阅读说明：本技术 一种五自由度磁轴承的智能双积分滑模控制方法及设备 (Intelligent double-integral sliding mode control method and equipment for five-degree-of-freedom magnetic bearing ) 是由 禄盛 史军辉 赵洋 朴昌浩 陈翔 于 2019-10-08 设计创作，主要内容包括：本发明公开了一种五自由度主动磁悬浮轴承的智能双积分滑模控制方法及设备,所述方法包括：计算五自由度主动磁悬浮轴承系统的动态模型,使用分散控制器将五自由度主动磁悬浮轴承系统的动态模型解耦为五个独立的子系统,使用改进比例-积分-微分神经网络MPIDNN观测器计算五个子系统的第一输出,使用智能双积分滑模控制器计算五个子系统的第二输出,利用所述五个子系统的第二输出来控制五自由度主动磁悬浮轴承转子的位置,本发明能够减轻主动磁悬浮轴承系统的抖振,提高控制精度,具有更强的稳定性。(The invention discloses an intelligent double-integral sliding mode control method and equipment for a five-degree-of-freedom active magnetic suspension bearing, wherein the method comprises the following steps: the method comprises the steps of calculating a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system, decoupling the dynamic model of the five-degree-of-freedom active magnetic suspension bearing system into five independent subsystems by using a dispersion controller, calculating first outputs of the five subsystems by using an improved proportional-integral-derivative neural network MPIDNN observer, calculating second outputs of the five subsystems by using an intelligent double-integral sliding mode controller, and controlling the position of a rotor of the five-degree-of-freedom active magnetic suspension bearing by using the second outputs of the five subsystems.)

1. An intelligent double-integral sliding mode control method of a five-degree-of-freedom active magnetic suspension bearing is characterized by comprising the following steps of:

step 1, establishing a mathematical model of the five-degree-of-freedom active magnetic suspension bearing system according to the five-degree-of-freedom active magnetic suspension bearing system to obtain a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system;

step 2, decoupling the dynamic model of the five-freedom-degree active magnetic suspension bearing system into five independent subsystems by using a decentralized controller, wherein the five independent subsystems comprise x of the left-side radial active magnetic suspension bearing₁、y₁Two radial subsystems, x of the right-hand radial active magnetic suspension bearing₂、y₂Two radial subsystems and a z-axis subsystem of the thrust active magnetic suspension bearing;

step 3, calculating first outputs of the five subsystems by using an improved proportional-integral-derivative neural network MPIDNN observer;

and 4, calculating second outputs of the five subsystems by using an intelligent double-integral sliding mode controller according to the first outputs of the five subsystems calculated by the improved proportional-integral-derivative neural network MPIDNN observer, and controlling the position of the five-degree-of-freedom active magnetic suspension bearing rotor by using the second outputs of the five subsystems.

2. The method of claim 1, wherein step 1 comprises:

according to the dynamic model of the rotor of the five-freedom-degree active magnetic suspension bearing system about the gravity center motion, calculating the dynamic model of the five-freedom-degree active magnetic suspension bearing system and expressing as follows:

wherein the content of the first and second substances,

3. The method of claim 1, wherein step 2 comprises:

decoupling a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system, wherein the decoupled model is obtained by:

wherein the content of the first and second substances,

4. The method of claim 1, wherein step 3 comprises:

an optimal improved proportional-integral-derivative neural network MPIDNN observer is established, and the output expression of the observer is as follows:

y＝y^*(e|W^*)+ε＝W^*TO+ε，

wherein, y^*Is an observation target, e is an adjustment error, W^*Is the best weighted vector, T is the transpose operation, ε is the minimum reconstruction error, O is the hidden layer output;

the first outputs of the five subsystems are calculated using the optimal mpidn observer as:

wherein the content of the first and second substances,

5. The method of claim 1, wherein step 4 comprises:

step 401, calculate robust controller U_rThe output of (t) is:

wherein, B_n ^-1Is the inverse of the system parameter nominal value matrix,

step 402, calculating second outputs of the five subsystems as:

U_IDISMC(t)＝U_r(t)+U_y(t)，

wherein, U_r(t) is the output of the robust controller, U_y(t) first outputs of five subsystems calculated for the mpidn observer;

and 403, simultaneously and independently controlling the position of the five-degree-of-freedom active magnetic suspension bearing rotor by using the corresponding second outputs of the five subsystems.

