CN104793645B - A kind of magnetic levitation ball position control method - Google Patents

A kind of magnetic levitation ball position control method Download PDF

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CN104793645B
CN104793645B CN201510180614.7A CN201510180614A CN104793645B CN 104793645 B CN104793645 B CN 104793645B CN 201510180614 A CN201510180614 A CN 201510180614A CN 104793645 B CN104793645 B CN 104793645B
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CN104793645A (en
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彭辉
覃业梅
阮文杰
高家成
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Central South University
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Central South University
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Abstract

The invention discloses a kind of magnetic levitation ball position control method, the shortcoming of precise physical model is difficult to set up for maglev ball system, sets up tape function weight coefficient type autoregression model to describe the non-linear dynamic characteristic between electromagnetism winding input voltage and steel ball position using system identifying method.The model weight coefficient of the once linear function of steel ball position as Gauss RBF networks, and with function type coefficient of the RBF networks as non linear autoregressive model, the model is preferably portrayed the dynamic characteristic of maglev ball system.At a time regression coefficient is constant to the model, similar to a linear ARX model.Based on this, the present invention one time-varying of design, local linear predictive controller, by being controlled in each moment line solver quadratic programming come the quick optimal location for realizing steel ball, meets maglev ball system stabilization, quickly required.

Description

A kind of magnetic levitation ball position control method
Technical field
The present invention relates to automatic control technology field, particularly a kind of magnetic levitation ball position control method.
Background technology
Magnetic levitation technology is to integrate electromagnetism, electronic technology, control engineering, signal transacting, mechanics, dynamics , typical electromechanical integration technology.The features such as magnetic levitation technology is because its is contactless, without friction, low noise is widely used to The engineering fields such as magnetic suspension train, magnetic suspension bearing, magnetic suspension motor.Maglev ball system is mainly by logical to electromagnetism winding Electromagnetic force is produced with certain electric current, it is balanced each other with steel ball gravity, makes steel ball hang in the air and in poised state, reaches To the purpose of system stable operation.Maglev ball system with single direction has the non-linear, open-loop unstable, fast of essence The characteristics of speed response, easily influenceed by power supply and external environment, some parameters have stronger uncertainty, it is impossible to accurate to survey Amount.And electromagnetic field magnetic saturation phenomenon causes in electromagnetic field between input current and magnetic induction intensity, the magnetic flux of electromagnetism winding It is not proportional, increase the non-linear of system and cause the electromagnetic force model of system can not use simple math equation table Reach;Meanwhile, the steel ball in electromagnetic field produces current vortex, the inductance of electromagnetism winding will be influenceed in turn so that electromagnetism winding Inductance be not constant, but the function of the air gap g on steel ball to electromagnet pole surface, and with it into nonlinear dependence System.Therefore, the precise physical model for setting up maglev ball system is extremely difficult, and this is that maglev ball system realizes stable control Where the difficult point of system.
PID control is simple in construction, and can adjust current/voltage makes steel ball hang, is not required to set up magnetic suspension system Physical model, but control parameter need manually adjust, adaptivity is poor, to effective control range of Nonlinear Magnetic Suspension System Smaller, especially when steel ball change in location is quick, overshoot is larger, and steel ball shake is larger.PID control is automatically adjusted with fuzzy reasoning Parameter processed, can improve the ability that parameter changes and changed with air gap between steel ball and electromagnet.But this method is dependent on fuzzy rule Then storehouse, its foundation is limited by the experience of designer.On the other hand, it is false at some by analyzing magnetic suspension system operation principle If on the basis of condition, setting up physical model, then Self Adaptive Control, synovial membrane control, PREDICTIVE CONTROL etc. can be implemented to steel ball.This The maximum difficult point that a little methods are realized is the precise physical model of more difficult acquisition energy accurate description magnetic suspension system dynamic characteristic, because For some assumed conditions are difficult to be met in engineer applied.In addition, being carried out using linearization technique to physical model linear Change is handled, and is then designed linear control strategies, can be accelerated On-line Control optimal speed, but have lost mission nonlinear characteristic, weak Descriptive power of the model to magnetic suspension system is changed, so as to reduce control effect.
The content of the invention
The technical problems to be solved by the invention are, in view of the shortcomings of the prior art, providing a kind of magnetic levitation ball position control Method.
In order to solve the above technical problems, the technical solution adopted in the present invention is:A kind of magnetic levitation ball position control method, Suitable for the single-degree-of-freedom magnetic levitation ball system moved up and down, the single-degree-of-freedom magnetic levitation ball system includes producing electromagnetic field Coil windings and the photoelectric sensor of detection steel ball position;The electromagnetism winding input voltage is given by controller control drive circuit Go out;The steel ball position signalling of the photoelectric sensor collection sends control computer to by data collecting card.To magnetic levitation ball System sets up autoregression model:
Wherein, g (t) is the position of magnetic levitation ball;U (t) is electromagnetism winding input voltage;ξ (t) is white noise;V0、Vi gAnd Vj uIt is steel ball position for the weight coefficient of RBF networks Once linear function;For constant coefficient, pass through SNPOM optimization sides Method is recognized, and is calculated and obtained with least square method on the basis of nonlinear parameter is obtained.
The autoregression model design predictive controller is then based on, optimizes following quadratic programming function J and obtains optimal control Amount processed, controls the position g (t) of magnetic levitation ball:
Wherein,Walked for t l Steel ball position prediction variable forward, the autoregression model according to t obtains the expression formula of l step predictions, i.e.,WithFor system prediction coefficient matrix, as described in t from Regression model and multi-step prediction variable are obtained;gr(t+l) it is t Given l step forward references position;U (t+p), p=0,1,2,3 are t The moment electromagnetism winding input voltage to be optimized, only takes Section 1 u (t) to act on controlled magnetic levitation ball;△ u (t)=u (t)-u (t-1) is input voltage increment;For state vector; φ0、φi gAnd φj uFor the regression function coefficient of autoregression model, φ7 u=0;I is unit matrix.
