An Anti-windup Algorithm for PID Controller of PMSM SVPWM Speed. Control System

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1 3r Internatonal Conference on Mechatroncs, Robotcs an Automaton (ICMRA 215) An Ant-wnu Algorthm for PID Controller of PMSM SVPWM See Control System Bngyang Luo 1, a, Mengchao L 1, b, Png Wang 1, c, anyuan Yu 1, 1 School of Automaton, Wuhan Unversty of technology, Wuhan, Hube, 437, Chna a @qq.com, b @qq.com, c @qq.com, @qq.com Keywors: PMSM See Control System; PID control; Ant-wnu; MALAB & smulaton. Abstract. PID controller s one of the most wely use n ermanent magnet synchronous motor see control system. Better control effect s to be obtane whle ale n the see-ajuste system for PMSM. o the roblem of wnu n the PID controller [1], ths aer rooses an ant-saturaton PID algorthm. he effectveness s teste by usng MALAB&Smulaton. Usng ths new mrove PID controller algorthm we can reuce the overshoot of the see regulatng system an shorten the stablzaton tme. Introuctons he basc ea of PMSM control [2] comes from the ornary three-hase AC motor to smulate DC motor see control. In the PMSM SVPWM control, through the control of the stator current to mrove erformance of motor torque control, an the stator current s fnal control object. Uner the three-hase statc coornate, the AC currents a, b, c coul be transforme to, q uner synchronous rotatng coornate system by Clar an Par transformaton. Meanwhle comarng the see comman sgnal an the rotor see etecton sgnal, after ajustng through the see loo PID controller, outut ref, qref. q an qref, an ref were further comare wth, an get through the current loo PID controller, we obtan the outut axs voltage V ref an V qref uner the -q coornate system. Agan through the Par nverse transform, outut vector voltage unerα-β coornate system, the three-hase nverter IGB were rve by the sx-channel PWM sgnal whch were the outut of the vector voltage through SVPWM moule, to rouce a contnuous an varable frequency, amltue three hase snusoal current to nut PMSM stator armature, thus comletng the tas of ouble close loo vector control of PMSM [3]. PMSM vector control system conssts of fve arts: the oston an see etecton, see loo an current loo PI regulator, Clar an Par transformaton, SVPWM sace vector control moules. PID Control heory As the most wely use controller, PID controller s use as see loo an current loo controller n the PMSM see control system whch s smle, effectve, an ractcal. heory of PID control system shown n Fg.1, the system s manly conssts of PID controller an controlle object [4] he authors - Publshe by Atlants Press 529

2 Fg.1 PID control system PID controller s a n of lnear regulator, through roortonate, ntegrate an ervate the evaton of gven value r (t) an the actual outut value y (t), the lnear combnaton of those three mae u the control quantty to control the object. 2.1 he Functon of Varous Correcton Ln of PID Controller Proorton: roortonately reacton to the evaton sgnal e (t) of control system, once rouce, controller wll act mmeately to mnmze evaton. Integraton: t s manly use to elmnate statc error. he strength of the ntegral acton eens on the ntegral tme constant r, the bgger the r to be, the weaer ntegral acton s, an vce versa. Dfferentaton: Reflect the change tren of evaton sgnal (rate of change), an before the evaton sgnal becomes too bg, an effectve early correcton sgnal s leae nto system, thus acceleratng the movement see of system, reucng the ajustng tme. ratonal PID controller has two algorthms: Poston an Incremental, after usng DSP evces, tycally usng gtal PID control analog PID control functons. PID controller equaton s able to screte comutng. 2.2 Poston Dgtal PID Control Algorthm he fferental equaton of PID controller: t È 1 e( t) (1) u( t) K Íe( t) + Ú e( t) t + Î t K s roortonal gan; s ntegral tme constant; u (t) s outut control quantty; e (t) s evaton; e (t)r(t)-y(t). We can obtan the followng aroxmate transformaton: t Ú e() t t ª Â e() e() t e( ) - e( -1) t ª (2) hen the fferental equaton of PID controller translates nto: Â [ ] u( ) K e( ) + K e( ) + K e( ) - e( - 1) K K K K ; (3) Due to Poston PID control algorthm s the total amount of outut, so each oututs are relate wth the ast state, e() has to accumulate when calculatons, comutng worloa. Moreover, because the comuter outut u () corresons to the actual oston of the actuator, f the comuter fals, a substantal change n u () wll cause a substantal change n oston of the actuator, may cause sgnfcant accents, n orer to avo ths stuaton, Incremental PID control algorthm s roose 2.3 Incremental PID Control Algorthm From the above analyss, fferental equaton of PID controller s: 53