6. The utility model provides an intelligent double integral sliding mode controlgear of five degrees of freedom initiative magnetic suspension bearings, is connected with five degrees of freedom initiative magnetic suspension bearings, its characterized in that includes:

the dynamic model establishing module is used for establishing a mathematical model of the five-degree-of-freedom active magnetic suspension bearing system according to the five-degree-of-freedom active magnetic suspension bearing system to obtain a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system;

a decentralized controller for decoupling the dynamic model of the five-degree-of-freedom active magnetic suspension bearing system into five independent subsystems including x of the left-side radial active magnetic suspension bearing₁、y₁Two radial subsystems, x of the right-hand radial active magnetic suspension bearing₂、y₂Two radial subsystems and a z-axis subsystem of the thrust active magnetic suspension bearing;

the improved proportional-integral-derivative neural network MPIDNN observer is used for calculating first outputs of the five subsystems;

the intelligent double-integral sliding mode controller is used for calculating second outputs of the five subsystems according to the first outputs of the five subsystems calculated by the MPIDNN observer, and controlling the position of the five-degree-of-freedom active magnetic suspension bearing rotor by utilizing the second outputs of the five subsystems.

7. The apparatus of claim 6, wherein the dynamic model building module is configured to:

according to the dynamic model of the rotor of the five-freedom-degree active magnetic suspension bearing system about the gravity center motion, calculating the dynamic model of the five-freedom-degree active magnetic suspension bearing system and expressing as follows:

wherein the content of the first and second substances,

8. The apparatus of claim 6, wherein the decentralized controller is configured to:

decoupling a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system, wherein the decoupled model is obtained by:

wherein the content of the first and second substances,

9. The device of claim 6, wherein the MPIDNN observer is configured to:

an optimal improved proportional-integral-derivative neural network MPIDNN observer is established, and the output expression of the observer is as follows:

y＝y^*(e|W^*)+ε＝W^*TO+ε，

wherein, y^*Is an observation target, e is an adjustment error, W^*Is the best weighted vector, T is the transpose operation, ε is the minimum reconstruction error, O is the hidden layer output;

the first outputs of the five subsystems are calculated using the optimal mpidn observer as:

wherein the content of the first and second substances,

10. The apparatus of claim 6, wherein the intelligent double-integration sliding-mode controller is configured to:

robust controller U for calculation_rThe output of (t) is:

wherein, B_n ^-1Is the inverse of the system parameter nominal value matrix,as second derivative of the reference position, A_nx (t) is the product of the system parameter nominal value matrix and the actual displacement of the five-freedom active magnetic suspension bearing rotor,

calculating second outputs of the five subsystems as follows by using an intelligent double-integral sliding mode controller:

U_IDISMC(t)＝U_r(t)+U_y(t)，

wherein, U_r(t) is the output of the robust controller, U_y(t) first outputs of five subsystems calculated for the mpidn observer;

and simultaneously and independently controlling the position of the five-freedom-degree active magnetic suspension bearing rotor by utilizing the corresponding second outputs of the five subsystems.

Technical Field

The invention relates to the field of magnetic suspension bearing control, in particular to an intelligent double-integral sliding mode control method and equipment for a five-degree-of-freedom active magnetic suspension bearing.

Background

An active magnetic suspension bearing (active magnetic bearing) is a new type of bearing that stably suspends a rotor at a predetermined position and supports the rotation of the rotor by controlled electromagnetic force. Based on the non-contact and friction-free characteristics, the active magnetic suspension bearing has more advantages than the traditional bearing, such as longer service life, lower friction loss during rotation, higher rotating speed, no need of lubrication and the like.

The control performance of the active magnetic suspension bearing is an important aspect of magnetic suspension bearing research, and the quality of the control performance determines the quality of the active magnetic suspension bearing. Since the active magnetic bearing system is a typical nonlinear system, an excellent control method is required for control.

