阅读说明：本技术 一种基于微分几何解耦控制的无轴承异步电机径向力悬浮控制系统 (A kind of induction-type bearingless motor radial force suspension control system based on differential geometrical decoupled control ) 是由 杨泽斌 王丁 孙晓东 贾培杰 梅海涛 吴家杰 于 2019-07-05 设计创作，主要内容包括：本发明公开了一种基于微分几何解耦控制的无轴承异步电机径向力悬浮控制系统,包括微分几何控制器和复合被控对象,微分几何控制器包括线性闭环控制器和精确线性化解耦系统,复合被控对象的输出反馈到线性闭环控制器的输入,线性闭环控制器的输出连接精确线性化解耦系统的输入,精确线性化解耦系统的输出连接复合被控对象的输入；通过微分几何解耦控制器,将非线性、多变量、强耦合的无轴承异步电机径向力悬浮子系统解耦为两个位移二阶积分线性子系统,实现了非线性系统的精确线性化,将复杂的非线性问题转换到线性问题来进行解决,大大减小了控制难度。(The invention discloses a kind of induction-type bearingless motor radial force suspension control system based on differential geometrical decoupled control, including differential geometry control device and composite controlled object, differential geometry control device includes linear closed-loop controller and exact linearization method decoupled system, the output feedback of composite controlled object arrives the input of linear closed-loop controller, the input of the output connection exact linearization method decoupled system of linear closed-loop controller, the input of the output connection composite controlled object of exact linearization method decoupled system；Pass through differential geometrical decoupled control device, it is two displacement Second Order Integral linear subsystems by the induction-type bearingless motor radial force Suspension Subsystem decoupling of non-linear, multivariable, close coupling, realize the exact linearization method of nonlinear system, complicated nonlinear problem is transformed into linear problem to solve, substantially reduces control difficulty.)

1. a kind of induction-type bearingless motor radial force suspension control system based on differential geometrical decoupled control, which is characterized in that Including differential geometry control device (4) and composite controlled object (1), the differential geometry control device (4) includes linear closed-loop control The output of device (2) and exact linearization method decoupled system (3), the composite controlled object (1) is fed back to linear closed-loop controller (2) Input, linear closed-loop controller (2) output connection exact linearization method decoupled system (3) input, exact linearization method decoupling The input of output connection composite controlled object (1) of system (3).

The control 2. a kind of induction-type bearingless motor radial force based on differential geometrical decoupled control according to claim 1 suspends System processed, which is characterized in that the building method of the exact linearization method decoupled system (3) are as follows:

S1 chooses corresponding state variable according to the mathematical model of induction-type bearingless motor, so that it is different to obtain corresponding bearing-free Walk motor status equation；

S2 seeks Lie derivative to the third horizontal type of state equation and the 4th horizontal type using Differential Geometry Lie derivative, according to seeking Lie derivative judgement carry out exact linearization method decoupling；

S3 is coordinately transformed state equation to obtain new state equation and control rate；To obtain exact linearization method decoupling System.

The control 3. a kind of induction-type bearingless motor radial force based on differential geometrical decoupled control according to claim 2 suspends System processed, which is characterized in that the state equation indicates are as follows:

Wherein, the state variable x of equation₁、x₂Respectively x-axis and y-axis direction displacement x, y, x₃、x₄Respectively x-axis and y-axis are displaced Derivative,Respectively x₁、x₂、x₃、x₄First derivative, M be two windings mutual inductance, m be rotor matter Amount, i_s1d、i_s1qRespectively component of the torque winding current in d, q axis, f_x、f_yWhat respectively rotor was subject in x-axis and y-axis is outer The system of boundary's active force, the equation inputs u₁、u₂Respectively component i of the suspending windings electric current in d, q axis_s2d、i_s2q, system output y₁、y₂Respectively x-axis and y-axis direction displacement x, y.

4. a kind of induction-type bearingless motor radial force based on differential geometrical decoupled control according to claim 2 or 3 is outstanding Floating control system, which is characterized in that judgement carries out the process of exact linearization method decoupling in the S2 are as follows:

S2.1, respectively in state equationWithLie derivative is sought, corresponding relationship degree r is obtained₁And r₂, and then calculate Relativeness degree r=r₁+r₂；

S2.2 meets the necessary and sufficient condition of exact linearization method if relativeness degree r is equal with system dimensions n.

