CN100439892C - Recognization method for object rotary inertia having complex irregularity structure - Google Patents

Abstract

The present invention relates to a recognization method for the moment of inertia of an object with complex irregular structure, which belongs to the technical fields of object moment of inertia measurement and automatic identification technique application. The present invention is characterized in that four springs arranged on a rigid girder are symmetrically supported at the bottom surface of an object being measured; four electromagnets symmetric to the object being measured are arranged at the inner sides of the springs; four displacement sensors are fixedly arranged on the object being measured perpendicular to the electromagnets; then, the electromagnets are connected to a voltage-controlled current source and a DSP in sequence. As long as excitation signals are input into the DSP to cause the DSP to output four voltages twice corresponding to X and Y axes respectively, the respective moment of inertia around the X and Y axes of the object being measured and the electromagnets jointly can be estimated with a publicly known automatic identification technique, and the moment of inertia of the object being measured can be obtained by subtracting the moment of inertia of the electromagnets therefrom. The present invention has the advantages of strong adaptability, simple method and high precision of identification.

Description

The discrimination method of irregular structure object rotation inertia

Technical field

The discrimination method of irregular structure object rotation inertia belongs to the object rotation inertia field of measuring technique, especially relates to the application of the measuring method and the identification technique of complicated irregularly shaped object moment of inertia.

Background technology

In the design of some large-scale kinematic systems, the moment of inertia of system is an important technical parameter.With the automobile is example, and (automobile is walked around the yaw moment of inertia J of the vertical axis Z of its barycenter to its three axial rotation inertia _zWalk around the pitch rotation inertia J of the horizontal cross shaft Y of its barycenter _yInclination moment of inertia J around automobile roll axis m-m _m) be the important technology parameter in the running car dynamics.They are to the important influence such as control stability, riding comfort and driving safety of automobile.Grasping these technical parameters is to carry out the basic premise that automobile dynamics is researched and analysed.

In known technology, the universal method that obtains object rotation inertia can be divided into two big classes.A kind of is to calculate moment of inertia by the labor to object materials and structure.Ansys finite element analysis software for example, and and the piecewise linearity computing method mentioned in " calculating piecewise linearity square beam new method of deformation, Shandong Institute of Architecture ﹠ Engineering 's journal, Vol.11, no.3,1996 " of document.The deficiency of these class methods is that it requires the testee material even, and composition is known, and tactical rule, otherwise can can't use because the error of calculation is too big.Another kind of method is object under test to be placed on the special-purpose rotation inerttia instrument measure.As patent CN2493919Y a kind of device that utilizes torsional oscillation method to measure special-shaped object rotation inertia has been proposed, patent US6098025 then utilizes the rotation of driven by motor measured object, by measuring barycenter and the moment of inertia that rotational angular velocity and current of electric calculate measured object, a covering device and method have been proposed thus.Though these class methods can be applied to the irregular contour object rotation inertia, for the volume and the quality of measured object very high restriction is arranged all, can't be applied to some large scale systems.Except the measuring method of these versatilities, also having some known technologies is the moment of inertia that are used to measure special object.Proposed a kind of method of measuring the internal combustion engine moment of inertia as patent US5656768, determined moment of inertia by the rotating speed and the torque of measuring in motor acceleration and the moderating process, obviously, this method range of application is too single.Disclosed automobile power assembly barycenter of patent CN2527992Y and inertia square test board utilize the concrete mechanism of physical pendulum principle and power assembly to design, the deficiency of this method is, this apparatus structure is big and complicated, install and experimental implementation requirement height, volume and weight to measured object still has certain limitation, and is to be exclusively used in automobile component.The moment of inertia test board of mentioning in the document " research of moment of inertia test board magnetic suspension system electromagnetic damping, XI AN JIAOTONG UNIVERSITY Subject Index, vol.35, no.12,2001 " remains and uses the method for rocking to measure.It utilizes electromagnetic bearing that measuring table and measured object are suspended, and dials the driven by motor dial by fork and rotates, and makes workbench around the free torsional movement of its work, by measuring the moment of inertia of corner and torque calculation measured object.The deficiency of this method is to require platform suspension, thereby needs the design of feedback controller, and this is a quite thing of difficulty.