The mode-change structure control has strong anti-interference capability, and is particularly suitable for state identification and control of a nonlinear system, so that the mode-change structure control is widely researched. The integral sliding mode control method was earlier applied to active magnetic bearings, but the method does not perform particularly well in terms of stability.

Disclosure of Invention

The invention provides an intelligent double-integral sliding mode control method and equipment for a five-degree-of-freedom active magnetic suspension bearing, aiming at solving the problems.

According to one aspect of the invention, an intelligent double-integral sliding mode control method for a five-degree-of-freedom active magnetic suspension bearing is provided, which comprises the following steps:

step 1, establishing a mathematical model of the five-degree-of-freedom active magnetic suspension bearing system according to the five-degree-of-freedom active magnetic suspension bearing system to obtain a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system;

step 2, decoupling the dynamic model of the five-freedom-degree active magnetic suspension bearing system into five independent subsystems by using a decentralized controller, wherein the five independent subsystems comprise x of the left-side radial active magnetic suspension bearing₁、y₁Two radial subsystems, x of the right-hand radial active magnetic suspension bearing₂、y₂Two radial subsystems and a z-axis subsystem of the thrust active magnetic suspension bearing;

step 3, calculating first outputs of the five subsystems by using an improved proportional-integral-derivative neural network MPIDNN observer;

and 4, calculating second outputs of the five subsystems by using an intelligent double-integral sliding mode controller according to the first outputs of the five subsystems calculated by the MPIDNN observer, and controlling the position of the five-degree-of-freedom active magnetic suspension bearing rotor by using the second outputs of the five subsystems.

According to another aspect of the invention, an intelligent double-integral sliding mode control device of a five-degree-of-freedom active magnetic suspension bearing is provided, which comprises:

the dynamic model establishing module is used for establishing a mathematical model of the five-degree-of-freedom active magnetic suspension bearing system according to the five-degree-of-freedom active magnetic suspension bearing system to obtain a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system;

a decentralized controller for decoupling the dynamic model of the five-degree-of-freedom active magnetic suspension bearing system into five independent subsystems including x of the left-side radial active magnetic suspension bearing₁、y₁Two radial subsystems, x of the right-hand radial active magnetic suspension bearing₂、y₂Two radial subsystems and a z-axis subsystem of the thrust active magnetic suspension bearing;

the improved proportional-integral-derivative neural network MPIDNN observer is used for calculating first outputs of the five subsystems;

the intelligent double-integral sliding mode controller is used for calculating second outputs of the five subsystems according to the first outputs of the five subsystems calculated by the MPIDNN observer, and controlling the position of the five-degree-of-freedom active magnetic suspension bearing rotor by utilizing the second outputs of the five subsystems.

The invention provides an intelligent double-integral sliding mode control method and equipment for a five-degree-of-freedom active magnetic suspension bearing, which are characterized in that an MPIDNN observer with four accurate functions in a hidden layer is connected to an intelligent double-integral sliding mode controller to complete the design of the intelligent double-integral sliding mode controller with self-adaptive PID control gain and online centralized uncertainty observation. The intelligent double-integral sliding mode controller provided by the invention combines the advantages of integral sliding mode control, self-adaptive control and a neural network, can reduce buffeting of an active magnetic suspension bearing system, improves control precision and has stronger stability.

Drawings

Fig. 1 is a flowchart of an intelligent double-integral sliding mode control method for a five-degree-of-freedom active magnetic suspension bearing according to an embodiment of the present invention;

FIG. 2 is a geometric diagram of a rotor of a five-degree-of-freedom active magnetic suspension bearing system according to an embodiment of the present invention;

fig. 3 is a network architecture diagram of an mpidn observer according to an embodiment of the present invention;

fig. 4 is a structural diagram of an intelligent double-integral sliding mode control device of a five-degree-of-freedom active magnetic suspension bearing according to an embodiment of the present invention;

fig. 5 is a structural diagram of another intelligent double-integral sliding mode control device for a five-degree-of-freedom active magnetic suspension bearing according to an embodiment of the present invention.

