Aailable olie at www.sciecedirect.com Procedia Egieerig 7 (2) 442 446 Procedia Egieerig (2) Procedia Egieerig www.elseier.com/locate/procedia www.elseier.com/locate/procedia 2 Smposium o Securit Detectio ad Iformatio Processig Applicatio of Kalma Filter i the CNC Sero Cotrol Sstem Weibig Wag a Pegbig Zhao b * a School of Mechaical Egieerig, Xi'a Uiersit of Sciece ad echolog,xi'a,754,chia b he Ke Laborator of Cotemporar Desig ad Itegrated Maufacturig echolog,miistr of Educatio,Northwester Poltechical Uiersit,Xi a,772,chia Abstract he primar objectie of this research is to costruct a kid of PID ler which ca adapt to the oliear ad time-ariatio of the CNC sero sstem. Accordig to the trait ad performace requiremet of the CNC sero sstem, based o the traditioal PID ad kalma filter theor, a kid of special PID ler has bee desiged, usig the kalma filter to oercome the ifluece of measuremet oise ad oise i the CNC sero sstem, thus, the sstem possesses better self-adaptie abilit ad strog disturbace resistig performace. Seeral sets of experimets were carried out based o MALAB/Simulik eiromet to test the alidit of this PID ler. he damic simulatio results show that the ler achiees better performace tha the classic oe, ad it ca restrai the oise ad has better damic respose characteristics. his research gies solutio to the difficult labilit of oliear ad time-ariatio sstem, which has importat theoretical sigificace ad egieerig practical alue. 2 Published b Elseier Ltd. Ope access uder CC BY-NC-ND licese. Kewords: CNC sero sstem; Kalma filter; PID ; Sigal processig; Simulatio. Itroductio I the techolog of moder stochastic optimal ad stochastic sigal processig, sigal ad oise are ofte the multi-dimesioal o-statioar stochastic process. Because of the time-ariatio ad o-fixig power spectrum, the kalma filter theor was proposed i 96, this theor realizes the data filterig processig i computer accordig to recursie algorithm i time domai[]. Kalma filter is the best liear estimatio based o the criterio of least mea-square error, thus, it ot ol ca be applicable to the statioar sstem of scalar estimatio, but also ca be suitable for o-statioar time-ariatio sstems of the multi iput multi output. Kalma filter utilizes the state equatio ad recurrece method to estimate, ad especiall implemets easil o computer [5]. Because of the limitatios of traditioal PID ler, the parameters are difficult to adjust i the sstem that with oise iterferece, ad it is difficult to achiee ideal effect, therefore, combiig the kalma filter with the traditioal PID ler ca reduce the impact of oise o sstem, the kalma filter ca the filterig sigal to the PID ler. Cosequetl, the composite PID ler ca improe the qualit [4]. * Correspodig author. el.:3572289478. E-mail address: zhpb83@63.com. 877-758 c 2 Published b Elseier Ltd. Ope access uder CC BY-NC-ND licese. doi:.6/j.proeg.2..73
W. Wag, P. Zhao / Procedia Egieerig 7 (2) 442 446 443 Weibig WagPegbig Zhao/ Procedia Egieerig (2) he CNC feed sero sstem hae the strog couplig, time-ariatio ad oliear, so the strateg is er complex, desigig the better strateg ca ot ol compesate the shortcomig of hardware, but also ca improe the sstem performace[3]. he high-performace sero sstem requires the strateg hae followig characteristics, such as fast damic respose, high damic ad static precisio, ad the sstem is isesitie to chages ad disturbaces of parameters. 