Owing to lack easy measuring method, usually adopt some experimental formula estimation moment of inertia values in the actual engineering.This method lacks versatility, and the error of result of calculation is also bigger.

System Discrimination is a kind of theory and the method for setting up mathematical model of controlled plant and estimating unknown parameter.Its means are to extract the parameter that is studied mathematics model or estimates to require from the experimental data that contains noise.A kind of discrimination method commonly used is a least square method.Be characterized in without any need for statistical information, and can prove theoretically under very weak condition consistent Estimation is provided about measuring error and external disturbance.Simultaneously, this method also has the calculating characteristic of simple.This method is used the input signal of maximum length linear shift register sequence (being called for short the M sequence) signal as system usually.The M sequence signal is a kind of pseudo-random code.It has the character of approximate white noise, can guarantee good identification precision, and is easy on the engineering realize.

Summary of the invention

The objective of the invention is for overcoming the weak point of prior art, propose a kind of method of estimation of the irregular structure object rotation inertia based on the System Discrimination technology.Adopt the present invention, can measure the moment of inertia of any irregular structure object, and for the shape of measured object, volume, structure all without limits, have good versatility and operability, can be used to measure moment of inertia such as large scale systems such as automobiles.

The required hardware facility of the enforcement of this method is by rigid support beam (1), electromagnet (2), spring (3), DSP (digital signal processor, include D/A) (4), displacement transducer (5), voltage-controlled current source formations such as (6), in order to measure the moment of inertia of testee (7).System chart as shown in Figure 1, the diagonal angle sectional view is as shown in Figure 3.

The estimation of object rotation inertia may further comprise the steps among the present invention:

1. testee is supported on the buckstay with 4 springs, the strong point is positioned at A shown in Figure 2 ₁, A ₂, A ₃, A ₄The place;

2. 4 electromagnet and 4 displacement transducers are installed on testee, and mounting points is positioned at B shown in Figure 2 ₁, B ₂, B ₃, B ₄The place, sectional view is as shown in Figure 3;

3. connect DSP, voltage-controlled current source and electromagnet;

4. design a M sequence signal U,, utilize known programming technique to make DSP output shown in Figure 1 satisfy u as the identification pumping signal ₁=u ₂=-u ₃=-u ₄=U (or u ₁=-u ₂=-u ₃=u ₄=U), and the measurement data of record 4 displacement transducers this moment ${\hat{z}}_1(=\mathrm{\Δ}{z}_1),{\hat{z}}_2(=\mathrm{\Δ}{z}_2),{\hat{z}}_3(=\mathrm{\Δ}{z}_3),{\hat{z}}_4(=\mathrm{\Δ}{z}_4);$

5. according to the voltage signal u that imports ₁Measurement data with displacement transducer

Obtain transport function between the input and output with least square method or other discrimination methods on computers;

6. according to the transport function of identification, calculate the moment of inertia of testee around Y-axis (or X-axis).

Identification process

In the analysis of following 1-4 part, the testee of loading onto electromagnet is done as a wholely to treat, be called for short object.Its identification process is as follows:

1. set up the motion model of object, geometric position, size and direction coordinate are as shown in Figure 2.

The input and output equation of voltage-controlled current source:

i _n＝cu _n+j _n，n＝1～4 (1)

I in the formula _nBe electric current in the magnet coil; C is a constant, is determined by the voltage-controlled current source self character; J is the coil current of object when being in initial rest position; u _nControl voltage for input.

The electromagnetic attraction equation that electromagnet provides:

$F_n=K\frac{{i_n}^2}{{z_n}^2},n=1~4---\left(2\right)$

F in the formula _nThe electromagnetic attraction that provides for electromagnet to object; K _nBe constant, determine by the coil self character; z _nThe distance on Z-direction for brace summer and electromagnet center.

