Design of Temperature Compensation Module of the Industrial Robot Wrist Force Sensor Based on Multivariate Regression Method

Transcription

1 Sesors & rasducers, Vol. 7, Issue 6, Jue 04, pp. 3-0 Sesors & rasducers 04 by IFSA Publishig, S. L. Desig of emperature Module of the Idustrial Robot Wrist Force Sesor Based o Multivariate Regressio Method Yua Chualai, Zhag Yueyi, Xiao Shepig, Kog Ligshuag College of Electrical ad Iformatio Egieerig, Hua Uiversity of echology, Zhuzhou, 4000, Chia Chagsha Vocatioal & echical College, Chagsha, 40, Chia el.: Received: April 04 /Accepted: 30 May 04 /Published: 30 Jue 04 Abstract: his paper takes software method to compesate temperature agaist the drift problem of piezoresistive waist force sesor. he compesatio algorithm is modeled through usig the method. Ad compesatio module is desiged based o multiple regressio method. Accordig to the simulatio results, the system desiged meet the basic pheomeo for drift correctio. Fially, the actual data is used to validate this algorithm. Copyright 04 IFSA Publishig, S. L. Keywords: Wrist force sesor, emperature compesatio, modelig, Multivariate regressio.. Itroductio Alog with the rapid developmet of moder detectio techiques, the applicatio of piezoresistive wrist force sesors i idustrial productio practice is more ad more wide. I the twety-first cetury, moder scietific ad techological revolutio is to come. he sesor techology has attracted wide degree attetio of domestic electroic iformatio idustry. It ca eve be said that the techical level of sesors is oe of the importat criteria to measure the level of a atioal sciece ad techology. I recet years, the developmet of foreig wrist force sesor compesatio techology is very quickly, ad the developmet directio is committed to itelligece, miiaturizatio, itegratio, ad digital. I order to correct ad compesate for the sesor, may compaies have lauched iteral itegrated itelliget sigal coditioig chip withi the wrist force sesor to compesate for the imbalace, temperature drift ad o-liearity ad other parameters. he computer system is also used to achieve correctio ad compesatio of sesor. his method has high compesatio accuracy, stability, small size ad is easy to trasport. he mai bottleeck of piezoresistive wrist sesor i practical process is the temperature drift problem. Sice the birth day of piezoresistive wrist sesor, the study of temperature drift compesatio has begu, compesatio is also developed from the hardware to the software compesatio stage. Software compesatio ca achieve high compesatio accuracy, high accuracy ad liearizatio of digital circuits, ad ca also promote the developmet of sesor temperature compesatio techology. Software compesatio techology is relatively simple, ad the compesatio effect is obvious, it is a importat way to improve the accuracy of wrist force sesor. So, most of moder popular wrist sesor temperature compesatio are the software compesatio methods. 3

2 Sesors & rasducers, Vol. 7, Issue 6, Jue 04, pp. 3-0 America psychologist Charies Spearma proposed PCA (also kow as factor aalysis method) i 904, the Hotellig has improved ad developed a multivariate statistical aalysis method, it has reduced system dimesio ad pricipal compoet extractio characteristics. Successively, B. M. Wise [] ad other scholars have applied the method to process moitorig fields. he multivariate statistical process cotrol (MSPC) theoretical framework proposed by J. F. MacGregor combies the kids of statistical aalysis methods PCA ad cotrol theory ad promotes the multivariate statistical methods further applicatios i idustrial processes [-5]. he major step of pricipal compoet aalysis (PCA) is the pricipal compoet extractio which mies ad aalyses multivariate historical data to extract the fiite elemet mai variables. Pricipal compoet aalysis ca reduce high-dimesioal data dimesioality to avoid loss of data. Ad it makes it simple ad easy to operate data aalysis [6-7]. Origial data ca be coverted by the data space (p ad p directio vector) that is the projectio by the projectio vector to obtai a ew variable (Fig. ) ad the form the mai compoet vector, this method is the pricipal compoet extractio. So far, the pricipal compoet extractio method has bee able to adapt to the dyamic process ad o-liear process. ) Sesor head sectio. he sectio maily icludes pressure strai body, strai bridge ad preamp, etc. he force sigals could be coverted ito electrical sigals which ca also be pre-amplified. ) Sigal processig sectio. his part is maily for amplificatio, sigal filterig, A/D coversio, while the other iformatio is set to the computer for data ad temperature compesatio process. he sigal processig portio has a stroger processig capability to optimize complex algorithms, ad achieve the microcomputer cotrol, etc... he Mechaical Structure of Wrist Force Sesor his paper takes the cross beam type wrist force sesor as example to describe the basic mechaical structure of wrist force sesor. Cross beam type sesor have a pair of elastic strai gauges i the frot ad back wrist ad two side beams each. he strai gauge positio of the wrist force sesor is show by Fig.. he strai gauges attach to the cross beam ear the ceter part i medial patch mode, ad the priciple of the patch positio selectio is high sesitivity, greater resolutio, small dimesio betwee iterferece.. he Structure of Idustrial Robot Wrist Force Sesor his sectio describes the basic structure of a idustrial robot commo wrist force sesor, ad fids the drift of the sesor accuracy ad sesitivity i the structure. R4 R8 R3 R5 R6 R6 R7 R5.. System Architecture of Wrist Force Sesor As is show i Fig., a idustrial robot wrist force sesor is maily composed of the followig two parts: Fig.. Cloth diagram of cross elastic beam..3. he Circuit Structure of Wrist Force Sesor Equivalet bridge cofiguratio of wrist force sesor is show i Fig. 3, whe the strai gauge is uder pressure, the two sides are also uder the pressure at the same time, the resistor of a opposite sides icreases/ decreases, the other sides decreases / icreases. Assumig that the iput voltage is Ui, the output voltage is Uo, accordig to the priciple of the bridge, the relatioship betwee them is show i Equatio. Fig.. System diagram of wrist force sesor. V O = ( R+Δ R)( R3+ΔR3) ( R ΔR)( R4 ΔR4) ( R + R +ΔR Δ R )( R + R +ΔR ΔR ) () 4

