in the negative half-plane, but now the poles of the closed-loop system need to be accurately configured to the corresponding region to ensure that the system has certain dynamic and stable characteristics. By restricting the poles of the closed-loop system to an appropriate region in the plane, it can be ensured that the damping ratio, undamped natural frequency, and natural angular frequency satisfy certain upper bounds, thereby further satisfying some dynamic indicators of the system such as the maximum overshoot, decay time, rise time, and settling time during the transient process. Then how to describe this region? There is a theoretical proof that this region can be characterized by a linear matrix inequality, called the LMI region. A necessary and sufficient condition for the eigenvalues of a matrix to be all in such an LMI region is that an appropriate linear matrix inequality is feasible. Thus, the feedback controller K that makes the poles of the closed-loop system in a certain region of the complex plane can be obtained by solving an effective method that satisfies the linear matrix inequality. u Next, it will be described in detail how to find the appropriate LMI region and obtain the feedback controller K by solving the inequality group that satisfies this LMI region. u .

[0084] How to accurately describe a specific LMI region? The characteristic function of the LMI region is used to describe the LMI region. The definition of the region characteristic function is given below.

[0085] Definition 2:

[0086] For the region D in the complex plane, if there exists a symmetric matrix M ∈ R m×m and a matrix N ∈ Rm×m such that

[0087]

[0088] Then \(E\) is called a linear matrix inequality region (abbreviated as LMI region). The matrix-valued function is called the characteristic function of the LMI region \(D\).

[0089]

[0090] The LMI region sought can, under certain conditions, make the calculated feedback controller \(K_u\) meet the corresponding requirements, that is, it can ensure that the asymmetric large-inertia magnetic levitation rotor system can stably levitate and has good dynamic response characteristics during the speed-up process and within the entire maximum speed range. With the help of the PID cross-feedback control algorithm on the existing laboratory platform, the parameters of the decentralized PID controller are shown in Table 1.

[0091] Table 1

[0092]

[0093] By establishing the mathematical model of the asymmetric large-inertia rotor system and conducting simulation analysis, the system closed-loop pole diagram of the PID cross-feedback control method can be obtained using the Matlab toolbox, and then the corresponding LMI region can be obtained by dividing the closed-loop pole diagram of the PID cross-feedback control method. Analyzing the LMI region divided from the obtained closed-loop system pole diagram, it can be seen that the LMI region is obtained by the intersection of two basic regions:

[0094] The first basic region is the left half-plane where \(x\lt\alpha\)

[0095] \(D\) α =\(\{s\in\mathbb{C}:\text{Re}(s)\lt-\alpha\}\) (17)

[0096] Its characteristic function is:

[0097]

[0098] The second basic region is an open triangular region, which is the part included between two rays starting from the origin in the left half-plane

[0099]

[0100] Its characteristic function is:

[0101]

[0102] The LMI region has been defined and characterized above. The following gives the \(D\)-stability analysis.

[0103] Definition 3:

[0104] For a given LMI region \(D\) in the complex plane and a matrix \(A\in R^{n\times n}\), if all the eigenvalues of matrix \(A\) lie in the region \(D\), that is then matrix \(A\) is said to be \(D\)-stable.

[0105] After giving the above related definitions about the LMI region, for the magnetic bearing rotor system at a fixed rotational speed, the regional pole placement needs to satisfy the following two theorems.

[0106] Theorem 1:

[0107] For the given described LMI region \(D\), then matrix \(A\in R\) n*n is \(D\)-stable if and only if there exists a symmetric positive definite matrix \(X\in R\) n*n , such that

[0108] M D (A, X)<0 (21)

[0109] where:

[0110]

[0111] Theorem 2:

[0112] For two given LMI regions \(D_1\) and \(D_2\), matrix \(A\) is \(D_1\)-stable and \(D_2\)-stable simultaneously if and only if there exists a symmetric positive definite matrix \(X\) such that

[0113] M D1 (A, X)<0, M D2 (A, X)<0 (23)

[0114] The LMI region obtained by the above PID cross-feedback control has obtained the basic graphical shape of the LMI region of the robust control method in this embodiment. In this embodiment, this LMI region is denoted as \(S(\alpha,\theta)\). From the above analysis, this region can be regarded as the intersection of a half-plane region \(D\) with \(\alpha\)-stability degree α and a conical sector \(s(0,\theta)\). According to the definition and theorem, the necessary and sufficient condition for all the eigenvalues of matrix \(A\) p to be in the region \(S(\alpha,\theta)\) is that there exists a symmetric positive definite matrix \(X\) such that