The elastic force equation that spring provides:

F _n′＝kz _n′，n＝1～4 (3)

F in the formula _n' the elastic force that provides for spring to object; K is the coefficient of stiffiness of spring; z _n' be the deformation length of spring.The equation of motion of object:

$M\frac{d^{2}z}{{\mathrm{dt}}^2}=F_z---\left(4\right)$

$T_x=I_x\frac{d^2\mathrm{\α}}{{\mathrm{dt}}^2}---\left(5\right)$

$T_y=I_y\frac{d^2\mathrm{\β}}{{\mathrm{dt}}^2}---\left(6\right)$

In the formula, M is the quality of object; Z is the displacement of object mass center on Z-direction; F _zBe object suffered make a concerted effort on Z-direction; T _xBe the object resultant moment suffered with respect to X-axis; I _xBe the moment of inertia of object around X-axis; α is the corner of object around X-axis; T _yBe the object resultant moment suffered with respect to Y-axis; I _yBe the moment of inertia of object around Y-axis; β is the corner of object around Y-axis.

Geometric relationship:

$\left[\begin{array}{c}{\hat{z}}_1\\ {\hat{z}}_2\\ {\hat{z}}_3\\ {\hat{z}}_4\end{array}\right]=\left[\begin{array}{c}\mathrm{\Δ}{z}_1\\ \mathrm{\Δ}{z}_2\\ \mathrm{\Δ}{z}_3\\ \mathrm{\Δ}{z}_4\end{array}\right]=\left[\begin{array}{c}z+\frac{1}{2}l\sin \mathrm{\β}\cos \mathrm{\α}+\frac{1}{2}b\sin \mathrm{\α}\cos \mathrm{\β}\\ z+\frac{1}{2}l\sin \mathrm{\β}\cos \mathrm{\α}-\frac{1}{2}b\sin \mathrm{\α}\cos \mathrm{\β}\\ z-\frac{1}{2}l\sin \mathrm{\β}\cos \mathrm{\α}-\frac{1}{2}b\sin \mathrm{\α}\cos \mathrm{\β}\\ z+\frac{1}{2}l\sin \mathrm{\β}\cos \mathrm{\α}+\frac{1}{2}b\sin \mathrm{\α}\cos \mathrm{\β}\end{array}\right]---\left(7\right)$

$\left[\begin{array}{c}{{\hat{z}}_1}^{\′}\\ {{\hat{z}}_2}^{\′}\\ {{\hat{z}}_3}^{\′}\\ {{\hat{z}}_4}^{\′}\end{array}\right]=\left[\begin{array}{c}\mathrm{\Δ}{z_1}^{\′}\\ \mathrm{\Δ}{z_2}^{\′}\\ \mathrm{\Δ}{z_3}^{\′}\\ \mathrm{\Δ}{z_4}^{\′}\end{array}\right]=\left[\begin{array}{c}z+\frac{1}{2}L\sin \mathrm{\β}\cos \mathrm{\α}+\frac{1}{2}B\sin \mathrm{\α}\cos \mathrm{\β}\\ z+\frac{1}{2}L\sin \mathrm{\β}\cos \mathrm{\α}-\frac{1}{2}B\sin \mathrm{\α}\cos \mathrm{\β}\\ z-\frac{1}{2}L\sin \mathrm{\β}\cos \mathrm{\α}-\frac{1}{2}B\sin \mathrm{\α}\cos \mathrm{\β}\\ z+\frac{1}{2}L\sin \mathrm{\β}\cos \mathrm{\α}+\frac{1}{2}B\sin \mathrm{\α}\cos \mathrm{\β}\end{array}\right]---\left(8\right)$

In the formula, l, L, b, B as shown in Figure 2, Δ z _nBe the displacement with respect to the equilibrium position on the Z axle of magneticaction point, Δ z _n' be the displacement with respect to the equilibrium position on the Z axle of spring force application point.

2. set the equilibrium position of object

Set when object is in the equilibrium position, the magnetic gap between brace summer and the magnet is z ₀, and this moment, the magnet spool electric current was j=cu ₀, u ₀Output voltage for DSP this moment.