3 Sesors & rasducers, Vol. 7, Issue 6, Jue 04, pp. 3-0 Fig. 3. Bridge circuit of wrist force sesor. Fig. 4. System architecture of temperature compesatio. From Equatio, wrist force sesor is maily based o the chage i resistace strai gauges to calculate the size of the pressure. Whe the temperature chages, the resistace value will chage, ad this will affect the accuracy ad sesitivity of the sesor. hus, the bridge output chage is maily caused by the chage i resistace. Simplify the formula, igore the chage i resistace, the quadratic is: (RR 3+ RR 4) R Δ i (R R3+ RR 4) U= Up= Ui = Ui πσ ( R+ R 4) (R+ R 3) Ri ( R+ R 4) (R+ R 3) () ΔRi Amog () = πσ Ri As ca be see from Equatio, the mai cause of sesitivity variatio is piezoresistive coefficiet [8-0]. here are two mai factors affectig the piezoresistive coefficiet: the diffusio impurity cocetratio ad ambiet temperature. Whe the diffusio impurity cocetratio icreases (decreases), the piezoresistive coefficiet decreases (icreases). Ad whe the surface impurity cocetratio is low, the temperature icreases, the piezoresistive coefficiet decreases fastly; whe the surface impurity cocetratio is high, the temperature icreases, the piezoresistive coefficiet decreases slowly. While reduce the temperature, icrease the diffusio impurity cocetratio, the piezoresistive coefficiet will also be reduced, ad the output sesitivity is affected..4. emperature Module Aalyze As is show i Fig. 4, the system uses lumped cotrol architecture, each wrist force sesor is equipped with a temperature compesatio module. Each temperature compesatio module which is coected to the MCU cotrol module via the bus way is evetually set to the ma-machie iterface through the serial port. 3. emperature Module Based o Multivariate Regressio Method Multiple liear regressio, whose optimizatio goal is that the sum of absolute errors of domiat variable is miimal, aalyzes the auxiliary variable through liear regressio method. Multivariate statistical aalyze theory is through a large umber of historical ad curret data, establish statistical aalysis model of the process variables ad the mai factor variables, whose modelig process is relatively simple, model structure is uified, ad the desig of overall system is easy. he mai thig is that the method is tried i high-dimesioal complex object model, ad ca establish high precisio liear or oliear models. 3.. Multiple Regressio Method PCA method is based o the variace of the data chages as a idicator to determie the correspodig directio variable of the PCA variable. he historical data could be extracted effectively ad dimesio is also reduced through the vector trasformatio ad solvig. he basic idea of PCA method is: Fid a ew set of variables which is a liear combiatio of the origial variable istead of the origial oe. From the perspective of optimizatio, pricipal compoet variables, whose umber is fewer tha the origial variables, ca carry the useful iformatio of the origial data to the largest extet ad are urelated betwee themselves. It icludes the defiitio ad acquisitio of the pricipal compoet, as well as the data recostructio. It belogs to the category regressio method, but it does ot show a oliear relatioship model. So far, PCA methods are emergig i edlessly, such as: KPCA, NPCA ad so o. he kerel pricipal compoet aalysis (KPCA) has attracted widespread attetio of scholars i recet years, the variable is trasformed ito a highdimesioal space by oliear mappig, ad the 5