2. Mathematical model of CNC sero sstem 2.. Compositio of CNC sero sstem As the importat part of CNC, the mai task of feed sero sstem is to the displacemet, directio ad elocit of the moemet of executie compoet. As show i Fig., it composes of mechaical trasmissio ad electric drie sstem [3]. he former icludes worktable, tool holder, ball screw ad trasmissio gear, the latter icludes motor, drie sstem, power amplifier ad detectig elemet. So far, because of the better damic ad static performace, the high-precisio feed sero sstem usuall uses the AC sero sstem drie b PMSM. he PMSM AC sero sstem is composed of permaet maget schroous sero motor, elocit ad positio sesor, power ierter ad PWM geeratio, ad positio-elocit-curret ler. he AC motor is a strog couplig, time-ariatio ad oliear sstem, so it is difficult to. CNC positio sero drie sstem speed curret mechaical trasmissio ad executie compoet positio speed curret sero driig deice PMSM positio measuremet deice Fig. he compositio of CNC feed sero sstem 2.2. Costructio of Mathematical model u q Ls R i q K e K c e L Js B r Fig.2 he flow chart of PMSM feed sero sstem he mathematical model of PMSM AC sero sstem is show i Fig.2, the mathematical model i the fieldorieted mode ca be expressed as followig trasfer fuctio: Kc GM () s () 2 LJs ( RJ LB) s BR KcKe I the equatio(), Kc (3 p f) / 2 is the torque coefficiet; Ke p f is the back emf costat; L is the widig iductace; R is the coil resistace; J is the total momet of iertia, which icludes lead screw momet of iertia J s, the gear momet of iertia J ad J 2, ad the motor shaft momet of iertia J M ; B is the total iscosit
444 W. Wag, P. Zhao / Procedia Egieerig 7 (2) 442 446 Weibig WagPegbig Zhao / Procedia Egieerig (2) dampig coefficiet, which icludes the lead screw dampig B s, the gear dampig B ad B 2, ad the motor shaft 3 dampig B ; seeral simulatio parameters are gie as follows: L8.5 ( H), R 2.875( ), M 3 2.8 ( km m ) J, B.2( N m/ ( rad / s)), f.75( Wb) ad p 4. Put all the parameters ito the equatio, we ca obtai the followig expressio:.27 GM () s (2) 6 2 3 6.85 s 2.4 s.824 3. Priciple of kalma filter ad costructio of sstem For the discrete liear sstem [6]: x( k) Ax( k ) B( u( k) w( k)) (3) ( k) Cxk ( ) k ( ) (4) I the equatio, x( k) is the sstem state i k time, uk ( ) is the quatit i k time. A ad B are the sstem parameters, for the multi-model sstem, the are expressed b matrix. ( k) is the measured alue i k time, C is the parameter of measuremet sstem, wk ( ) is the process oise sigal, k ( ) is the measuremet oise sigal, ad Ewk [ ( )] Ek [ ( )], Ewkw [ ( ) ( j)] Q, Ek [() ()] j R, Ewk [ ( ) ( j)], these equatios illustrates that process oise is ot releat with measuremet oise, Exw [ ( k)] Ex [ ( k)] shows that iitial state ad oise is idepedet. he recursie algorithm of discrete kalma filter is [9]: PkC ( ) M ( k) (5) CP( k) C R Pk ( ) APk ( ) A BQB (6) Pk ( ) ( I M ( kcpk ) ) ( ) (7) x( k) Ax( k ) M ( k)( ( k) CAx( k )) (8) e ( k) Cx( k) (9) he coariace of error is: Ec ( k) CP( k) C () he costructio of kalma filter is show i Fig.3 [7], ad the costructio of PID sstem based o kalma filter is show i Fig.4. Compared with traditioal PID sstem, the kalma filter is added to the output alue of the led object, the measuremet oise ad the iterferece alue is reduced b the filter, the reductio process is reflected b that the output alue after filterig is fed back to the sstem, therefore, the performace of the sstem is ehaced. u w e ri u w out e Fig.3 costructio of kalma filter o kalma filter Fig.4 costructio of PID sstem based
W. Wag, P. Zhao / Procedia Egieerig 7 (2) 442 446 445 Weibig WagPegbig Zhao/ Procedia Egieerig (2) 4. Simulatio aalsis Coert the trasfer fuctio ito discrete state equatio b Z-trasform, this ca facilitate the simulatio experimet [6, 8]. he discrete state equatio of the led object is: x( k ) Ax( k) B( u( k) w( k)) () k ( ) Cxk ( ) (2) he output with measuremet oise of the led object is: ( k) Cxk ( ) k ( ) (3).656.734 I the equatio A. B C.89.728 D. he followig simulatio experimet is to erif the performace of the kalma filter, the simulatio program is show i Fig.5, ad the