3. near the linear model the equilibrium position

Systematic parameter when being in the equilibrium position based on above-mentioned motion model and object can be derived the linear model that object moves near the equilibrium position.Particularly,

1) satisfies u when input voltage signal ₁=u ₂=-u ₃=-u ₄The time, the transport function between the input and output is

$G_1\left(s\right)=\frac{{\hat{z}}_1\left(s\right)}{u_1\left(s\right)}=\frac{l^{2}s}{(I_y{s}^2-l^2\frac{2j^{2}K}{z_0^3}+L^{2}k)\frac{2\mathrm{jK}}{z_0^2}c}---\left(9\right)$

At this moment, the second order resonant frequency point ω of this model ₁With the moment of inertia I of object around Y-axis _yBetween relation be

$I_y=(L^{2}k-l^2\frac{2j^{2}K}{z_0^3})/{\mathrm{\ω}}_1^2---\left(10\right)$

2) satisfy u when input voltage signal ₁=-u ₂=-u ₃=u ₄The time, the transport function between the input and output is

$G_2\left(s\right)=\frac{{\hat{z}}_1\left(s\right)}{u_1\left(s\right)}=\frac{b^{2}s}{(I_x{s}^2-b^2\frac{2j^{2}K}{z_0^3}+B^{2}k)\frac{2\mathrm{jK}}{z_0^2}c}---\left(11\right)$

At this moment, the second order resonant frequency point ω of this model ₂With the moment of inertia I of object around X-axis _xBetween relation be

$I_x=(B^{2}k-b^2\frac{2j^{2}K}{z_0^3})/{\mathrm{\ω}}_2^2---\left(12\right)$

4. estimate the moment of inertia of object

Design an identification pumping signal U (as the M sequence), make input signal u ₁=u ₂=-u ₃=-u ₄=U obtains output data then by experiment

According to data u ₁With

Utilize least square method or other system discrimination method to obtain transport function G between the input and output ₁(s) and the resonant frequency point.Utilize formula (10) can calculate the moment of inertia of object around Y-axis.

Make input signal u again ₁=-u ₂=-u ₃=u ₄=U obtains output data then by experiment

According to data u ₁With

Utilize least square method or other system discrimination method to obtain transport function G between the input and output ₂(s) and the resonant frequency point.Utilize formula (12) can calculate the moment of inertia of object around X-axis.

5. calculate the moment of inertia of testee

What the 4th step obtained is the moment of inertia sum of testee and electromagnet.Because the quality of electromagnet is easy to record, the quality of establishing each electromagnet is m, then can obtain the moment of inertia I of testee around X-axis _XxWith moment of inertia I around Y-axis _YyBe respectively

I _xx＝I _x-mb ²，I _yy＝I _y-ml ² (13)

It is pointed out that the theoretical model that formula (9), (11) provide is a continuous time model.And the model that the measurement data identification that utilizes the output data of DSP and displacement transducer obtains is a discrete time model, is the discretization model of theoretical model.The sampling time interval of discretize depends on the frequency of operation of DSP, the slewing rate of A/D and the bandwidth of displacement transducer.When using this method, should be noted that the mutual conversion of this two class model.

In addition, the condition that formula (9), (11) are set up is that the geometric center and the barycenter of testee overlaps, just the barycenter of testee should with Fig. 2 in 0 overlap.This requires not so difficult satisfied, because general kinematic system always is designed to be symmetry.Even be not like this, also can meet the demands by the method for counterweight, from measurement result, reject the moment of inertia of mass then.

The invention is characterized in that it contains following steps successively:

(1) near testee edge, be supported on the buckstay roof beam structure with 4 identical spring handle measured objects of coefficient of stiffiness k, the strong point will carry out counterweight with the standard weight to testee to the geometric center symmetry of measured object, and its barycenter is overlapped with geometric center;

(2) at the place, inboard that corresponds respectively to above-mentioned 4 springs, below measured object, connection is also installed 4 electromagnet that electromagnetic constant K is identical, the installation site of electromagnet will and will be lower than above-mentioned buckstay roof beam structure to the center of measured object symmetry, above the measured object corresponding to 4 electromagnet, 4 identical displacement transducers of fixed installation on the position longitudinally;

(3) measure distance L and B between each electromagnet respectively, measure between each spring strong point apart from l and b;

(4) be electrically connected DSP, commercially available voltage-controlled current source and electromagnet successively, again above-mentioned each parameter k, K, L, B, l, the quality m of b and electromagnet, voltage-controlled current source amplification coefficient c store in the PC;