4 Sesors & rasducers, Vol. 7, Issue 6, Jue 04, pp. 3-0 most importat iformatio i the data is cotaied to the first pricipal compoet variable, so KPCA is a simple ad effective oliear PCA method. algorithm as a multivariate liear regressio techique was first proposed ad used i the field of ecoomics to deal with the high-dimesioal data by scholar Wood. Ulike PCA algorithm, while PCA extractio, the iteral model relatioship of pricipal compoet iput ad output variables is established, it ca reder the exteral physical cotact betwee variables of system. combies the PCA with caoical correlatio aalysis ad iherits characteristics of both algorithms, so it reduces dimesioality ad establishes the characteristic relatioship betwee iput ad output variables of the model. I the, through usig the priciple of maximizig the covariace, solve the pricipal compoet which could reflect the relatioship betwee the iput ad output variables successively, the pricipal compoet extractio ad model regressio are simultaeous i the process. ypically, model cosists of two parts, i.e. the iteral model ad exteral model, characterize regressio process ad pricipal compoet extractio process respectively. Wherei the exteral model R * r r i= X E = t p = P (3) ё tr = h r(t r ) = XW R * r r i= (4) Y F = u q = UQ (5) U = YC (6) From the Formula 3-6, it ca be see that the origial high-dimesioal data matrix ca be decomposed ito the sum of the vector product. Where E *, F * represet the residual matrix after pricipal compoet extractio. r, pr are the r th iput pricipal compoet ad load vector;, P are the implicit variable matrix ad directio matrix for respose; Ur, qr represet r th output pricipal compoet ad load vector; U, Q are correspodig matrix form; W, C are iput ad output projectio vector respectively. he iteral model is obtaied by liear regressio of ad U So, the model formula is: U ˆ = B (7) * Y= UQ + F= BQ + F (8) cotrol diagram is show i Fig. 5. Fig. 5. cotrol block diagram. 3.. he Applicatio of Multiple Regressio Method i the emperature I this paper, multivariate regressio method is desiged for the wrist force sesor stress chip temperature compesatio. If the experimetal method is adopted, i the rage of -40 o C~5 o C, the various temperature compesatio coefficiets are measured to establish the iput ad output data sets. Uder ormal circumstaces, the limited discrete poits are selected to correct the wrist force sesor, ad the we record compesatio coefficiets o these poits, get compesatio coefficiet at each temperature by usig the software method. I the stadard, a give process data are ofte divided ito two data blocks, the depedet variable data X=(x ij ) xm ad the idepedet variable data Y=(y ij ) x, i.e. iput ad output data of the system, l, m, deote the observatio umber, the dimesio umber of iput ad output variable. Exteral model ca extract the pricipal compoet through iterative calculatio of iput data X ad output data Y, as is show i Equatio 5. he iteral model of algorithm characterizes the mathematical relatioship betwee the iput pricipal compoet variable t r ad output pricipal compoet variable u r : b = ut/tt (9) r r r r r u b t = (0) r r r where F* is the modelig error, b r is the regressio parameter of the r th pricipal compoet variable space, the pricipal compoet spatial regressio matrix B characterizes the correlatio degree betwee the data i the projectio space. he traditioal modelig method ofte igores the dyamic characteristics of system that is the dyamic model relatioship, but merely idicates steady-state relatioships betwee data. herefore, may scholars itroduce the dyamic characteristics model establishmet ito algorithm as improvemet for this deficiecy. he dyamic relatioship of iteral model withi the model proposed by Ray ad Kasper ca express approximately the mathematical descriptio 6

