CN110131312B - Five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller and construction method - Google Patents
Five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller and construction method Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
- F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
- F16C32/0406—Magnetic bearings
- F16C32/044—Active magnetic bearings
- F16C32/0444—Details of devices to control the actuation of the electromagnets
- F16C32/0451—Details of controllers, i.e. the units determining the power to be supplied, e.g. comparing elements, feedback arrangements with P.I.D. control
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- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
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- F16C32/0474—Active magnetic bearings for rotary movement
- F16C32/0489—Active magnetic bearings for rotary movement with active support of five degrees of freedom, e.g. two radial magnetic bearings combined with an axial bearing
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- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2300/00—Application independent of particular apparatuses
- F16C2300/20—Application independent of particular apparatuses related to type of movement
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- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2322/00—Apparatus used in shaping articles
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- F16C2326/00—Articles relating to transporting
- F16C2326/47—Cosmonautic vehicles, i.e. bearings adapted for use in outer-space
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- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
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Abstract
The invention discloses a five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller and a construction method, which are composed of five self-adaptive disturbance rejection controllers with the same internal structure and connected in series before a compound controlled object, wherein the five self-adaptive disturbance rejection controllers respectively control the single-degree-of-freedom controlled object, each self-adaptive disturbance rejection controller is composed of a tracking differentiator, a nonlinear state error feedback control law, a self-adaptive extended state observer, a BP neural network, a first compensation factor and a second compensation factor, the internal disturbance and the external disturbance of the controlled object can be automatically compensated by constructing the self-adaptive extended state observer of a system, the excellent control performance of the system is realized by adopting the state error feedback control law, the key parameters are set by utilizing the property that the neural network approximates to a nonlinear function, the on-line self-setting of the key parameters of the self-disturbance rejection decoupling controller is realized, and the control performance of the self-disturbance rejection decoupling controller is improved.
Description
Technical Field
The invention belongs to the field of high-speed and ultra-high-speed electric transmission, and relates to a controller of a five-degree-of-freedom alternating current active magnetic bearing, which provides conditions for efficient and precise support of a high-speed rotating shaft and is suitable for high-speed machine tools, flywheel energy storage, aerospace, nuclear energy and the like.
Background
The magnetic bearing suspends the rotor in the air through electromagnetic force, so that no mechanical contact exists between the stator and the rotor, and the magnetic bearing has the outstanding advantages of no friction, no abrasion, no lubrication, long service life, high precision, high speed and the like, and particularly in a high-speed machine tool spindle system, the supporting mode of the spindle largely determines the cutting speed, the machining precision and the application range which can be achieved by a machine tool, and the magnetic bearing is applied to the support of the high-speed machine tool spindle, thereby creating favorable conditions for improving the technical level of the high-speed machine tool spindle.
The five-degree-of-freedom alternating current active magnetic shaft system is a strong-coupling nonlinear multi-input multi-output system, and the system needs to be subjected to linear decoupling control in order to realize high-speed high-precision stable operation of the magnetic bearing. The usual linearization decoupling control method is as follows: approximate linearization, differential geometry, analytical inverse system, and the like. The approximate linearization method can only perform static decoupling on the system, and factors such as critical rotation speed, system parameter change and interference can reduce the control performance. The differential geometry method adopts a comparatively abstract mathematical tool, is complex in calculation and is not beneficial to popularization and application. The method for analyzing the inverse system requires that specific system parameters and mathematical models of controlled objects are known, but in practical engineering application, the analytical solution of the inverse model is often extremely difficult to be obtained, and the nonlinear characteristics of the system are difficult to be accurately described.
At present, the advantage that the active disturbance rejection controller does not depend on an accurate mathematical model of a controlled object is widely applied to a complex control system, for example, a document named as an axial magnetic bearing active disturbance rejection controller for flywheel energy storage is proposed to control an axial magnetic bearing by using the active disturbance rejection controller in a Chinese patent application number 201310491326.4, but the active disturbance rejection controller only controls the axial magnetic bearing by using the active disturbance rejection controller, does not have decoupling performance on the magnetic bearing, and only carries out self-tuning on one parameter of the active disturbance rejection controller.