5. a kind of induction-type bearingless motor radial force based on differential geometrical decoupled control according to claim 2 or 3 is outstanding Floating control system, which is characterized in that the process of the S3 are as follows:

Radial force suspension system state equation is abbreviated as by S3.1

Wherein, thenIn formula G indicates that system inputs u₁、u₂Coefficient； It is output y to the r of external force f₁Rank Lie derivative,It is output y to the r of external force f₂Rank Lie derivative,Indicate output y to the single order Lie derivative of external force f, then the whole single order Lie derivative to coefficient g；

S3.2, then simplified state equation is coordinately transformed to obtain 2 virtual input quantitiesIt obtains New control law u=A^-1(ν-B)；Wherein, A is coefficient matrix, and B is applied external force matrix, and ν is input moment matrix.

The control 6. a kind of induction-type bearingless motor radial force based on differential geometrical decoupled control according to claim 1 suspends System processed, which is characterized in that the composite controlled object (1) includes sequentially connected Clark inverter (11), current mode tracking Inverter (12) and induction-type bearingless motor radial force model suspending (13).

Technical field

The invention belongs to Electrified Transmission decoupling control technology fields more particularly to a kind of based on differential geometrical decoupled control Induction-type bearingless motor radial force suspension control system.

Background technique

Induction-type bearingless motor is a technological innovation of motor field, not only have bearing-free motor without friction, Without abrasion, without lubrication, the service life is long, high speed and the features such as ultrahigh speed, also the structure with asynchronous machine it is simple, securely, make The advantages that valence is low, air gap is uniform, cogging torque is stable and weak-magnetic speed-regulating is good, be bearing-free motor most with prospects it One.Application of the motor in fields such as flywheel energy storage, chemical industry chemistry, communications and transportation and aerospaces is to acquire a special sense And can not replace.

Induction-type bearingless motor system is the strongly coupled system of a Nonlinear Multivariable.Since the x and y-axis of motor are radial Suspending power is unified to be generated by a suspending windings, this make the radial suspension force when electrical power is run in both direction it Between there is the phenomenons that intercouples.When rotor-position is interfered in a certain direction, since the control force of both direction is deposited In the influence that coupling causes entire suspending module that can all be interfered.Therefore, it realizes between radial suspension force in both direction Decoupling be to reduce interference effect to guarantee the prerequisite that preferably runs of motor.

Currently, there are many kinds of the decoupling control methods of induction-type bearingless motor.Chinese Patent Application No. is CN200610038711.3, title are as follows: bearing-less AC asynchronous motor neural network inverse decoupling control method, using nerve net The inverse algorithm of network carries out decoupling control to induction-type bearingless motor.Chinese Patent Application No. is CN201210275854.1, title Are as follows: the building method of induction-type bearingless motor support vector machines inverse decoupling controller, using the algorithm construction that support vector machines is inverse Induction-type bearingless motor decoupling controller.Chinese Patent Application No. is CN201510104159.2, title are as follows: bearing-free is different The stator magnetic linkage oriented reversed decoupling control system of motor is walked, it is asynchronous to bearing-free to realize using stator magnetic linkage oriented inverse algorithm The decoupling of electric system.The process described above all has a biggish defect: three kinds of method of inverse are asynchronous to bearing-free When motor is partially or completely decoupled, accurate mathematical model is all relied on, and in actual operating condition, the essence of system True model hardly results in, this makes the precision of decoupling control method be difficult to be guaranteed.In addition, all using above method It is more or less there are calculation amounts it is larger, control speed is slow the problems such as.

Summary of the invention

The present invention proposes a kind of bearing-free based on differential geometrical decoupled control according to problems of the prior art Asynchronous machine radial force suspension control system, in order to realize to the solution between induction-type bearingless motor radial suspension force Coupling control, and a kind of building method of induction-type bearingless motor differential geometrical decoupled control device is provided, it is transported to reduce in motor Rotor Position disturbance is to the influence between the radial suspension force in both direction in row, so that entire decoupled system has well Control performance.

The technical solution adopted in the present invention is as follows:

A kind of induction-type bearingless motor radial force suspension control system based on differential geometrical decoupled control, including differential are several What controller and composite controlled object, the differential geometry control device include linear closed-loop controller and exact linearization method decoupling System, the output feedback of the composite controlled object arrive the input of linear closed-loop controller, and the output of linear closed-loop controller connects Connect the input of exact linearization method decoupled system, the input of the output connection composite controlled object of exact linearization method decoupled system.