5 Sesors & rasducers, Vol. 7, Issue 6, Jue 04, pp. 3-0 of dyamic filter added before modelig. Assumig H(*) is filter model added before the modelig, the data E ~ is obtaied through addig filters o the basis of the steady-state model, that is: E = H( E ), () r where E r is the residual matrix after the r th step pricipal compoet extractio, the directio vector, which is used at r step pricipal compoet extractio, is obtaied by solvig the largest eigevalue. At this time, the parameters of the are: w = vector (H(E )F F E, r λmax r r r r tr = Er wr = H(E r )w, r p = H E t /t t, ( ) r r r r r r () where H (*) which is a diagoal matrix ca be trasformed ito the iteral model filter h r (*) i each pricipal compoet variable space. hrough the matrix trasformatio, the Equatio ca be expressed as: ё tr = h r ( tr) = Er wr ё tr = h r(t r ) (3) Amog them, the projectio of primitive variable i vector w r is t r, the projectio of dyamic data i the w r after addig filter is t r. herefore, the iteral model i the dyamic model ca be expressed approximately as a combiatio of filter model ad static iteral model. At this time, the structure of dyamic exteral model i the model ca be expressed as: ё Y F= H BQ = H(E0W)BQ (4) he dyamic characteristic of the system is obtaied by itroducig the filter i each pricipal compoet variable space. I order to describe the dyamic characteristic of the system better, this paper combies auto-regressio model ARX with to characterize the dyamic characteristics of the system through applyig ARX model ito the dyamic descriptio i iteral model of, at this time, it becomes ARX- model. he represetatio of this dyamic iteral model is: u = H t r r r = = Y F H Q H q R r= r r = H diag(h t,,h t ) R R (5) Amog (5), H r (t r ) is the dyamic model of r th sub-system with liear ARX form i hidde variable space. he system ca be broke dow ito separate small systems to facilitate algorithm desig through this method. However, the specific idetificatio method of the system eeds further itroductio. Combiig the model expressed by Equatio 5, the optimizatio propositio of origial spatial variables is put forward: mijo = ( yk y ( k) ) ( yk y ( k) ) (6) k= y( k ) ad y k are origial output ad the output obtaied by ARX- modelig at time k respectively. However, the propositio is expressed the optimizatio propositio of pricipal compoet output variable: mij= ( uk u ( k) ) ( uk u ( k) ) (7) k= u( k ) ad u k are the output of pricipal compoet ad ARX- iteral model at time k respectively. = R = u k [u k,u k,,u k ] u k [u k,u k,,u k ] R (8) hus, the optimizatio propositio of the Formula (8) ca be substituted for: mij = u k u k = mij + mij mij + mij R ( ) + + r R r = k = Amog: Jr = u( k) u ( k) k = (9) u r (k) ad u r (k) are the output of r th depedet variable subspace ad the correspodig ARX. he iput ad output i the pricipal compoet variable space i the ARX model at time k are: u k = φ k θ k (0) r r r ρ r r r( ) r( ) φ k = [u k,u k,, u k,t k d, tr k d,,tr k d m ] iclude the curret ad historical iformatio of iput ad output variables i the r th pricipal compoet variable space, wherei d r is the lag time coefficiet of subsystem, m, are the iput ad output order of the various subsystems. 7

6 Sesors & rasducers, Vol. 7, Issue 6, Jue 04, pp. 3-0 = θr k [ ar k, ar k,, ar k, br k, br k,, br k ] iclude the regressio parameters of the r th hidde variable ARX model at time k, the propositio o the subsystems is: Jr = ( u( k) u ( k) ) = ( ur( k) φr( k) θr( k) ) k= k= () he parameters are obtaied usig the system idetificatio method [-] for propositio, that is: θ k = (φ k φ k ) φ k θ k () r r r r r he parameters m, ad d r have bee predetermied before parameter idetificatio of the ARX- model. 4. he Simulatio Results 4.. Performace Idex he sesitivity of wrist force sesor is impacted by temperature greatly. he coefficiet of thermal sesitivity is used to compare forth with back temperature compesatio effect of the sesor. Accuracy is expressed as the size of measuremet data error of wrist force sesor i the whole size rage. he coefficiet of thermal sesitivity drift is defied as: Y Y() Y Y() FS ( )Y Y () C f i 0 i f 0 Ks 00% i f 0 (3) Y f ( i ) - the correspodig output to full-scale value of wrist force sesor at the temperature of i. he accuracy, which is the percetage of the maximum absolute error of the sesor uder predetermied coditio with respect to measuremet rage, is typically used to idicate the relative value of measuremet error. Ad it is defied as: ΔA A = 00% (4) Y F.S Δ A represets the allowable Amog (4), absolute maximum error i the measuremet rage, Y F.S meas the full-scale output. 4.. Experimetal Data Because of equipmet limitatio, this article does ot carry out the measured data. he comparative data used for the validatio experimets of the algorithm is performace ad measuremet accuracy data of test sesors which are the two PA-0 types Keller wrist force sesor from precisio istrumet ad optoelectroics egieerig of iaji uiversity withi C rage for compesatio ad 0-0 kpa for the sesor rage. ake eight test poits from -40 C~00 C temperature rage to take: -40 C, -30 C, -5 C, 0 C, 0 C, 50 C, 70 C, 00 C. Set five poits withi each cycle test poits, keep applyig pressure more tha 30 secods o each pressure poit ad the measure the output of the sesor with voltmeter. he test results of the sesor are show i able ad able. able. he test data sheet of sesor A. emperature Value able. he test data sheet of sesor B. emperature Value