Disclosure of Invention
The invention aims to overcome the defects of the decoupling control technology of the existing five-degree-of-freedom alternating current active magnetic bearing system, and provides a self-adaptive active disturbance rejection decoupling controller of a five-degree-of-freedom alternating current active magnetic bearing and a construction method thereof, which can realize decoupling control between radial and axial five-degree-of-freedom displacement variables of the five-degree-of-freedom alternating current active magnetic bearing system, can also enable the system to obtain good dynamic and static performances, and can effectively improve the control performance of the whole system.
The invention adopts the technical proposal that the five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller adopts: the system consists of five self-adaptive active disturbance rejection controllers which are connected in series in front of a composite controlled object and have the same internal structure, and respectively control the controlled object with single degree of freedom, wherein the input of a first self-adaptive active disturbance rejection controller is radial displacement x a And an expected value x of radial displacement a * Output is the control current expected value i ax * The input of the second adaptive active disturbance rejection controller is radial displacement y a And an expected value y of radial displacement a * Output is the control current expected value i ay * The input of the third adaptive active disturbance rejection controller is radial displacement x b And an expected value x of radial displacement b * The output being the control current desiredValue i bx * The input of the fourth adaptive active disturbance rejection controller is radial displacement y b And an expected value y of radial displacement b * Output is current expected value i by * The input of the fifth adaptive active disturbance rejection controller is the axial displacement z and the expected value z of the axial displacement * Output is the control current expected value i z * The method comprises the steps of carrying out a first treatment on the surface of the Each self-adaptive active disturbance rejection controller consists of a tracking differentiator, a nonlinear state error feedback control law, a self-adaptive extended state observer, a BP neural network, a first compensation factor and a second compensation factor, wherein the inputs of the five tracking differentiators are respectively the expected value x of radial displacement a * 、ya*、x b * 、y b * And an expected value z of axial displacement * The output of the first tracking differentiator being the corresponding tracking signal x 1 And differential signal x 2 The input of the first self-adaptive extended state observer is the output displacement x of the composite controlled object a Three parameters beta 01 、β 02 And beta 03 Control amount u, output is x 1 、x 2 Is the estimated value z of (2) 1 、z 2 And the estimated value z of the total disturbance 3 The input of the first nonlinear state error feedback control law is the error e 1 ＝x 1 -z 1 And e 2 ＝x 2 -z 2 Output is control quantity u 0 The input of the first BP neural network is the error e 1 、e 2 Displacement x a And offset value 1, output as three parameters beta 01 、β 02 And beta 03 The first compensation factor is input as an error u 0 -z 3 Output as current i to controlled object with single degree of freedom a * The input of the first and second compensation factors is the current i a * The output is the control amount u to the adaptive extended state observer.
The construction method of the five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller adopts the technical scheme that the construction method comprises the following steps:
step A: the first is constructed byTracking differentiator to obtain tracking signal x 1 And differential signal x 2 ：
And (B) step (B): constructing a first adaptive extended state observer to obtain an output z thereof 1 、z 2 And z 3 ：
u (k) is a disturbance compensation formation control amount u (k) = (u) 0 (k)-z 3 (k))/b 0 ，u 0 (k) To control the quantity u 0 A value at time k; fal is a nonlinear function whose expression:
z 1 (k)、z 2 (k)、z 3 (k) Z respectively 1 、z 2 、z 3 The value at time k, z 1 (k+1)、z 2 (k+1)、z 3 (k+1) is z 1 、z 2 、z 3 The value at time k+1, x a (k) Is x a The value at time k, e is the error, h is the sampling period, b 0 For the estimated value of the first compensation factor, b is the value of the second compensation factor, b=1/b 0 ；α 1 Taking 0.5, alpha 2 Take 0.25, delta 1 > 0, the sampling period5-10 times of the period.
Step C: by u 0 ＝β 1 fal(e 1 ,α 3 ,δ 2 )+β 2 fal(e 2 ,α 4 ,δ 2 ) Constructing a first nonlinear state error feedback control law to obtain a control quantity u 0 The method comprises the steps of carrying out a first treatment on the surface of the fal is a nonlinear function, error e 1 ＝x 1 -z 1 ，e 2 ＝x 2 -z 2 ，α 3 Taking 0.5, alpha 4 Take 0.25, delta 2 More than 0, taking 5-10 times of sampling period;
step D: setting three parameters beta by adopting a first BP neural network 01 、β 02 And beta 03 。
The invention has the advantages that:
1. the self-adaptive self-immunity decoupling controller is connected in series before a compound controlled object, so that the five-degree-of-freedom alternating current active magnetic bearing system with strong coupling and nonlinear characteristics is decoupled into a non-coupling linear system, internal and external disturbance of the controlled object can be automatically compensated by constructing a self-adaptive extended state observer of the system, and excellent control performance of the system is realized by adopting a state error feedback control law.
