A modeling method for magnetic levitation motor

Abstract

The present invention relates to a magnetic levitation motor modeling method, and proposes a two-point magnetic levitation motor modeling and balance control method. Based on the physical model, a linear mathematical model is established, and then the poles can be arbitrarily configured. The method simplifies the model, the algorithm is simpler than other methods, the computing resource consumption is less, and the required control requirements can be met. It can also be used as a theoretical premise for similar control strategies, and provide certain ideas and methods for improving the characteristics of magnetic levitation motors.

Description

Technical Field

[0001] The invention relates to motor control, and in particular to a magnetic levitation motor modeling method, which is specifically used for controlling the balance of a rotor in the magnetic levitation motor. Background Art

[0002] In order to overcome the lack of mechanical bearings and mechanical friction in traditional rotating motors, various contactless magnetic bearings have been developed to replace mechanical bearings. Typical magnetic bearings include radial magnetic bearings and radial thrust magnetic bearings. Magnetic levitation motors have a series of advantages such as no friction and wear, no lubricating oil pollution, and long life. With the changes in market demand and the recognition of user experience, the number and models of magnetic bearings used will increase in the future.

[0003] In the design of magnetic bearings, in order to achieve higher and better performance requirements, the development of control strategies plays an increasingly important role in the system. The characteristics of magnetic bearings still have a lot of room for control and optimization, which mainly depends on the control strategy used. Taking into account as many factors that affect the balance of magnetic bearings as possible and making the rotor run smoothly is the direction of continuous improvement of control strategies. Summary of the invention

[0004] The purpose of the present invention is to provide a magnetic levitation motor modeling method, which solves the problem of how to quickly adjust the rotor.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] The present invention provides a magnetic levitation motor modeling method, which comprises the following steps:

[0007] S1: Establish a simplified physical model of the two-point magnetic levitation motor, including static equations and dynamic equations;

[0008] S2: Based on the simplified physical model established, a local linearization idea is proposed near the reference point to obtain the system matrix A;

[0009] S3: Linearize the system near the equilibrium point and obtain the input matrix B;

[0010] S4: According to the output of the system, write the output matrix C, and finally get the simplified linear system mathematical model;

[0011] S5: Perform pole configuration on the simplified linear system to obtain the feedback matrix.

[0012] Preferably, based on the tilt state of the rotor in the vertical direction, two points on the rotor are taken for calculation to establish a physical model. , where G is the gravity of the rigid body and the moment of inertia , f1 and f 2 They are the electromagnetic forces generated by the two currents at the two points. , the electromagnetic force formula is as follows:

[0013] ;

[0014] It also satisfies the following physical relationship:

[0015] ;

[0016] Substituting the above equation into the dynamic equation, we can get:

[0017] ;

[0018] Simplified,

[0019] ;

[0020] Take the state variables as follows:

[0021] ;

[0022] Then we have:

[0023]

[0024] Two currents are input quantities, namely , the output is ;

[0025] The general formula of a nonlinear system is , linearize it, and we get

[0026] ;

[0027] Approximately , which can be simplified into the force equation:

[0028] ;

[0029] , and find the other three partial derivatives;

[0030] Finally, the system matrix A is simplified to:

[0031] ;

[0032] Matrix B is linearized at the equilibrium point to obtain

[0033] ;

[0034] Finally, Substituting into the matrix B, it can be simplified to:

[0035] ;

[0036] The output of the system is the displacement Z 1 and Z 2 , then

[0037] ;

[0038] Assume that the values ​​of the unknown parameters are as follows:

[0039] ;

[0040] Substituting the above parameters into the three matrices A, B, and C, we can get

[0041] ;

[0042] The linear state space expression for this problem is

[0043]

[0044] This system is modified and the system poles are configured. Here, state feedback is selected to configure the poles. The eigenvalues ​​of the A matrix obtained from the above code are

[0045] ;

[0046] Assume that the poles of the system are , and get the loading feedback matrix:

[0047] .

[0048] Preferably, before putting the motor control into practice, simulation is performed in Matlab or Simulink to evaluate whether the time it takes for the rotor to reach a balanced state meets the requirements.

[0049] Preferably, the rotor adjustment time is controlled within 0.35-0.45 s.

[0050] Preferably, the setting should achieve an ideal balance , the reference input is .

[0051] Due to the application of the above technical solution, the present invention has the following advantages compared with the prior art:

[0052] The magnetic levitation motor modeling method of the present invention proposes a motor balance control method based on a physical model, converts a complex nonlinear magnetic levitation model into a linear model, and establishes the equation of the linear system. Compared with nonlinearity, the control based on the linear model is faster. By selecting appropriate poles, the poles of the simplified linear system are configured to obtain a feedback matrix, and the magnetic levitation motor model is established simply and effectively, and the purpose of achieving a fast balance state is achieved, thereby realizing the optimized control of the balance of the magnetic levitation motor rotor. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Hereinafter, some specific embodiments of the present invention will be described in detail in an exemplary and non-limiting manner with reference to the accompanying drawings. The same reference numerals in the accompanying drawings indicate the same or similar components or parts. It should be understood by those skilled in the art that these drawings are not necessarily drawn to scale. In the accompanying drawings:

[0054] Figure 1 is a schematic diagram of the model;

[0055] Figure 2 It is a SIMULINK model;

[0056] Figure 3 is the Z1 change image;

[0057] Figure 4 is the Z2 change image. DETAILED DESCRIPTION

[0058] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] First, according to the schematic diagram, a two-point magnetic levitation motor physical model is established. Here, Z1 and Z2 can be measured by displacement sensors.