Detailed Description

The following description of specific embodiments of the present invention is provided to further illustrate the starting points and corresponding technical solutions of the present invention.

Fig. 1 is a flowchart of an intelligent double-integral sliding mode control method for a five-degree-of-freedom active magnetic suspension bearing according to an embodiment of the present invention, where the method includes the following steps:

step 101, establishing a mathematical model according to the five-degree-of-freedom active magnetic suspension bearing system to obtain a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system.

For a rotor with rigid and symmetric characteristics, the relationship between the gravity center CG of the rotor and the five-DOF active magnetic suspension bearing is shown in FIG. 2, where m is the mass of the rotor, g is the gravitational constant, and x is_c、y_cAnd z_cIs the coordinate of the center of gravity of the rotor, f₁To f₁₀Ten electromagnetic forces, f, generated by five pairs of electromagnets_dx、f_dyAnd f_dzIs the external disturbance force of the rotor corresponding to the X-Y-Z axis_x、θ_yAnd theta_zShowing the deflection and rotation angle around the X-Y-Z axis of the rotor, a, b and c showing the radial active magnetic bearing from CG to the left, right respectivelyAnd the distance between the side radial active magnetic suspension bearing and the external disturbance, wherein l is a + b. Notably, when the rotor is stabilized at the reference position (x)_c＝y_c＝z_c＝θ_x＝θ_y0), the rotational speed of the rotor is available

And (4) showing.

The control characteristics of a five-degree-of-freedom active magnetic suspension bearing system are highly non-linear and time-varying because of system parameter variations, external disturbances and inherent non-linearities, such as coupling effects between five axes and gyroscopic effects. Thus, the rotor position x of a five-degree-of-freedom active magnetic bearing system₁、x₂、y₁、y₂And z is affected by it.

The dynamic model of the five-degree-of-freedom active magnetic suspension bearing system rotor about the motion of the gravity center thereof can be expressed as follows:

wherein J is the transverse moment of inertia of the rotor about the X-Y axis, J_zIs the polar moment of inertia of the rotor about the Z axis,

as a parameter related to gyroscopic effect, F_x1，F_x2，F_y1,F_y2,F_zIs the total electromagnetic attraction of the axes.

The total electromagnetic attraction force of each axis can be represented by the following linear electromagnetic force model:

wherein the content of the first and second substances,

is the control current in the X direction of the left radial active magnetic suspension bearing,

is the control current in the X direction of the right radial active magnetic suspension bearing,

is the control current in the Y direction of the left radial active magnetic suspension bearing,

is the control current i in the Y direction of the right radial active magnetic suspension bearing_zIs the control current k in the Z direction of the five-freedom active magnetic suspension bearing_rp,k_riForce-displacement stiffness coefficient and force-current stiffness coefficient, k, in X direction and Y direction of five-degree-of-freedom active magnetic suspension bearing_ap,k_aiThe five-degree-of-freedom active magnetic suspension bearing is a force-displacement stiffness coefficient and a force-current stiffness coefficient in the Z direction.

Since the rotor is rigid and has a small displacement, the rotor position (x)₁,x₂,y₁,y₂) Coordinates (x) of center of gravity of rotor_c,y_c,z_c) Can be expressed as follows:

the formula (1) is substituted by the formula (2), the formula (3), the formula (4) and the formula (5), and the obtained dynamic model of the five-degree-of-freedom active magnetic suspension bearing system can be expressed as follows:

wherein the electromagnetic force vector

External interference vector D ═ f_dxf_dyf_dz]^TThe gravity vector C ═ 00-1-10]^T，G,K,ERespectively a gyro effect matrix, an electromagnetic force matrix and an external disturbance matrix.

Gyro effect matrixGElectromagnetic force matrixKAnd external disturbancesEThe matrix is defined as follows:

wherein alpha is₁＝aJ_zω/Jl,α₂＝bJ_zω/Jl,β₁＝(1/m)+(a²/J),β₂＝(1/m)-(ab/J),β₃＝(1/m)+(b²/J),β₄＝1/m,γ₁＝(1/m)-(ac/J),γ₂＝(1/m)+(bc/J),γ₃＝(1/m)。

Observation matrixGAndKthe coupling effect is severe in the five-degree-of-freedom active magnetic suspension bearing system, and therefore, a decoupling operation is further required.