2. Because the standard active disturbance rejection controller needs more parameters to be set, and mutual influence exists among some parameters, the parameter setting is very difficult. The disturbance to the five-degree-of-freedom alternating current active magnetic bearing is often unfixed, so that a set of fixed parameters are difficult to meet the control requirement of a system.
Drawings
FIG. 1 is a schematic diagram of a five degree of freedom AC active magnetic bearing structure;
fig. 2 is a schematic structural diagram of the composite controlled object 4;
FIG. 3 is a general block diagram of a five degree of freedom AC active magnetic bearing adaptive immunity decoupling controller according to the present invention;
FIG. 4 is a block diagram of one of the adaptive immunity controllers of FIG. 1;
in the figure: a. b, radial active magnetic bearing; c. an axial active magnetic bearing; d. a high-speed motor; f1, f2. radial displacement sensors; f3. an axial displacement sensor; g1, g2. auxiliary bearings; h1, h2. end caps; i. a sleeve; m, rotating shaft; 1. five-degree-of-freedom alternating current active magnetic bearing; 2. a power driver; 3. transforming coordinates; 4. compounding the controlled object; 5. an active disturbance rejection controller; 21. 22, a current tracking inverter; 23. a switching power amplifier; 31. inverse clark transform; 51. 52, 53, 54, 55. Adaptive active disturbance rejection controller; 511. tracking the differentiator; 512. a nonlinear error state feedback control law; 513. an adaptive extended state observer; bp neural network; 515. a first compensation factor; 516. a second compensation factor; 517. a single degree of freedom controlled object.
Detailed Description
As shown in fig. 1, the five-degree-of-freedom alternating current active magnetic bearing 1 is composed of two radial active magnetic bearings a and b, an axial active magnetic bearing c and a high-speed motor d; the two radial active magnetic bearings a and b, the axial active magnetic bearing c and the high-speed motor d are coaxially arranged in the sleeve i and share the same rotating shaft m, the two axial ends of the rotating shaft m are respectively supported by auxiliary bearings g1 and g2, and the auxiliary bearings g1 and g2 are respectively fixed on corresponding end covers h1 and h2. Two radial displacement sensors f1 and f2 are respectively fixed on two sides of the corresponding radial active magnetic bearings a and b, and are used for measuring the radial displacement of the rotor. The axial displacement sensor f3 is fixed on the end cover h2 and is positioned on the axis of the rotating shaft m to measure the axial displacement of the rotor.
As shown in fig. 2, the composite controlled object 4 is formed by sequentially connecting a coordinate transformation module 3, a power driver 2 and a five-degree-of-freedom alternating current active magnetic bearing 1 in series. The power driver 2 is composed of two current tracking inverters 21, 22 and a switching power amplifier 23, and is connected in series in front of the five-degree-of-freedom alternating current active magnetic bearing 1, the two Clark inverse transformation modules 31, 32 are used as a coordinate transformation module 3, the coordinate transformation module 3 is connected in series in front of the power driver 2, wherein the first Clark inverse transformation module 31 is connected in series in front of the first current tracking inverter 21,the second Clark inverse transformation module 32 is connected in series before the second current tracking inverter 22, and the coordinate transformation module 3, the power driver 2 and the five-degree-of-freedom alternating current active magnetic bearing 1 together form a composite controlled object 4. Radial equivalent control current expected value i of radial active magnetic bearing a ax * 、i ay * Transformed into a three-phase current desired value i by a first Clark inverse transformation module 31 au * 、i av * 、i aw * Radial equivalent control current expected value i of radial active magnetic bearing b bx *、i by * Transformed into a three-phase current desired value i by a second Clark inverse transformation module 32 bu * 、i bv * 、i bw * . The first current tracking inverter 21 tracks the three-phase current expected value and outputs the driving current i of the radial active magnetic bearing a au 、i av 、i aw . The second current tracking inverter 22 tracks the three-phase current expected value and outputs the driving current i of the radial active magnetic bearing b bu 、i bv 、i bw . Axial control current desired value i z * Is input to the switching power amplifier 23, and the switching power amplifier 23 controls the current expected value i according to the axial direction z * Output axial drive current i z . The input of the composite controlled object 4 is the equivalent control current expected value i ax * 、i ay * 、i z * 、i bx * 、i by * The output is displacement x in five directions of the rotating shaft m a 、y a 、z、x b 、y b . Displacement x of the axis of rotation m in five directions a 、y a 、z、x b 、y b The expected value i of the control current can be obtained according to the displacement of the rotating shaft m in five directions by measuring the displacement sensors f1, f2 and f3 respectively ax * 、i ay * 、i z * 、i bx * 、i by * 。
As shown in fig. 3, the five-degree-of-freedom ac active magnetic bearing active disturbance rejection decoupling controller according to the present invention is composed of five adaptive active disturbance rejection controllers, namely, first, second, third, fourth and fifth adaptive active disturbance rejection controllers 51, 52, 53, 54 and 55.