(5) setting comprises the initial position of the object of electromagnet, the gap z between record electromagnet this moment and buckstay roof beam structure ₀And store in the PC;

(6) the output signal u of adjusting DSP ₀, make object be in the initial position that step (5) is set, and measure magnet spool electric current j=cu this moment ₀

(7) the identification pumping signal U input DSP that a data length that designs is in advance determined utilizes and the supporting emulator of DSP, dsp program is made 4 output signal u of DSP with known method ₁, u ₂, u ₃, u ₄Satisfy u ₁=u ₂=-u ₃=-u ₄=U; Set output frequency and sampling period, write down the output of intrinsic displacement sensor during this period of time

And it is deposited in PC;

(8) PC is according to the voltage signal u of input ₁Measurement data with displacement transducer

Transport function G between being imported, export with least square method ₁(s), s is the Laplace operator;

$G_1\left(s\right)=\frac{{\hat{z}}_1\left(s\right)}{u_1\left(s\right)}=\frac{l^{2}s}{(I_y{s}^2-l^2\frac{2j^{2}K}{z_0^3}+L^{2}k)\frac{2\mathrm{jK}}{z_0^2}c},$

I wherein _yFor the measured object after the counterweight and electromagnet jointly around the moment of inertia of Y-axis, Y-axis is by the measured object center and be parallel to the line of two strong points of B apart, X-axis is by the center and be parallel to the line of two strong points of L apart, measured object coordinate plane of living in is determined jointly that by X-axis and Y-axis the Z axle is by the center and perpendicular to this plane;

The Bode figure that PC draws by the order of the bode in the known Matlab software makes and can find second order resonant frequency ω ₁Pairing limit, the conversion by discrete-continuous time model obtains ω again ₁

PC calculates I by following formula again _y:

$I_y=(L^{2}k-l^2\frac{2j^{2}K}{z_0^3})/{\mathrm{\ω}}_1^2;$

(9) utilize again and emulator that DSP is supporting to dsp program, make 4 of DSP to export u ₁, u ₂, u ₃, u ₄Satisfy u ₁=-u ₂=-u ₃=u ₄=U, the output of record displacement transducer this moment Deposit in the PC;

(10) PC is according to the voltage signal u of input ₁Measurement data with displacement transducer

Transport function G between being imported, export with least square method ₂(s):

$G_2\left(s\right)=\frac{{\hat{z}}_1\left(s\right)}{u_1\left(s\right)}=\frac{b^{2}s}{(I_x{s}^2-b^2\frac{2j^{2}K}{z_0^3}+B^{2}k)\frac{2\mathrm{jK}}{z_0^2}c},$

I wherein _xFor the measured object after the counterweight and electromagnet jointly around the moment of inertia of X-axis;

PC obtains second order resonant frequency ω with the described method of step (8) ₂PC calculates I by following formula again _x:

$I_x=(B^{2}k-b^2\frac{2j^{2}K}{z_0^3})/{\mathrm{\ω}}_2^2;$

(11) PC calculates measured object after the counterweight around the moment of inertia I of X-axis according to following formula again _XxAnd around the moment of inertia I of Y-axis _Yy:

I _xx＝I _x-mb ²，I _yy＝I _y-ml ²，

Again from I _XxAnd I _YyIn reject the moment of inertia of mass, obtain testee around the moment of inertia of X-axis and around the moment of inertia of Y-axis.

From experimental data as can be seen, the moment of inertia and the design load that obtain with method provided by the present invention differ very little, and relative error is in 5%.By contrast, the adaptability of this method wants much extensive.For not being the object of using Ansys software design structure, calculate with this software with regard to being difficult to, and our rule can be without any the generalized case that is applied to of difficulty.

Complicated irregularly shaped object method for identification of rotational inertia provided by the present invention is realized simple, identified parameters precision height, shape, size, quality to testee all have no requirement, and are applicable to the object of moment of inertia, the especially large scale structure of measuring any complicated irregularly shaped object.

Description of drawings

Fig. 1 is a hardware block diagram of realizing this discrimination method.