102, decoupling a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system into five independent subsystems including x of the left-side radial active magnetic suspension bearing by using a decentralized controller₁、y₁Two radial subsystems, x of the right-hand radial active magnetic suspension bearing₂、y₂Two radial subsystems, and a z-axis subsystem of the thrust active magnetic suspension bearing.

In order to realize the distributed control, the dynamic model of the five-freedom-degree active magnetic suspension bearing system is decoupled into five independent subsystems, including x₁、x₂、y₁And y₂Four radial subsystems and one z axial subsystem.

Preferably, in order to decouple the original dynamic model equation (6) as the dynamic model of the five independent subsystems under distributed control, equation (6) may be further rewritten as equation (7), and the decoupled model is as follows:

wherein the content of the first and second substances,is a vector of coupling terms that is ignored,

is a vector of the control current that is,M、AandBrespectively, the mass, stiffness and control gain matrices, and are defined as follows:

due to the state of the dynamic model in a diagonal matrixM、AAndBaspects are fully decoupled, therefore, the proposed decentralized controller can be easily applied to decoupled dynamic models to control the rotor position x at the center simultaneously and separately₁、x₂、y₁、y₂And z.

Step 103, calculating first outputs of the five subsystems by using the modified proportional-integral-derivative neural network MPIDNN observer.

Fig. 3 is a network structure diagram of an mpinn observer according to an embodiment of the present invention, where the used architecture of the mpinn observer includes an input layer (a first layer), an implicit layer (a second layer), and an output layer (a third layer).

First layer (input layer) of the mpidn observer:

the input of MPIDNN is designed as e₁(N) e (N) and

where N represents the nth iteration.

Second layer (hidden layer) of the mpidn observer:

the input to the hidden layer is expressed as a performance index u_j(N)：

Wherein the content of the first and second substances,

is the connection weight between the input layer and the hidden layer, and j is the number of layers of the hidden layer.

Implicit layer o of observation path with corresponding P control, I control, D control and centralized uncertainty_jThe outputs of (N) are calculated as follows:

wherein f is_P,f_I,f_D,f_LP control, I control, D control and centralized uncertainty observation functions.

Third layer (output layer) of the mpidn observer:

output of MPIDNCan be obtained as follows:

wherein the content of the first and second substances,

the weight of the connection between the hidden layer and the output layer.

The first three products of the outputs of MPIDNN shown in equation (8)

Can be considered as an improved PID control, wherein

And

respectively PID control gain K_P、K_IAnd K_D. The final product shown in equation (8)

For observing the central uncertainty-L (x; t), i.e. defined in L (x; t)Wherein

Is the central uncertainty observation gain, denoted as K_L. Therefore, using the MPIDNN observer

The output of (a) can be used to observe an observation target y defined in the intelligent double-integration sliding mode controller, and is expressed as follows:

therefore, the designed MPIDNN observer can perform ingenious mapping between the network architecture and the observation target. Not only PID controls gain K according to online learning of MPIDNN_P、K_IAnd K_DIs real-time adaptive, and the on-line observation is centralized with uncertainty L. Output equation (9) for mpidn is further rewritten as:

wherein O is [ O ═ O₁o₂o₃o₄]^TAnd

preferably, by the general approximation theorem, there is an optimal mpidn observer of the form (11) as follows:

y＝y^*(e|W^*)+ε＝W^*TO+ε (11)

wherein, y^*Is an watchTarget, e is the adjustment error, W^*Is the best weighted vector, T is the transpose operation, epsilon is the minimum reconstruction error, and O is the hidden layer output.

Assuming that the absolute value ε is greater than the normal value δ_εSmaller, i.e. | ε | < δ_ε. During the observed iterations, the best weighting vector W is assumed^*And the minimum reconstruction error epsilon is constant. The above assumption is valid in the actual digital processing of the observer because of the comparison with W^*The sampling period, i.e. the execution interval of the observer program, is sufficiently short compared to the variation of epsilon.