Each degree of freedom of the five-degree-of-freedom alternating current active magnetic bearing is controlled by a second-order adaptive active disturbance rejection controller. The first and second adaptive active disturbance rejection controllers 51 and 52 control two radial degrees of freedom of the radial alternating current magnetic active bearing a, and the input of the first adaptive active disturbance rejection controller 51 is radial displacement x a And an expected value x of radial displacement a * Output is the equivalent control current expected value i of the compound controlled object 4 ax * The input to the second adaptive immunity controller 52 is the radial displacement y a And an expected value y of radial displacement a * Output is the equivalent control current expected value i of the compound controlled object 4 ay * The method comprises the steps of carrying out a first treatment on the surface of the The third and fourth adaptive active disturbance rejection controllers 53 and 54 control two radial degrees of freedom of the radial alternating current active magnetic bearing b, and the input of the third adaptive active disturbance rejection controller 53 is radial displacement x b And an expected value x of radial displacement b * Output is the equivalent control current expected value i of the compound controlled object 4 bx * The input to the fourth adaptive immunity controller 54 is the radial displacement y b And an expected value y of radial displacement b * Output is the equivalent control current expected value i of the compound controlled object 4 by * The method comprises the steps of carrying out a first treatment on the surface of the The fifth adaptive active disturbance rejection controller 55 controls the single-degree-of-freedom axial active magnetic bearing c, and the input of the fifth adaptive active disturbance rejection controller 55 is the axial displacement z of the rotating shaft m and the expected value z of the axial displacement * Output is the equivalent control current expected value i of the compound controlled object 4 z * 。
The five adaptive immunity controllers 51, 52, 53, 54, 55 have the same structure and algorithm, and only the first adaptive immunity controller 51 will be described as an example. As shown in fig. 4, the first adaptive active disturbance rejection controller 51 is composed of a tracking differentiator 511, a nonlinear state error feedback control law 512, an adaptive extended state observer 513, a BP neural network 514, a first compensation factor 515, and a second compensation factor 516, and controls a controlled object 517 with a single degree of freedomThe single-degree-of-freedom controlled object 517 refers to a radial one-degree-of-freedom radial alternating-current magnetic active bearing a in the composite controlled object 4, namely, radial displacement x is controlled a Corresponding to the first adaptive active-disturbance-rejection controller 51, a radial displacement x is achieved by the first adaptive active-disturbance-rejection controller 51 a And (5) controlling. The first adaptive active disturbance rejection controller 51 is constructed as follows:
1. construction of tracking differentiators
Expected value x of radial displacement a * As an input to the tracking differentiator 511, the tracking differentiator 511 reasonably extracts the tracking signal x according to the control requirements of the composite controlled object 4 1 And differential signal x 2 . The tracking differentiator is as follows:
wherein:
as the fastest synthesis function, h 0 Is the integral step length; r is (r) 0 Is a velocity factor; h is a sampling period; x is x a * (k) For radial displacement x a * A value at time k; x is x 1 (k) Is x 1 A value at time k; x is x 1 (k+1) is x 1 A value at time k+1; x is x 2 (k) Is x 2 A value at time k; x is x 2 (k+1) is x 2 A value at time k+1.