Compared with prior art, the advantageous effect of present invention is that:The thought that the present invention is modeled using System Discrimination, The dynamic of maglev ball system is set up using relevant information of the input/output data comprising system dynamic characteristic of running States model, the dynamic characteristic of system can be depicted most possibly, and without considering magnetic saturation phenomenon and eddy current effect to mould The influence of type (these influences have been included in Identification Data).This method is applied to this kind of strong nonlinearity, strong probabilistic Complication system, may extend to other similar systems;The RBF net coefficients of tape function that the present invention is set up power RBF-ARX models according to Position of the steel ball in electromagnetic field is stored in, the Function approximation capabilities of RBF networks are improved, makes one group of pseudo- linear ARX mould of acquisition Type can preferably describe the dynamic characteristic of non-linear maglev ball system.System one-step prediction output modeling error ± Within 0.4%;The present invention weighs RBF-ARX modelling time-varying, local linear predictive controller based on tape function, can be quick Optimization calculates optimum control amount, reduces the on-line optimization time, is conducive to completing within the maglev ball system sampling period (5 milliseconds) Optimization is calculated, and realizes quick, stability contorting to steel ball position.
Brief description of the drawings
Fig. 1 is maglev ball system structure chart of the present invention.
Embodiment
The system architecture of maglev ball system of the present invention is only capable of the above-below direction movement of control steel ball as shown in figure 1, being one Single-mode system.PC 9 is transferred to electromagnetism winding drive circuit by controller output control voltage through D/A converter 8 6, electromagnetism winding 2 produces electromagnetic induction in the case where passing to phase induced current, in winding electromagnetic field formed below, in field Steel ball 1 apply electromagnetic induction power F, make steel ball up/down move, adjustment electromagnet and steel ball between air gap g (i.e. steel ball position), Until electromagnetic force F and steel ball gravity G is balanced;Meanwhile, LED/light source 3 is used for detecting steel ball with the photoelectric sensor that electro-optical package 4 is constituted Position, corresponding voltage signal is passed PC back through process circuit 5 and A/D converter 7 and exported.In system shown in Figure 1, steel ball 1 Radius is 12.5 millimeters, quality is 22 grams, and the number of turn of electromagnetism winding 2 is that 2450, equivalent resistance is 13.8 ohm.
Maglev ball system of the present invention is influenceed by magnetic saturation and eddy current effect, also by power supply and external interference Influence.Therefore, using the modeling method that RBF-ARX models are weighed based on tape function, building electromagnetism winding input voltage and electromagnetic field The dynamic model of relation between middle steel ball position.In the present invention, using data identification technology, using the linear function of steel ball position RBF networks that make weight coefficient, Gaussian kernel are used as the function coefficients in Nonlinear A RX models.The model is a kind of with linear The nonlinear time-varying model of ARX model structure, its independent variable is electromagnetism winding input voltage, the regressor of steel ball position, steel Ball position is characterizes the semaphore of system mode, using the normal of the function approximation RBF neural related to steel ball position linearity Number power, then carries out real-time online adjustment with the RBF structures to model parameter.Tape function weighs RBF-ARX models in local line Property it is interval in it is very approximate with linear ARX model, its parameter can be automatically updated, automatically with mission nonlinear state in addition Adjustment, with good global adaptive character.
Build the function weight coefficient type RBF-ARX moulds of dynamic performance model between steel ball position and electromagnetism winding input voltage Type, using row dimension Bouguer Ma Kuier special formulas method (Levenberg-Marquardt Method, LMM) and linear least square The SNPOM optimization methods that (Least Square Method, LSM) is combined (are referred to:Peng H,Ozaki T,Haggan- Ozaki V, Toyoda Y.2003, A parameter optimization method for the radial basis Function type models) model parameter is recognized, obtain following structure:
Wherein,
G (t) is the position of steel ball, is also the air gap between steel ball and electromagnet;U (t) is electric for the input of electromagnetism winding Pressure;φ0、φi gAnd φj uThe respectively regression function coefficient of autoregression model;W (t-1) is system work dotted state, System work dotted state is characterized with steel ball position g (t-1);V0WithFor the once linear letter of steel ball position Number, is used as the function weight coefficient of RBF neural;| | | | it is 2 norms;ξ (t) is white noise;For linear constant coefficient, pass through SNPOM optimization sides Method is recognized, and is calculated and obtained with LSM on the basis of nonlinear parameter is obtained.Order Formula (1) is rewritten asThen
Wherein,For the observation data of steel ball position, numbers are observed using 4000 altogether when SNPOM carries out Model Distinguish According to.
Utilize the characteristic design time-varying of maglev ball system local linear, linear predictive controller.Formula (1) is rewritten as Multinomial
Wherein,
The state variable of definition system:
Then the state-space model of formula (1) is:
Here
φ in above formula0、φi gAnd φj uIt is not constant, but changes with steel ball position g (t).Define related prediction Variable:
Wherein,It is multistep forward prediction state vector,It is steel ball position multistep forward prediction vector,It is Winding input voltage multistep forward prediction vector.Assuming that u (t+j)=u (t+3) (j >=4), from (5)~(7), can be obtained:
Here,WithFor system prediction coefficient matrix, it can be obtained by formula (5)~(8), during dependent on t The position of steel ball in electromagnetic field is carved, is the value changed with steel ball position g (t).
So the local linear characteristic design of RBF-ARX models can be weighed in the tape function of t for maglev ball system The linear predictive controller changed with t.
Define controlling incrementAnd desired output variable
Then there is the quadratic programming majorized function that Local-region Linear Prediction is controlled
Wherein,I is unit matrix.
To maglev ball system, formula (13) is the optimization problem of a quadratic programming, can be obtained most by on-line optimization Excellent controlled quentity controlled variable.It is changing with steel ball location status, linear so as to which the PREDICTIVE CONTROL of non-linear maglev ball system be reduced to PREDICTIVE CONTROL, can greatly save the on-line optimization time of optimum control amount, steel ball is rapidly reached stable state.