Using the established optimal mpidn observer, calculating the first outputs of the five subsystems as:

wherein the five subsystems are x₁、x₂、y₁And y₂Four radial subsystems and one z axial subsystem,

is the inverse of the system parameter nominal value matrix,

for the linear regression of the best output of the MPIDNN observer, t is a time variable.

In the proposed mpidn, the regulation error and the derivative of the regulation error are considered as indicators to obtain faster and more accurate control performance. Compared to a conventional neural network NN, the proposed mpidn has a more compact structure and a simpler inference algorithm.

And 104, calculating second outputs of the five subsystems by using an intelligent double-integral sliding mode controller according to the first outputs of the five subsystems calculated by the MPIDNN observer, and controlling the position of the five-degree-of-freedom active magnetic suspension bearing rotor by using the second outputs of the five subsystems.

By using the MPIDNN observer, intelligent double-integral sliding mode control has the capability of adaptively controlling gain and concentrating uncertainty observation on line.

The standard second-order state equation of the subsystem of the five-degree-of-freedom active magnetic suspension bearing is as follows:

wherein x (t) is the system state, A, B are the nominal values of the system parameters, h (t) is the ignored coupling term, and U (t) is the control law.

If the control law U is designed to obtain x₁Of shaft-active magnetic suspension bearing subsystems

Then the equation x is x₁、A＝k_rpβ₁、B＝k_riβ₁And

remain unchanged. Furthermore, since it is difficult to obtain accurate values of the system parameter A, B and the neglected coupling term h in practical applications, the overwrite dynamic pattern (13) is as follows, taking into account the separation of the nominal parameters and the parameter variations:

wherein the content of the first and second substances,

A_n,B_nis a matrix of nominal values of the system parameters A (t) and B (t), Δ A (x; t), Δ B (x; t) change of the system parameters with time, t is a time variable, L (x; t) is a centralized uncertainty defined as:

L(x；t)＝ΔA(x；t)x(t)+ΔB(x；t)U(t)+h(t)

the bound for the lumped uncertainty has been fixed and satisfies the inequality as follows:

|L(x；t)|＜δ

wherein, delta is a normal number and is used as the control gain of integral sliding mode control.

To improve steady state control performance, a double integral sliding mode is defined as follows:

wherein e (t) is an adjustment error,

to adjust the first derivative of the error, t is a time variable, and c is a parameter₁、c₂And c₃Gains K for D-control, P-control and I-control, which can be considered PID-control, respectively_D、K_PAnd K_IAnd has a great influence on the control performance.

s₂(t) is derived with respect to time and can be obtained according to equation (14):

wherein the content of the first and second substances,

as second derivative of the reference position, A_n,B_nAnd respectively, respectively using a system parameter nominal value matrix, wherein L (x; t) is centralized uncertainty, x (t) is actual displacement of the five-freedom-degree active magnetic suspension bearing rotor, and U (t) is a control law.

In order to realize the stability of the active magnetic suspension bearing subsystem, the control law of ideal intelligent double-integral sliding mode control is designed as follows:

wherein, B_n ^-1Is the inverse of the system parameter nominal value matrix,

as second derivative of the reference position, A_nx (t) is a system parameter nominal value matrix and five-degree-of-freedom active magnetProduct of the actual displacements of the suspension bearing rotor, s₂And (t) is a double-integral sliding mode surface, delta is a normal number and is used as a control gain of integral sliding mode control, and sat () is a saturation function.

Intelligent double integral sliding mode control for ideal observation and integral term

Embedded in the double integral slip-form surface. Due to integral termIs only reflected in the control lawIn equation (16), therefore, ideal smart double-integration sliding-mode control with I control feature can improve steady-state error performance.