Fig. 2 is the motion model synoptic diagram of testee.

Fig. 3 is the sectional view at an angle of the diagonal of testee.

Fig. 4 is the embodiment process flow diagram of the irregular structure object rotation inertia discrimination method that proposes of the present invention.

Embodiment

The method of estimation embodiment process flow diagram of the present invention proposes a kind of irregular structure object rotation inertia based on the System Discrimination technology as shown in Figure 4, it specifically may further comprise the steps:

1. with 4 identical spring (coefficient of stiffiness k=1.109 * 10 ⁴N/m ²) measured object is supported on the buckstay, the strong point requires about object center symmetry, particular location is not limit, but with near the measured object edge for well, in this example as A among Fig. 2 ₁, A ₂, A ₃, A ₄Shown in;

2. 4 electromagnet (electromagnetic constant K=1.660 * 10 are installed on testee ^-4Nm ²/ A ², quality m=1.320kg) and 4 displacement transducers (ST-1 of Beijing Collihigh Sensor Technology Center type current vortex sensor), symmetry also need be satisfied in the installation site, particular location is not limit, but should be in the spring inboard, in this example as B among Fig. 2 ₁, B ₂, B ₃, B ₄Shown in, sectional view is as shown in Figure 3;

3. the distance between the measurement electromagnet---L and B, L=0.595m wherein, B=0.490m; Distance between the measuring spring strong point---l and b, l=0.397m wherein, b=0.327m;

4. connect DSP (the C32SS plate of floating type DSPTMS320C32), voltage-controlled current source (commercially available) and electromagnet;

5. set the equilibrium position of object, the gap z of record electromagnet this moment and buckstay roof beam structure ₀=0.005m;

6. regulate the output signal u of DSP ₀, make object be in the equilibrium position of appointment, and measure magnet spool electric current j=cu this moment ₀=1.717A;

7. length of idinput function design of utilizing Matlab software is 20000 identification pumping signal U;

8. with the supporting TMS320 emulator of DSP, it is programmed, make its output satisfy u with known method ₁=u ₂=-u ₃=-u ₄=U, output frequency is set at 100Hz, and promptly experimental period is 200 seconds, writes down the output of intrinsic displacement sensor during this period of time

(sample frequency also is made as 100Hz);

According to data U and

Utilize the least square identification function arx of Matlab to obtain one 6 rank transfer function model, order its Bode figure that draws with bode again, finding its resonant frequency to put pairing limit is 0.958 ± j0.246, can obtain ω by discrete-knowledge that continuous time model transforms mutually again ₁=25.09rad/s;

The result who obtains according to back and and given data, calculate the moment of inertia I of object by formula (10) around Y-axis _y=4.271kgm ²

11., make the output of DSP satisfy u again to dsp program ₁=-u ₂=-u ₃=u ₄=U, the output of record displacement transducer this moment

Obtain transfer function model 12. use the same method, finding its resonant frequency to put pairing limit is 0.950 ± j0.277, so ω ₂=28.38rad/s;

13. the result who obtains according to back and and given data, calculate the moment of inertia I of object by formula (12) around X-axis _x=2.265kgm ²

14. utilize formula (13) to calculate the moment of inertia I of testee _Xx=2.124kgm ²And I _Yy=4.063kgm ²

In the present embodiment, measured object is also customized with the Ansys finite element analysis software design of U.S. Ansys company exploitation as a shape and all very regular experiment porch of structure, and its moment of inertia just is determined at the beginning of design.The contrast of its design load and the estimated value that obtains with this method is as shown in table 1.