Further, the building method of the exact linearization method decoupled system are as follows:

S1 chooses corresponding state variable according to the mathematical model of induction-type bearingless motor, to obtain corresponding shaftless Hold asynchronous machine state equation；

S2 seeks Lie derivative to the third horizontal type of state equation and the 4th horizontal type using Differential Geometry Lie derivative, according to The Lie derivative judgement sought carries out exact linearization method decoupling；

S3 is coordinately transformed state equation to obtain new state equation and control rate；To obtain exact linearization method Decoupled system；

Further, the state equation indicates are as follows:

Wherein, the state variable x of equation₁、x₂Respectively x-axis and y-axis direction displacement x, y, x₃、x₄Respectively x-axis and y-axis The derivative of displacement,Respectively x₁、x₂、x₃、x₄First derivative, M be two windings mutual inductance, m is rotor Quality, i_s1d、i_s1qRespectively component of the torque winding current in d, q axis, f_x、f_yRespectively rotor in x-axis and y-axis by External forces, the system of the equation inputs u₁、u₂Respectively component i of the suspending windings electric current in d, q axis_s2d、i_s2q, system Export y₁、y₂Respectively x-axis and y-axis direction displacement x, y, then

Further, the process of progress exact linearization method decoupling is judged in the S2 are as follows:

S2.1, respectively in state equationWithLie derivative is sought, corresponding relationship degree r is obtained₁And r₂, Jin Erji Calculate relativeness degree r=r₁+r₂

S2.2 meets the necessary and sufficient condition of exact linearization method if relativeness degree r is equal with system dimensions n.

Further, the process of the S3 are as follows:

Radial force suspension system state equation is abbreviated as by S3.1

Wherein, then G indicates that system inputs u in formula₁、u₂Coefficient； It is output y to the r of external force f₁Rank Lie derivative,It is output y to the r of external force f₂Rank Lie derivative, L_giL_fy_jIndicate output y to the single order Lie derivative of external force f, then the whole single order Lie derivative to coefficient g；

S3.2, then simplified state equation is coordinately transformed to obtain 2 virtual input quantities Obtain new control law u=A^-1(ν-B)；Wherein, A is coefficient matrix, and B is applied external force matrix, and ν is input moment matrix；

Further, the composite controlled object includes sequentially connected Clark inverter, current mode tracking inverter and nothing Bearing asynchronous machine radial force model suspending；

Beneficial effects of the present invention:

1, the present invention passes through the differential geometrical decoupled control device of construction, and non-linear, multivariable, the bearing-free of close coupling is different Walking the decoupling of motor radial force Suspension Subsystem is two displacement Second Order Integral linear subsystems.Differential used by this process Geometrical principle is fed back by non-linear scale state and state, realizes the exact linearization method of nonlinear system, by the non-of complexity Linear problem is transformed into linear problem to be solved, and substantially reduces control difficulty, and this method utilizes Taylor with traditional Expansion carries out local linearization mothed difference, it does not neglect any higher order term, this makes differential decoupling controller be height Precision.

2, induction-type bearingless motor radial force model suspending of the present invention is 2 input, 2 output of 4 state variables Nonlinear system, all outputs of the system are all influenced by input, when this causes some to input to have interference, entirely System can be all affected by it, and use this differential decoupling controller that can reduce interference to entire with effective solution this problem The influence of system.

3, differential geometrical decoupled control device of the present invention solves various Inverse Decoupling methods and excessively relies on accurately Controlled device mathematical model the problem of, and its operation method is simple, different from the excessive calculating of neural network inverse approach, Increase a possibility that it is applied in practical projects.

4, differential geometrical decoupled control device of the present invention effectively realizes diameter on two direction of induction-type bearingless motor To the decoupling between suspending power, the good operation of motor is realized, and be adapted to other types of bearing-free motor control system And the various types electric machine control system of magnetic bearing support, therefore be with a wide range of applications.

Detailed description of the invention

Fig. 1 is a kind of system block diagram of induction-type bearingless motor differential geometrical decoupled control device of the present invention；

Fig. 2 is a kind of system schematic of induction-type bearingless motor differential geometrical decoupled control device of the present invention；

In figure, 1, composite controlled object, 2, linear closed-loop controller, 3, exact linearization method decoupled system, 4, Differential Geometry decoupling Controller, 11, Clark inverter, 12, current mode tracking inverter, 13, induction-type bearingless motor radial force model suspending.

Specific embodiment

In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right The present invention is further elaborated.It should be appreciated that described herein, the specific embodiments are only for explaining the present invention, and It is not used in the restriction present invention.

Since there are larger couplings in the control to the direction motor x, y position for the output of linear closed-loop controller, so that Realize that the independent control difficulty in motor both direction increases, therefore proposed by the present invention a kind of based on Differential Geometry decoupling control The induction-type bearingless motor radial force suspension control system of system, including linear closed-loop controller 2, exact linearization method decoupled system 3 With composite controlled object 1.