2. Constructing an adaptive extended state observer
An adaptive extended state observer 512 is constructed based on the input and the output of the composite controlled object 4, wherein the input of the adaptive extended state observer 512 is the output displacement x of the composite controlled object 4 a And three adjustable parameters beta of the adaptive extended state observer 512 01 、β 02 And beta 03 The method comprises the steps of carrying out a first treatment on the surface of the The output of the adaptive extended state observer 512 is z 1 、z 2 And z 3 ，z 1 、z 2 Respectively x 1 And x 2 Estimated value of z 3 An estimate of the total disturbance; the extended state observer takes the form:
where u (k) is a disturbance compensation formation control amount u (k) = (u) 0 (k)-z 3 (k))/b 0 ，u 0 (k) To control the quantity u 0 A value at time k; fal is a nonlinear function whose expression:
β 01 、β 02 、β 03 、α 1 、α 2 、δ 1 、b、b 0 is an adjustable parameter of the extended state observer; z 1 (k)、z 2 (k)、z 3 (k) Z respectively 1 、z 2 、z 3 The value at time k, z 1 (k+1)、z 2 (k+1)、z 3 (k+1) is z 1 、z 2 、z 3 The value at time k+1, x a (k) Is x a A value at time k; e is error, h is sampling period, b 0 For the estimated value of the first compensation factor 55, b is the value of the second compensation factor 516, b=1/b 0 The method comprises the steps of carrying out a first treatment on the surface of the The input of the first compensation factor 515 is the difference u 0 -z 3 Output current i a * (k)＝(u 0 -z 3 )/b 0 The input of the second compensation factor 516 is the current i a * (k) The output is the control amount u=u 0 -z 3 ，u 0 Is the nonlinear state error feedback control law 513 outputs the control quantity. When 0 < alpha 1 、α 2 When < 1, the fal function has the characteristics of small error and large gain, and the large error and the small gain are usually alpha 1 Taking 0.5, alpha 2 Taking 0.25; delta 1 More than 0, generally 5-10 times of the sampling period can be taken; beta 01 、β 02 、β 03 Is set by BP neural network 514, which automatically adjusts the parameter beta of the extended state observer according to the changes and disturbances of the controlled object 4 01 、β 02 、β 03 I.e. an adaptive extended state observer.
3. Constructing nonlinear state error feedback control law
The two outputs x of the differentiator 511 will be tracked 1 And x 2 Respectively subtracting the two outputs z of the extended state observer 512 1 And z 2 Obtaining a systematic error e 1 ＝x 1 -z 1 And e 2 ＝x 2 -z 2 The error is input to the nonlinear state error feedback control law 513, and the nonlinear state error feedback control law 513 outputs a control amount u 0 . For an alternating radial magnetic bearing system, the nonlinear state error feedback control law 72 is:
u 0 ＝β 1 fal(e 1 ,α 3 ,δ 2 )+β 2 fal(e 2 ,α 4 ,δ 2 )，
wherein: beta 1 And beta 2 Two parameters of the nonlinear state error feedback control law 513, fal being a nonlinear function, typically α 3 Taking 0.5, alpha 4 Take 0.25, delta 2 More than 0, typically 5 to 10 times the sampling period can be taken.
4.BP neural network-based parameter setting method for self-adaptive extended state observer
The BP neural network 514 adopts a three-layer structure, 4 nodes are input into the layer, 3 nodes are output from the layer, and the signal error e is selected 1 Differential error e of signal 2 System output x a And the bias value 1 is used as 4 input nodes of the BP neural network 514, 5 hidden layer nodes are selected by trial and error by combining the composite controlled object 4, and three nodes of the output layer are three parameters beta of the self-adaptive extended state observer 513 01 、β 02 、β 03 . Thereby, on-line self-tuning of the parameters of the adaptive extended state observer 512 can be achieved.
The BP neural network 514 input layer inputs as
Where in represents an input layer, j represents four nodes of the input layer, j=1, 2,3,4; hidden typeThe input/output of the layer is->
Where im represents the hidden layer(s),
for the value of the hidden layer weighting coefficient k moment, k represents k moment, i represents five nodes of the hidden layer, i=1, 2,3,4,5; the input/output of the output layer is->
Wherein out represents the output layer, k represents the moment k, < > in->
For the value of the implicit layer weighting coefficient k instant, l represents three nodes of the output layer, l=1, 2,3.