Table 1

	Estimated value	Design load	Relative error
				Testee is around the moment of inertia I of Y-axis yy(kg·m 2)	4.063	4.203	3.33％
Testee is around the moment of inertia I of X-axis xx(kg·m 2)	2.124	2.194	3.19％

Claims (1)

1, the discrimination method of irregular structure object rotation inertia is characterized in that, it contains following steps successively:

(1) near testee edge, be supported on the buckstay roof beam structure with 4 identical spring handle measured objects of coefficient of stiffiness k, the strong point will carry out counterweight with the standard weight to testee to the geometric center symmetry of measured object, and its barycenter is overlapped with geometric center;

(2) at the place, inboard that corresponds respectively to above-mentioned 4 springs, below measured object, connection is also installed 4 electromagnet that electromagnetic constant K is identical, the installation site of electromagnet will and will be lower than above-mentioned buckstay roof beam structure to the center of measured object symmetry, above the measured object corresponding to 4 electromagnet, 4 identical displacement transducers of fixed installation on the position longitudinally;

(3) measure distance L and B between each electromagnet respectively, measure between each spring strong point apart from l and b;

(4) be electrically connected DSP, commercially available voltage-controlled current source and electromagnet successively, again above-mentioned each parameter k, K, L, B, l, the quality m of b and electromagnet, voltage-controlled current source amplification coefficient c store in the PC;

(5) setting comprises the initial position of the object of electromagnet, the gap z between record electromagnet this moment and buckstay roof beam structure ₀And store in the PC;

(6) the output signal u of adjusting DSP ₀, make object be in the initial position that step (5) is set, and measure magnet spool electric current j=cu this moment ₀

(7) the identification pumping signal U input DSP that a data length that designs is in advance determined utilizes and the supporting emulator of DSP, dsp program is made 4 output signal u of DSP with known method ₁, u ₂, u ₃, u ₄Satisfy u ₁=u ₂=-u ₃=-u ₄=U; Set output frequency and sampling period, write down the output of intrinsic displacement sensor during this period of time And it is deposited in PC;

(8) PC is according to the voltage signal u of input ₁Measurement data with displacement transducer

Transport function G between being imported, export with least square method ₁(s), s is the Laplace operator;

$G_1\left(s\right)=\frac{{\hat{z}}_1\left(s\right)}{u_1\left(s\right)}=\frac{l^{2}s}{(I_y{s}^2-l^2\frac{2j^{2}K}{z_0^3}+L^{2}k)\frac{2\mathrm{jK}}{z_0^2}c},$

I wherein _yFor the measured object after the counterweight and electromagnet jointly around the moment of inertia of Y-axis, Y-axis is by the measured object center and be parallel to the line of two strong points of B apart, X-axis is by the center and be parallel to the line of two strong points of L apart, measured object coordinate plane of living in is determined jointly that by X-axis and Y-axis the Z axle is by the center and perpendicular to this plane;

The Bode figure that PC draws by the order of the bode in the known Matlab software makes and can find second order resonant frequency ω ₁Pairing limit, the conversion by discrete-continuous time model obtains ω again ₁

PC calculates I by following formula again _y:

$I_y=(L^{2}k-l^2\frac{2j^{2}K}{z_0^3})/{\mathrm{\ω}}_1^2;$

(9) utilize again and emulator that DSP is supporting to dsp program, make 4 of DSP to export u ₁, u ₂, u ₃, u ₄Satisfy u ₁=-u ₂=-u ₃=u ₄=U, the output of record displacement transducer this moment

Deposit in the PC;

(10) PC is according to the voltage signal u of input ₁Measurement data with displacement transducer

Transport function G between being imported, export with least square method ₂(s):

$G_2\left(s\right)=\frac{{\hat{z}}_1\left(s\right)}{u_1\left(s\right)}=\frac{b^{2}s}{(I_x{s}^2-b^2\frac{2j^{2}K}{z_0^3}+B^{2}k)\frac{2\mathrm{jK}}{z_0^2}c},$

I wherein _xFor the measured object after the counterweight and electromagnet jointly around the moment of inertia of X-axis;

PC obtains second order resonant frequency ω with the described method of step (8) ₂PC calculates I by following formula again _x:

$I_x=(B^{2}k-b^2\frac{2j^{2}K}{z_0^3})/{\mathrm{\ω}}_2^2;$

(11) PC calculates measured object after the counterweight around the moment of inertia I of X-axis according to following formula again _XxAnd around the moment of inertia I of Y-axis _Yy:

I _xx＝I _x-mb ²，I _yy＝I _y-ml ²，

Again from I _XxAnd I _YyIn reject the moment of inertia of mass, obtain testee around the moment of inertia of X-axis and around the moment of inertia of Y-axis.

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