7 Sesors & rasducers, Vol. 7, Issue 6, Jue 04, pp. 3-0 able 3. he test data sheet of sesor A. emperature Value able 4. he test data sheet of sesor B. emperature Value Accordig to the above data, do data modelig based o method. Fig.6 shows the result of the predicted output ad the actual output through dyamic ARX- model. It ca be see that there are some errors of the system but the dyamic characteristics of the system ca tracked. he modelig parameters are obtaied as follow: P = Q = Wx = W y 0.57 = he iteral model dyamic is gotte through the multiple regressio method: H Z = 0.065z z.980z z 0.004z z.4087z z 0.000z z.449z z z.94z z z Modelig results are show i Fig. 7. It ca be see that dyamic compesatio model is applied to the sesor temperature compesatio to achieve better practical results. he experimetal results aalysis: ) he experimet measured data is obtaied i the warmig case, the residece time at each measuremet poit is 30 miutes, this case is cosistet with algorithm compesatio temperature, the real objective compesatio effect ca be reflected objectively to a certai extet. ) It ca be foud that the algorithm has sigificat improvemet for sesitivity drift by cotrastig Zero drift ad sesitivity drift data before ad after sesor compesatio, sesitivity temperature drift error has bee reduced o the order of magitude. 9

8 Sesors & rasducers, Vol. 7, Issue 6, Jue 04, pp ) he etire compesatio circuit is i the -40 C~00 C temperature rage, the liearity of curves at differet temperatures is better. 3) he etire compesatio circuit is i the -40 C~00 C temperature rage, the liearity of curves at differet temperatures is better. y y y p re y p re Fig. 6. he results of dyamic modelig. Fig. 7. Simulatio results of the system. We ca get the he experimetal results aalysis by the data i able 3, ad able 4. ) he experimet measured data is obtaied i the warmig case, the residece time at each measuremet poit is 30 miutes, this case is cosistet with algorithm compesatio temperature, the real objective compesatio effect ca be reflected objectively to a certai extet. ) It ca be foud that the algorithm has sigificat improvemet for sesitivity drift by cotrastig Zero drift ad sesitivity drift data before ad after sesor compesatio, sesitivity temperature drift error has bee reduced o the order of magitude. y y 5. Coclusio his paper proposes temperature compesatio model based o pricipal compoet aalysis agaist the existece of the defect for the slow covergece of pricipal compoet aalysis i the wrist sesor temperature compesatio, ad simulates compesatio for the wrist sesor temperature drift of the model. Refereces []. Xu Keju, Practical study method of dyamic characteristics of sesor, Uiversity of Sciece & echology Chia Press, 999. []. Wag Guotai, et al., Several problems i the developmet of six axis force sesor, he Robot, Vol. 9, Issue 6, 997, pp [3]. Xu Keju, Li Cheg, Study o static decouplig of multidimesioal wrist force sesor, Joural of HeFei Uiversity of echology, Vol., Issue, 999, pp. -6. [4]. Wu Jua, Study o the improvemet ad robot modelig six dimesio wrist force sesor, Master's Degree hesis of Southeast Uiversity, 00. [5]. Liu Zhegshi, he system error aalysis of six compoet wrist force sesor loadig test bech of robot, Acta Metrologica Siica, Vol. 9, Issue, 998, pp [6]. Wag Yaodog, Dyamic calibratio of robots wrist force sesor, Master's Degree hesis of Southeast Uiversity, 990. [7]. Xu Keju, Zhu Negcheg, Li Cheg, Experimetal modelig of six dimesio wrist force sesor step respose, he Robot, Vol., Issue 4, 000, pp [8]. Liu Zhegshi, Study o the dyamic load effect of robot wrist force sesor, he Robot, Vol. 0, Issue 3, 998, pp [9]. Wold S., M. Sjöström, et al., -regressio: a basic tool of chemometrics, Chemometrics ad Itelliget Laboratory Systems, Vol. 58, Issue, 00, pp [0]. Wag Huiwe, Liear ad oliear approach of partial least square regressio, Natioal Defece Idustry Press, Beijig, 006. []. Che J., Fag W., based dewma ru-to-ru cotroller for MIMO o-squared semicoductor processes, Joural of Process Cotrol, Vol. 7, 007, pp []. Zhao Z., Hu B., Liag J., Multi-loop adaptive iteral model cotrol based o a dyamic partial least squares model, Joural of Zhejiag Uiversity- SCIENCE A, Vol., Issue 3, 0, pp Copyright, Iteratioal Frequecy Sesor Associatio (IFSA) Publishig, S. L. All rights reserved. ( 0