kalma filter algorithm is completed b M-fuctio. he amplitudes of iterferece sigal wk ( ) ad measuremet oise sigal k ( ) are.; the are the white oise, as show i Fig.8, the amplitude of iput sigal is., frequec is.5hz, ad it is a siusoidal sigal. I the kalma filter, Q, R, simulatio time 3s, the simulatio result is show i Fig.6 ad Fig.7, the result show that the kalma filter has a good effect for the iterferece ad measuremet oise. Sie Wae ()=Cx()+Du() x(+)=ax()+bu() Discrete State-Space Clock MALAB Fuctio Kalma Filter Demux Scope Radom Number Scope3 Radom Number -K- Gai -K- Gai Scope2 Scope Fig.5 simulatio program based o kalma filter.4.2 with oise.4.2 filtered sigal -; -sigal with oise.8.6.4.2 with oise -.2.5.5 2 2.5 3 time(s) -; e-filtered sigal.8.6.4.2.5.5 2 2.5 3 time(s) Fig.6 ad with oise Fig.7 ad filtered sigal B programmig i the MALAB eiromet to erif the performace of the PID sstem based o kalma filter, the amplitudes of iterferece sigal wk ( ) ad measuremet oise sigal k ( ) are.2, the
446 W. Wag, P. Zhao / Procedia Egieerig 7 (2) 442 446 Weibig WagPegbig Zhao / Procedia Egieerig (2) are the white oise, ad the iput is a step sigal. Q, R, simulatio time s, k 8., k.8, k.2, the damic respose of PID with ad without kalma filter are show i Fig.9. p i d.4.2.3.2. -. -.2.8.6.4.2 PID with kalma filter PID without kalma filter -.3 -.4.5.5 2 2.5 3 -.2..2.3.4.5.6.7.8.9 Fig.8 white oise sigal with amplitude of. Fig.9 PID with ad without kalma filter Aalsis from the simulatio results show that the damic respose of sstem is slow, settlig time is log, stead precisio is low, ad the mai reaso is that there is costat error ad radom error i the sigal ad the sstem model is ot er accurate. As show i Fig.9, after usig the kalma filter, the effect of sstem has bee improed distictl, because the filter process the obseratio alues b liear recurrece, it ca calculate the optimal estimates of the sstem real-timel. 5. Coclusios B itroducig the kalma filter to estimate the effectie iformatio i the alues, the accurate iformatio has bee obtaied, ad the CNC feed sero sstem has bee optimized. he simulatio results show that combiig the kalma filter ad the reasoable PID parameters, we ca obtai the stable output, shorter peak time, less oise ad fewer shocks, simultaeousl, the sstem ca reach the stable state quickl. Cosequetl, compared with the traditioal PID, the PID based o kalma filter has fast respose, better stable performace, ad high precisio, therefore, it has importat theoretical sigificace ad egieerig practical alue. Refereces [] Greg Welch, Gar Bishop. A Itroductio to the Kalma Filter.UNC-Chapel Hill 26; 9(5): 4. [2] Ah KK, ruog DQ. Olie tuig fuzz PID ler usig robust exteded Kalma filter. Joural of Process Cotrol 29; 9:~23. [3] Huag X, Shi L. Simulatio o a fuzz-pid positio ler o the CNC sero sstem, i: Proceedigs of the IEEE Sixth Iteratioal Coferece o Itelliget Sstems Desig ad Applicatios, Chia, 26; 35~39. [4] Marzuki Mustafa M, Rozaimah S, et al.. Robust o-lie of hexaalet chromium reductio process usig a Kalma filter. Joural of Process Cotrol 22; 2:45~42. [5] Prakash J, Sriiasa K. Desig of oliear PID ler ad oliear model predictie ler for a cotiuous stirred tak reactor. ISA rasactios 29; 48: 273~282. [6] Homaou Najjara, Adrew Goldeberg. Real-time motio plaig of a autoomous mobile maipulator usig a fuzz adaptie Kalma filter. Robotics ad Autoomous Sstems 27; 55: 96~6. [7] Xie Xiue, Lia Feghui. Research o Applig Kalma Filters i PID lers. Egieerig & est 29; 9: 6~8. [8] WANG Hag-u, NI Yua. Research of PID Cotrol Sstem of Electric Vehicle Motor Based o Kalma Filter. Joural of Xi a echological Uiersit 28; 6: 267~269. [9] ZOU Lig, SUN Yuqiag. A Simulatio Stud of PID Cotrol Based o Kalma filter. Microcomputer Iformatio 27; 6: 79~8.