Control law with integral term as shown in equation (16)

In practical application, saturation control is easy to cause, and the control parameters of ideal intelligent double-integral sliding mode control comprise c₁、c₂、c₃δ and the function sat (), it is very difficult to design these parameters as a whole. Therefore, the mpidn observer needs to be used to adjust the control gain K of the ideal intelligent double-integral sliding mode control_P、K_IAnd K_DAnd simultaneously observing the centralized uncertainty L of the active magnetic suspension bearing subsystem. The optimal output of the mpidn observer, also called the observation target, consists of a constant PID control gain and an unknown centralized uncertainty, defined as follows:

wherein e (t) is an adjustment error,

to adjust the first derivative of the error, t is a time variable, and c is a parameter₁、c₂And c₃Gains K for D-control, P-control and I-control, which can be considered PID-control, respectively_D、K_PAnd K_IAnd L (x; t) is the uncertainty of convergence.

Preferably, step 104 specifically includes the following steps:

step 104-1, calculate robust controller U_rThe output of (t) is:

wherein the robust controller U_r(t) is represented by the formula of the adaptation lawThe design is carried out so as to obtain the product,linear regression as minimum reconstruction error

First derivative of, η_εIs an adaptive coefficient related to the minimum reconstruction error, B_n ^-1Is the inverse of the system parameter nominal value matrix,

as second derivative of the reference position, A_nx (t) is the product of the system parameter nominal value matrix and the actual displacement of the five-freedom active magnetic suspension bearing rotor,

linear regression for minimum reconstruction error, ξ is the uncertainty gain, s₂(t) is a double integral sliding mode surface, and t is a time variable;

step 104-2, calculating second outputs of the five subsystems by using the intelligent double-integral sliding mode controller as follows:

U_IDISMC(t)＝U_r(t)+U_y(t) (19)

wherein, U_r(t) is the output of the robust controller, U_y(t) first outputs of the five subsystems calculated by the mpidn observer in step 103;

and step 104-3, controlling the position of the five-degree-of-freedom active magnetic suspension bearing rotor simultaneously and independently by utilizing the second outputs corresponding to the five subsystems.

The invention aims to provide an intelligent double-integral sliding mode control method of a five-degree-of-freedom active magnetic suspension bearing, which can reduce buffeting of an active magnetic suspension bearing system, improve control precision and have stronger stability. The method provided by the invention is proved to have asymptotic stability by a Lyapunov function.

Fig. 4 is a structural diagram of an intelligent double-integral sliding mode control apparatus for a five-degree-of-freedom active magnetic suspension bearing, provided by an embodiment of the present invention, where the apparatus includes the following modules:

the dynamic model establishing module 401 is configured to establish a mathematical model of the five-degree-of-freedom active magnetic suspension bearing system according to the five-degree-of-freedom active magnetic suspension bearing system to obtain a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system;

a decentralized controller 402 for decoupling the dynamic model of the five-degree-of-freedom active magnetic suspension bearing system into five independent subsystems, including x for the left-hand radial active magnetic suspension bearing₁、y₁Two radial subsystems, x of the right-hand radial active magnetic suspension bearing₂、y₂Two radial subsystems and a z-axis subsystem of the thrust active magnetic suspension bearing;

a modified proportional-integral-derivative neural network MPIDNN observer 403 for calculating first outputs of the five subsystems;

and the intelligent double-integral sliding mode controller 404 is used for calculating second outputs of the five subsystems according to the first outputs of the five subsystems calculated by the MPIDNN observer, and controlling the position of the five-degree-of-freedom active magnetic suspension bearing rotor by using the second outputs of the five subsystems.

The control process of the intelligent double-integral sliding mode control equipment of the five-degree-of-freedom active magnetic suspension bearing provided by the embodiment of the invention can refer to the intelligent double-integral sliding mode control method of the five-degree-of-freedom active magnetic suspension bearing.

Preferably, the dynamic model establishing module 401 is specifically configured to:

according to the dynamic model of the rotor of the five-freedom-degree active magnetic suspension bearing system about the gravity center motion, calculating the dynamic model of the five-freedom-degree active magnetic suspension bearing system and expressing as follows:

wherein the content of the first and second substances,

is a second derivative vector of the rotor displacement of the five-degree-of-freedom active magnetic suspension bearing,is a first derivative vector of the displacement of a rotor of the five-degree-of-freedom active magnetic suspension bearing, F is an electromagnetic force vector, D is an external interference vector, C is a gravity vector,M，G,K,Erespectively a mass matrix, a gyro effect matrix, an electromagnetic force matrix and an external disturbance matrix, and g is a gravity constant.