The BP neural network corrects the weight coefficient of the network according to a gradient descent method, namely, the weight coefficient is searched and adjusted in the negative gradient direction according to the performance index function E (k). The iterative relation of the network connection weight of the traditional BP algorithm is that
The iterative relation of the network connection right after adding the dynamic term is +.>
Wherein n represents the number of times of adjusting the weight, E is an index function, w is a weighting coefficient, eta is a learning rate, alpha is a momentum factor, and 0 < alpha < 1; alpha delta w (n-1) is the added momentum term. An improved method for adding multiple motion items is to add a beta delta w (n-2) and gamma delta w (n-3) item on the basis of common addition of the motion item alpha delta w (n-1),
i.e.
That is, the weight change amounts when (n-2) and (n-3) are adjusted, beta and gamma are momentum factors, 0 < beta < 1, and 0 < gamma < 1.
The specific algorithm of the BP neural network self-adaptive active disturbance rejection controller is as follows:
1) Determining BP neural network structure, i.e. determining input layer node number and hidden layer node number, selecting inertial coefficients alpha, beta, gamma and learning rate eta, giving initial value of weighting coefficient of each layer
And->
Let k=1 at this time;
2) Sampling to obtain error e of k moment 1 (k) And e 2 (k)；
3) Calculating the input and output of each layer of neuron of the neural network, wherein the output of the output layer is three adjustable parameters beta in the self-adaptive extended state observer 01 、β 02 And beta 03 ；
4) Learning neural network, and weighting coefficient
And->
On-line adjustment is carried out to realize beta of three adjustable parameters of ESO 01 、β 02 And beta 03 Self-setting;
5) Setting k=k+l, returning to step 3) and recalculating until the system error meets the requirements.
5. The tracking differentiator 511, the nonlinear state error feedback control law 512, the adaptive extended state observer 513, the BP neural network 514, the first compensation factor 515 and the second compensation factor 516 are integrally formed into a first adaptive active disturbance rejection controller 51, and a controlled object 517 with single degree of freedom is controlled.
The second, third, fourth and fifth adaptive active disturbance rejection controllers 51, 52, 53, 54, 55 can be constructed in the same way to respectively control the corresponding single degree of freedom controlled objects, i.e. the radial displacement y a 、x b 、y b And an axial displacement z.
Claims (6)
1. A five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller is characterized in that: consists of five self-adaptive active disturbance rejection controllers with the same internal structure and connected in series in front of a composite controlled object (4) to respectively control the controlled object with single degree of freedom, wherein the input of a first self-adaptive active disturbance rejection controller (51) is radial displacement x a And an expected value x of radial displacement a * Output is the control current expected value i ax * The input to the second adaptive immunity controller (52) is the radial displacement y a And an expected value y of radial displacement a * Output is the control current expected value i ay * The input of the third adaptive immunity controller (53) is the radial displacement x b And an expected value x of radial displacement b * Output is the control current expected value i bx * The input to the fourth adaptive immunity controller (54) is the radial displacement y b And an expected value y of radial displacement b * Output is current expected value i by * The inputs of the fifth adaptive active disturbance rejection controller (55) are the axial displacement z and the desired value z of the axial displacement * Output is the control current expected value i z * The method comprises the steps of carrying out a first treatment on the surface of the Each self-adaptive active disturbance rejection controller consists of a tracking differentiator, a nonlinear state error feedback control law, a self-adaptive extended state observer, a BP neural network, a first compensation factor and a second compensation factor, wherein the inputs of the five tracking differentiators are respectively the expected value x of radial displacement a * 、y a *、x b * 、y b * And an expected value z of axial displacement * Wherein the output of the first tracking differentiator (511) is the corresponding tracking signal x 1 And differential signal x 2 The input of the first adaptive extended state observer (512) is the output displacement x of the composite controlled object a Three parameters beta 01 、β 02 And beta 03 Control amount u, output is x 1 、x 2 Is the estimated value z of (2) 1 、z 2 And the estimated value z of the total disturbance 3 First, firstThe nonlinear state error feedback control law (513) has an input of error e 1 ＝x 1 -z 1 And e 2 ＝x 2 -z 2 Output is control quantity u 0 The input to the first BP neural network (514) is the error e 1 、e 2 Displacement x a And offset value 1, output as three parameters beta 01 、β 02 And beta 03 The input of the first compensation factor (515) is the error u 0 -z 3 Output as current i to controlled object with single degree of freedom a * The input of the first second compensation factor (516) is the current i a * The output is a control amount u to the adaptive extended state observer (512).