Claims (2)

1. a kind of magnetic levitation ball position control method, it is characterised in that comprise the following steps:
1) autoregression model is set up to maglev ball system:
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Wherein, g (t) is the position of t magnetic levitation ball;U (t) is electromagnetism winding input voltage;ξ (t) is white noise;
It is the once linear function of steel ball position;For constant system Number, is recognized by SNPOM optimization methods;G (t-1) is the position of t-1 moment magnetic levitation balls;
2) predictive controller is designed based on the autoregression model, optimizes following quadratic programming function J and obtain optimum control amount, control The position g (t) of magnetic levitation ball processed:
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Wherein,gr(t+l) the l step forward references given for t Position, l=1,2 ..., 12;U (t+p) is what t to be optimized Electromagnetism winding input voltage, only takes Section 1 u (t) to act on controlled magnetic levitation ball, p=0,1,2,3;Δ u (t)=u (t)-u (t-1) is input voltage increment; WithFor system prediction coefficient matrix;For state vector; φ0WithFor the regression function coefficient of autoregression model,I is unit matrix;I12For 12 rank unit matrixs;I4For 4 Rank unit matrix.
2. magnetic levitation ball position control method according to claim 1, it is characterised in that
<mrow> <msub> <mover> <mi>B</mi> <mo>&amp;OverBar;</mo> </mover> <mi>t</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>B</mi> <mi>t</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mi>t</mi> </msub> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>B</mi> <mi>t</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>3</mn> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>A</mi> <mi>t</mi> </msub> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>B</mi> <mi>t</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>4</mn> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>3</mn> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>3</mn> </mrow> <mn>4</mn> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mrow> <mn>4</mn> <mo>-</mo> <mi>i</mi> </mrow> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>11</mn> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>10</mn> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>9</mn> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>3</mn> </mrow> <mn>11</mn> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mrow> <mn>11</mn> <mo>-</mo> <mi>i</mi> </mrow> </msup> <msub> <mi>B</mi> <mi>t</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein:
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mi>t</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>&amp;phi;</mi> <mn>1</mn> <mi>g</mi> </msubsup> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&amp;phi;</mi> <mn>2</mn> <mi>g</mi> </msubsup> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&amp;phi;</mi> <mn>6</mn> <mi>g</mi> </msubsup> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&amp;phi;</mi> <mn>7</mn> <mi>g</mi> </msubsup> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>B</mi> <mi>t</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>&amp;phi;</mi> <mn>1</mn> <mi>u</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&amp;phi;</mi> <mn>2</mn> <mi>u</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&amp;phi;</mi> <mn>6</mn> <mi>u</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>C</mi> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> 2
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