[0115] A p X + XA p T + 2\(\alpha\)X<0 (24)

[0116]

[0117] The state matrix \(A\) described above pThey are all constant matrices. However, in an asymmetric large inertia magnetic levitation rotor system, the rotational speed of the system is constantly changing before reaching the rated speed, and there are different state matrices A at each moment during the speed-up process. p , so the state matrix A of the system p is not a constant matrix but changes with the rotational speed. However, in this embodiment, several state matrices A at different rotational speeds can be selected. p , and it is required that the state matrices A p at these different rotational speeds have their eigenvalues configured into the corresponding LMI regions. The state feedback controller K u obtained by being restricted by these constraint conditions can keep the system stable during the entire speed-up process, thus solving the strong gyroscopic effect. After introducing the state feedback controller K u , the state matrix of the system becomes A p +B p K u .

[0118] According to the definitions and theorems, the necessary and sufficient condition for all eigenvalues of the matrix A p +B p K u to be in the region S(α, θ) is that there exists a symmetric positive definite matrix X such that

[0119] (A pω +B p K u )X + X(A pω +B p K u ) T +2αX < 0 (26)

[0120]

[0121] where A Pω is the different value of the system state matrix A P at different rotational speeds. At a certain moment of rotational speed, the state matrix becomes a constant matrix. Under different rotational speed limit conditions, after the system state matrix becomes a constant matrix, the feedback controller Ku can be obtained through the above definitions and theorems using the LMI toolbox of Matlab. Since the poles of the closed-loop system will move with the change of the rotational speed as a perturbation term, the LMI regions are different at different rotational speeds. The values of the LMI region parameters α and θ are different at different rotational speeds. Table 2 shows the different values of α and θ at different rotational speeds.

[0122] Table 2

[0123]

[0124] It should be noted that although increasing α or decreasing θ can improve the dynamic performance of the system and increase the nutation and precession damping of the system, blindly pursuing the perfection of parameters may lead to Matlab being unable to calculate a feasible solution, and thus unable to find such a feedback controller Ku. Therefore, appropriate parameters should be fully considered to solve for the appropriate feedback controller Ku, and to ensure that the asymmetric large-inertia magnetic levitation rotor system remains stable without instability, thereby avoiding the occurrence of strong gyroscopic effects and solving the problem of system instability caused by parameter perturbation.

[0125] Through the above analysis, all the data required for this embodiment have been fully prepared. Next, only by substituting the system parameters of the asymmetric large-inertia magnetic levitation rotor system can the controller Ku be solved. The parameters of the asymmetric large-inertia magnetic levitation rotor system are shown in Table 3.

[0126] Table 3

[0127]

[0128] After substituting the basic parameters of the asymmetric magnetic levitation rotor system in the above table, the feedback controller Ku can be solved through the LMI toolbox in Matlab. The solution of the LMI region inequality generally includes several key parts. The lmivar function is used to describe the matrix variables that appear in the linear matrix inequality system, and only one matrix variable can be described each time. The description of the matrix variable includes the structure of the matrix variable; the limterm function is used to determine the content of each term in each linear matrix inequality. This is an indispensable part after determining the matrix variable; after the above variable and inequality explanations, the feasp function is used to solve the linear matrix inequality. The specific usage and precautions of the function will not be elaborated here, and relevant materials can be referred to.

[0129] First, solve the controller according to the method mentioned above. From the above constraints, it can be known that the maximum rotational speed of the expected configuration of the asymmetric magnetic levitation system is ωmax = 2π * Frrmax. For the convenience of future narration, the rotational speed of the system is described by frequency in this embodiment. For example Figure 4As shown, since the gyroscopic effect of the asymmetric magnetic levitation system is most obvious when the rotational frequency is around 80 Hz under PID cross-feedback control, that is, the peak-to-peak value of the radial displacement of the system is the largest at this time, and the system is most likely to experience two modes of instability, nutation and precession. In order to compare the control stability of robust control and PID cross-feedback control when the gyroscopic effect is the strongest, the highest rotational speed in this experimental study is set to 200 Hz. It should be noted that the higher the highest rotational speed is set, the more stable the system can be at ultra-high speeds, but it is very likely that the Matlab toolbox cannot find a feasible solution, resulting in the inability to find such a state feedback matrix, thus causing the failure of the robust controller design. For example, when the rotational frequency is 100 Hz, the state space model of the system is known, and the characteristic matrix of the system is as follows:

[0130]

[0131] The other block square matrices of the system state matrix do not change with the rotational speed, and the matrix values are as follows:

[0132]

[0133]

[0134] After knowing the specific values of each matrix of the system state equation, a feasible solution of a state feedback controller can be obtained through the LMI toolbox of Matlab as follows:

[0135]

[0136] Since the sensitivity of the displacement sensor and the sensitivity of the current sensor are included in the controller Ku when establishing the system state space model, the controller parameters actually applied to the DSP program are:

[0137] K uDSP =K u K s -1

[0138] Among them,

[0139]

[0140] To sum up, the controller actually applied to the DSP program that satisfies the above constraints is:

[0141]

[0142] The embodiments described above are only descriptions of the preferred embodiments of this application, and do not limit the scope of this application. Without departing from the design spirit of this application, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of this application shall fall within the protection scope determined by the claims of this application.

Claims

1. The magnetic suspension molecular pump magnetic bearing stable control system is characterized in that Including: A sensor, a control module, an actuator, and a bearing-rotor module; The sensor is used to measure the axial displacement and radial displacement of the bearing-rotor module to obtain a measurement signal; The control module is used to calculate a control signal based on the measurement signal; The core of the control module is a DSP, and the DSP includes: an AD unit, an ECAP unit, an EPWM unit, and a CAN unit; the AD unit is used to convert the analog quantity of current displacement into a digital quantity that can be processed by the DSP; the ECAP unit is used to capture the square wave signal transmitted by the Hall sensor and convert the square wave signal into a corresponding rotational speed value; the EPWM unit is used to convert the digital control quantity generated by the DSP into a PWM signal with a variable duty cycle; the CAN unit is used to ensure the communication between the magnetic levitation molecular pump magnetic bearing stable control system and the upper computer; The actuator is used to generate electromagnetic force based on the control signal; the actuator includes: an optocoupler unit and an H-bridge circuit; the optocoupler unit is used to electrically isolate the control part and the high-power part in the magnetic levitation molecular pump magnetic bearing stable control system; the H-bridge circuit is used to convert the power energy into a PWM voltage with a variable duty cycle under the action of the drive circuit; Define the term that changes with the rotational speed as the parameter perturbation term, and set a state feedback matrix K to suppress the two vortex modes of precession and nutation during the entire speed-up process of the system; the steps include: By restricting the closed-loop system poles to a region in the plane, ensuring that the damping ratio, undamped natural frequency, and natural angular frequency satisfy upper bounds, thereby further meeting the dynamic indices of the system, the dynamic indices including: maximum overshoot, decay time, rise time, and settling time; the method for describing the preset region includes: using a linear matrix inequality to characterize the region, called the LMI region; obtaining a feedback controller K that places the closed-loop system poles in a certain region of the complex plane by solving an effective method that satisfies the linear matrix inequality u ; Next, by finding the LMI region and solving the inequality group that satisfies this LMI region to obtain the feedback controller K u ; The bearing-rotor module is used to support the asymmetric large-inertia rotor based on the electromagnetic force to achieve the stable suspension of the asymmetric large-inertia rotor.

2. The magnetic suspension molecular pump magnetic bearing stable control system according to claim 1, wherein The bearing-rotor module includes: a magnetic bearing and a rotor; The magnetic bearing includes: an axial magnetic bearing and a radial magnetic bearing; The rotor includes: an asymmetric large-inertia magnetic levitation rotor with an impeller.

3. The magnetic suspension molecular pump magnetic bearing stable control system according to claim 2, wherein The axial magnetic bearing is used to control the single-degree-of-freedom translation in the direction of the rotor's inertia axis; the radial magnetic bearing is used to control the two-degree-of-freedom translation and two-degree-of-freedom rotation in the radial direction of the rotor.

4. The magnetic suspension molecular pump magnetic bearing stable control system according to claim 1, characterized in that, The sensor includes an a-end sensor and a b-end sensor; The a-end sensor is located above the centroid of the asymmetric large-inertia magnetic levitation rotor; The b-end sensor is located below the centroid of the asymmetric large-inertia magnetic levitation rotor.

5. The magnetic bearing stable control system of the magnetic levitation molecular pump according to claim 4, characterized in that, The a-end sensor is used to measure the displacement of the asymmetric large-inertia magnetic levitation rotor at the a-end; the b-end sensor is used to measure the displacement of the asymmetric large-inertia magnetic levitation rotor at the b-end.

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