2. The five degree of freedom ac active magnetic bearing active disturbance rejection decoupling controller of claim 1, wherein: the composite controlled object (4) is formed by sequentially connecting a coordinate transformation module (3), a power driver (2) and a five-degree-of-freedom alternating current active magnetic bearing (1) in series, the power driver (2) is formed by two current tracking inverters (21 and 22) and a switching power amplifier (23), the coordinate transformation module (3) is formed by two Clark inverse transformation modules (31 and 32), the first Clark inverse transformation module (31) is connected in series before the first current tracking inverter (21), and the second Clark inverse transformation module (32) is connected in series before the second current tracking inverter (22).
3. A method of constructing a five degree of freedom ac active magnetic bearing active disturbance rejection decoupling controller as in claim 1 comprising the steps of:
step A: the first tracking differentiator (511) is constructed to obtain the tracking signal x 1 And differential signal x 2 ：
As the fastest synthesis function, h 0 Is the integral step length; r is (r) 0 Is a velocity factor; h is a sampling period; x is x a * (k) For radial displacement x a * A value at time k; x is x 1 (k) Is x 1 A value at time k; x is x 1 (k+1) is x 1 A value at time k+1; x is x 2 (k) Is x 2 A value at time k; x is x 2 (k+1) is x 2 A value at time k+1;
and (B) step (B): a first adaptive extended state observer (512) is constructed to obtain its output z 1 、z 2 And z 3 ：
u (k) is a disturbance compensation formation control amount u (k) = (u) 0 (k)-z 3 (k))/b 0 ，u 0 (k) To control the quantity u 0 A value at time k; fal is a nonlinear function whose expression:
z 1 (k)、z 2 (k)、z 3 (k) Z respectively 1 、z 2 、z 3 The value at time k, z 1 (k+1)、z 2 (k+1)、z 3 (k+1) is z 1 、z 2 、z 3 The value at time k+1, x a (k) Is x a The value at time k, e is the error, h is the sampling period, b 0 For the estimated value of the first compensation factor, b is the value of the second compensation factor, b=1/b 0 ；α 1 Taking 0.5, alpha 2 Take 0.25, delta 1 More than 0, 5-10 times of the sampling period;
step C: by u 0 ＝β 1 fal(e 1 ,α 3 ,δ 2 )+β 2 fal(e 2 ,α 4 ,δ 2 ) Constructing a first nonlinear state error feedback control law (513) to obtain a control quantity u 0 The method comprises the steps of carrying out a first treatment on the surface of the fal is a nonlinear function, error e 1 ＝x 1 -z 1 ，e 2 ＝x 2 -z 2 ，α 3 Taking 0.5, alpha 4 Take 0.25, delta 2 More than 0, taking 5-10 times of sampling period;
step D: setting three parameters beta using a first BP neural network (514) 01 、β 02 And beta 03 。
4. The construction method of the five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller according to claim 3, wherein the construction method is characterized in that: in step D, the first BP neural network (514) adopts a three-layer structure, the input layer is 4 nodes, and the output layer is 3 nodes.
5. The method for constructing the five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller according to claim 4, wherein the method comprises the following steps: the iterative relationship of the connection weights of the first BP neural network (514) is that
n represents the number of times of adjusting the weight, E is an index function, w is a weighting coefficient, eta is a learning rate, and alpha, beta and gamma are momentum factors.
6. The method for constructing the five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller according to claim 5, wherein the method comprises the following steps: giving initial values of weighting coefficients of layers of BP neural network
And->
Let k=1, sample to get the error e at k time 1 (k) And e 2 (k) Calculating the input and output of each layer of neuron of the neural network, wherein the output is three parameters beta 01 、β 02 And beta 03 The method comprises the steps of carrying out a first treatment on the surface of the Then learning the neural network, and weighting the weighting coefficient +.>
And->
On-line adjustment; and finally, setting k=k+l for recalculation until the error meets the requirement. />
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