[0060]

[0061] Among them, G is the gravity of the rigid body, and the moment of inertia , f 1 and f 2 The electromagnetic forces generated by the two currents are , the electromagnetic force formula is as follows:

[0062]

[0063] It also satisfies the following physical relationship:

[0064]

[0065] Substituting the above equation into the dynamic equation, we can get:

[0066]

[0067] Simplified,

[0068]

[0069] Next, we can take the state variables as follows:

[0070]

[0071] Then we have:

[0072]

[0073] Two currents are input quantities, namely , the output is .

[0074] Since the electromagnetic force is a nonlinear function of the current, the system equation is also nonlinear, so it needs to be linearized next.

[0075] The general formula of a nonlinear system is , linearize it, and we get

[0076]

[0077] In this system, it can be approximated that , which can be simplified into the force equation:

[0078]

[0079] because , the other three partial derivatives can be obtained similarly.

[0080] Finally, the system matrix A can be simplified as:

[0081]

[0082] Similarly, matrix B is linearized at the equilibrium point to obtain

[0083]

[0084] Finally, Substituting it into the matrix B, we can simplify it to:

[0085]

[0086] The output of the system is the displacement Z1 and Z 2 , then

[0087]

[0088] Assume that the values ​​of the unknown parameters are as follows:

[0089]

[0090] Substituting the above parameters into the three matrices A, B, and C, we can get

[0091]

[0092] The linear state space expression for this problem is

[0093]

[0094] Transform this system and configure the system poles. Here, select state feedback to configure the poles. From the above code, we can get the eigenvalues ​​of the A matrix as

[0095]

[0096] Assume that the poles of the system are . Get the loading feedback matrix:

[0097]

[0098] Establish the entire nonlinear system and state feedback SIMULINK model as follows Figure 2 shown.

[0099] In this example, to achieve the ideal balance , the reference input is .

[0100] The output changes as follows Figure 3 and 4 As shown in the figure. From the final Z1 and Z2 change images, they finally converged to 0.015. From the time required, it takes about 0.4S. Both time and effect are good.

[0101] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with this technology to understand the contents of the present invention and implement them accordingly. They cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A magnetic levitation motor modeling method, which The following steps are involved: S1: Establish a simplified physical model of the two-point magnetic levitation motor, including static equations and dynamic equations; S2: Based on the simplified physical model established, a local linearization idea is proposed near the reference point to obtain the system matrix A; S3: Linearize the system near the equilibrium point and obtain the input matrix B; S4: According to the output of the system, write the output matrix C, and finally get the simplified linear system mathematical model; S5: Perform pole configuration on the simplified linear system to obtain the feedback matrix Based on the tilt state of the rotor in the vertical direction, two points on the rotor are taken for calculation to establish a simplified physical model. , where G is the gravity of the rigid body and the moment of inertia , f 1 and f 2 They are the electromagnetic forces generated by the two currents at the two points. , the electromagnetic force formula is as follows: ； It also satisfies the following physical relationship: ； Substituting the above equation into the dynamic equation, we can get: ； Simplified, ； Take the state variables as follows: ； Then we have: Two currents are input quantities, namely , the output is ; The general formula of a nonlinear system is , linearize it, and we get ； Approximately , which can be simplified into the force equation: ； , and find the other three partial derivatives; Finally, the system matrix A is simplified to: ； Matrix B is linearized at the equilibrium point to obtain ； Finally, Substituting into the matrix B, it can be simplified to: ； The output of the system is the displacement Z 1 and Z 2 , then ； Assume that the values ​​of the unknown parameters are as follows: ； Substituting the above parameters into the three matrices A, B, and C, we can get ； The linear state space expression for this problem is This system is modified and the system poles are configured. Here, state feedback is selected to configure the poles, and the eigenvalue of the A matrix is ​​obtained as ； Assume that the poles of the system are , and get the loading feedback matrix: 。 2. The magnetic levitation motor modeling method according to claim 1, Features: Before putting the motor control into practice, simulate in Matlab or Simulink to evaluate whether the time it takes for the rotor to reach a balanced state meets the requirements.

3. The magnetic levitation motor modeling method according to claim 1, Features: Control the rotor adjustment time within 0.35-0.45s.

4. The magnetic levitation motor modeling method according to claim 1, Features: Setting the ideal balance , the reference input is .

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