As shown in Figure 1, 2, the Displacement Feedback that motor exports x and y-axis is arrived input terminal by linear closed-loop controller 2, and is distinguished It is poor to make with x and the displacement given value of y-axis, obtains the control error of induction-type bearingless motor radial force suspension decoupling and controlling system. The control electric current of motor radial displacement is finally obtained for the two error setting positioner 21 and controller 22 respectively again ν₁、 ν₂, in order to Linear Control is carried out to pseudo-linear system.

Input by the output of linear closed-loop controller 2 as exact linearization method decoupled system 3, since the reality of motor is answered Be with occasion it is changeable, i.e., there is a variety of interference such as external environment and Parameters variation in motor operation, so that the control of motor System must be existed simultaneously with decoupling, therefore linear closed-loop controller 2 and exact linearization method decoupled system 3 are serially connected altogether With composition differential geometrical decoupled control device 4, to realize the good control to electric system.Exact linearization method decoupled system 3 Constitution step is as follows:

S1 analyzes the working principle of induction-type bearingless motor suspending module, and Maxwell is utilized on the basis of principle Tensor Method seeks the mathematical model in x-axis and y-axis both direction, is according to obtained mathematical model selecting system state variableSystem input is u=[u₁ u₂]^T=[i_s2d i_s2q]^T, system output is y= [y₁ y₂]^T=[x y]^T, to obtain the state equation of motor:

Wherein, the state variable x of equation₁、x₂Respectively x-axis and y-axis direction displacement x, y, x₃、x₄Respectively x-axis and y-axis The derivative of displacement,Respectively x₁、x₂、x₃、x₄First derivative, M be two windings mutual inductance, m be turn The quality of son, i_s1d、i_s1qRespectively component of the torque winding current in d, q axis, f_x、f_yRespectively rotor in x-axis and y-axis by The system of the external forces arrived, the equation inputs u₁、u₂Respectively component i of the suspending windings electric current in d, q axis_s2d、i_s2q, it is System output y₁、y₂Respectively x-axis and y-axis direction displacement x, y, then

S2 seeks Lie derivative to the third horizontal type of state equation and the 4th horizontal type with Differential Geometry Lie derivative, according to asking The Lie derivative judgement taken carries out exact linearization method decoupling, and process is as follows:

S2.1 is rightLie derivative is sought, is obtained: L_fy₁ (x)=x₃、The most high-order for illustrating this group of Lie derivative is 2-1 rank, that is, is closed Degree of being r₁=2；It is rightLie derivative is sought, is obtained: L_fy₂(x)= x₄、The most high-order for illustrating this group of Lie derivative is also 2-1 rank, i.e. relationship degree r₂=2；

S2.2, relativeness degree r=r₁+r₂=4 is equal with system dimensions n=4, i.e. r=n=4 meets exact linearization method Necessary and sufficient condition；

S3 is coordinately transformed state equation to obtain new state equation and control rate；To obtain exact linearization method Decoupling controller；

S3.1 writes a Chinese character in simplified form radial force suspension system state equation are as follows:

Wherein,

S3.2, then simplified state equation is coordinately transformed to obtain 2 virtual input quantitiesTherefore new control law is written as u=A^-1(ν-B)；Wherein, A is coefficient matrix, and B is applied external force Matrix, ν are input moment matrix；During the work time, the control signal ν of exact linearization method decoupled system 3 is inputted₁、ν₂Respectively with Control law is multiplied, final output u₁And u₂；

The output of exact linearization method decoupled system 3 connects composite controlled object 1, and composite controlled object 1 includes being sequentially connected Clark inverter 11, current mode tracking inverter 12 and induction-type bearingless motor radial force model suspending 13, due to accurate line Property decoupled system 3 output be two-phase stationary coordinate system electric current, therefore tracked using Clark inverse transformation 11 and current mode inverse Become device 12 and convert it in three phase coordinate systems and formed three-phase alternating current, and then is input to induction-type bearingless motor radial force Model suspending 13 is realized and is controlled the suspending power of induction-type bearingless motor.

Above embodiments are merely to illustrate design philosophy and feature of the invention, and its object is to make technology in the art Personnel can understand the content of the present invention and implement it accordingly, and protection scope of the present invention is not limited to the above embodiments.So all Revealed principle, equivalent variations or modification made by mentality of designing according to the present invention, protection scope of the present invention it It is interior.