Preferably, the distributed controller 402 is specifically configured to:

decoupling a dynamic model of the five-degree-of-freedom active magnetic suspension bearing system, wherein the decoupled model is obtained by:

wherein the content of the first and second substances,

is a second derivative vector of the rotor displacement of the five-freedom-degree active magnetic suspension bearing, X is the rotor displacement vector of the five-freedom-degree active magnetic suspension bearing, H is a neglected coupling term vector, U is a control current vector,M、AandBrespectively a mass matrix, a stiffness matrix and a control gain matrix.

Preferably, the mpidn observer 403 is specifically configured to:

an optimal improved proportional-integral-derivative neural network MPIDNN observer is established, and the output expression of the observer is as follows:

y＝y^*(e|W^*)+ε＝W^*TO+ε，

wherein, y^*Is an observation target, e is an adjustment error, W^*Is the best weighted vector, T is the transpose operation, ε is the minimum reconstruction error, O is the hidden layer output;

the first outputs of the five subsystems are calculated using the optimal mpidn observer as:

wherein the content of the first and second substances,

is the inverse of the system parameter nominal value matrix,

linear regression of the best output of the mpidn observer.

Preferably, the intelligent double-integration sliding mode controller 404 is specifically configured to:

robust controller U for calculation_rThe output of (t) is:

wherein, B_n ^-1Is the inverse of the system parameter nominal value matrix,

as second derivative of the reference position, A_nx (t) is the product of the system parameter nominal value matrix and the actual displacement of the five-freedom active magnetic suspension bearing rotor,

linear regression, ξ, for minimal reconstruction errorFor uncertainty gain, s₂(t) is a double integral sliding mode surface, and t is a time variable;

calculating second outputs of the five subsystems as follows by using an intelligent double-integral sliding mode controller:

U_IDISMC(t)＝U_r(t)+U_y(t)，

wherein, U_r(t) is the output of the robust controller, U_y(t) first outputs of five subsystems calculated for the mpidn observer;

and simultaneously and independently controlling the position of the five-freedom-degree active magnetic suspension bearing rotor by utilizing the corresponding second outputs of the five subsystems.

Fig. 5 is a structural diagram of another intelligent double-integral sliding mode control device for a five-degree-of-freedom active magnetic suspension bearing according to an embodiment of the present invention. The displacement sensor detects the actual displacement x of the rotor and then compares it with a reference position x_dComparing to obtain a displacement difference, inputting the displacement difference into a double-integral sliding mode surface for integral calculation and an MPIDN observer respectively, inputting the calculated result of the double-integral sliding mode surface into an adaptive law and calculating through a learning algorithm respectively, inputting the calculated result into a robust controller, an adaptive PID control gain and an online observation centralized uncertainty respectively, obtaining the input of the control law through calculation, and combining an intelligent double-integral sliding mode controller U_IDISMCThe control signal is obtained and input into a second-order system, the control signal is converted into control current through a power amplifier, a new actual displacement x can be obtained according to the action of electromagnetic force generated by the control current on the rotor, and the steps are repeated, so that the rotor can be stabilized at a reference position finally, and the purpose of stable control is achieved.

Compared with the common integral sliding mode control, the intelligent double-integral sliding mode control method and the intelligent double-integral sliding mode control device for the five-degree-of-freedom active magnetic suspension bearing have the capability of I control enhancement, and can more directly and effectively deal with steady-state errors. Meanwhile, in order to solve the problem that several control parameters of the intelligent double-integral sliding mode controller are very difficult to design, an MPIDNN observer with four accurate functions in a hidden layer is designed and connected to the intelligent double-integral sliding mode controller, so that the design of the intelligent double-integral sliding mode controller with self-adaptive PID control gain and online centralized uncertainty observation is completed. The intelligent double-integral sliding mode controller provided by the invention combines the advantages of integral sliding mode control, self-adaptive control and a neural network. Furthermore, the proposed controller can be easily applied to other second order systems represented by the general form shown in equation (13).

While the invention has been described in connection with specific embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.