3 Â -1 [ ] u ( ) K e( ) + K e( ) + K e( ) - e( - 1) Â [ ] u ( - 1) K e( - 1) + K e( ) + K e( - 1) - e( - 2) (4) Subtractng the above two equatons: [ ] [ ] D u( ) u( ) - u( - 1) K e( ) - e( - 1) + Ke( ) + K e( ) - 2 e( - 1) + e( - 2) (5) K K K K ; PID Controller Wnu Phenomenon he so-calle wnu henomenon refers to f the system exst a recton of evaton, ue to the ntegral acton the outut of the PID controller accumulate an ncrease contnuously, causng the actuator to the lmt oston; If the controller outut u () s contnues to ncrease, the oenng egree of the actuator cannot be ncrease, then the control amount of comuter outut beyon the normal oeratng range an nto the saturate zone. Once the system has a reverse bas, u () graually wthraw from the saturate zone. he eeer the saturate zone get n, the longer to ext the saturate zone. Durng ths ero, the actuator remans at extreme oston, wthout mang the arorate changes mmeately when reverse bas exsts, the system just le out of control at ths tme, resultng n eteroraton of the control erformance, whch s calle ntegral wnu henomenon or runaway henomenon. In the PMSM see control system, when the see evaton rouce jum n a long tme, the outut of Poston PID wll ramatcally ncrease. Once the outut of system requres a long tme to reaches a gven value, urng ths tme the ntegral term wll rouce a large accumulate value. When the outut cumulatve value excees the saturaton values, the bas reverse, but ue to the larger accumulaton value of the ntegral, the control amount requre conserable ero of tme to out of the saturate zone. herefore, wnu henomenon wll ncrease overshoot of the system, the system stablzaton tme becomes longer, even uner certan contons cause system nstablty, thereby greatly reucng the overall system erformance. In the tratonal PID controller esgn rocess, the arameters of the PID controller tunng s n the lnear regon, gnorng the nonlnear factors cause by saturaton, so the erformance of tratonal esgn PID controller wll be worse than execte, n orer to reuce the effects of saturaton nonlnear factors on system erformance, resultng n ant-saturaton theory [5]. hs aer resents an ant-saturaton PID controller esgn metho, n orer to verfy the correctness of theoretcal analyss an effectveness of ths control metho, we conucte MALAB smulatons. Exermental results show that the ant-wnu PID controller can effectvely reuce the overshoot of see control system, shorten the settlng tme of the system an mrove the ablty of ant-system loa sturbance. Ant-wnu PID Controller Desgn hrough theoretcal analyss of the PID regulator shows that gtal PID controller fferental equaton s: Ï (6) u ( ) K Ì e ( ) + Â e ( ) + [ e ( ) - e ( - 1) ] Ó he PID controller n see control system often usng ncremental PID control: 531

4 [ ] [ ] D u( ) u( ) - u( - 1) K e( ) - e( - 1) + Ke( ) + K e( ) - 2 e( - 1) + e( - 2) K K K K ; (7) Kth PID controller outut u () can be exresse as: u( ) D u( ) + u( - 1) (8) From the above equaton classc ncremental PID control algorthm nees to reserve the value of the frst two moment s evaton. In ths aer, we target on the followng three asects to esgn ant-wnu PID controller: (1) Lmt the PID regulator outut For the PID regulator, when the evaton nut s large, the outut value wll be large, t s ossble comes to outut saturaton, t s often necessary for the PID controller to lmt outut. When u()>u max, assume u()±u max Smly lmt the outut, n normal oeraton, t s ossble that we unable to elmnate resual error. (2) Integraton searaton e () >e, thus evaton s large, use ure P control, an can nhbt ntegral saturate. e () e, thus evaton s small, use PI control; the ntegral coul elmnate the bas. (3) Weaen the ntegral metho when reach to the lmt When see control system s actually runnng, classc ncremental PID control algorthm nees to reserve the value of the frst two moment s evaton. hs metho s n the calculaton of u (), frst juges whether the uer tme amount of control u (-1) s beyon lmt or not If u (-1)>u, only accumulate negatve bas; If u (-1) u, only accumulate ostve bas; hs algorthm can avo a long stay n saturaton zone for control amount. Control rogram flow of gtal PID controller shown n Fgure 2. Fg.2 Control rogram flow of gtal PID controller 532

5 MALAB smulaton an results analyss In orer to verfy the erformance of ant-wnu PID controller, we use MALAB software smulaton [6], smulaton gven 3rm/mn see ste resonse, the samlng tme s 1ms. Usng ant-wnu algorthm to serse systems ste resonse smulaton results shown n Fgure 3. Usng the tratonal PID algorthm to serse system ste resonse, the ste resonse results shown n Fgure 4. As can be seen from the smulaton results, the use of ant-wnu PID metho can avo a long stay n saturaton zone for control amount, control the system overshoot. wo ns of PID algorthm wth the same arameters, from the exermental waveforms we now, the mrove PID algorthm rse tme s s, maxmum overshoot s 45rm, the tme to reach steay s s; ratonal PID control algorthm rse tme s s, maxmum overshoot s 44rm, an the tme to reach steay s.17s. hs shows that the overshoot an resonse tme of mrove ant-wnu PID control algorthm both less than the tratonal PID control algorthm, sgnfcantly mroves the erformance of the servo system. Fg.3 Imrove PID control algorthm (left: n; rght: e) Fg.4 ratonal PID control algorthm (left: n; rght: e) Concluson ratonal PID control algorthm gnores the nonlnear factors cause by saturaton, so usng tratonal methos esgne PID controller wll get a worse erformance than execte. Ant-wnu functon PID control algorthm roose n ths aer effectvely suresses wnu; accelerate the see of control system resonsveness. heoretcal analyss an exerments show that the algorthm can qucly follow the target see, low the overshoot, an slght the concusson, also t remans the steay-state erformance of tratonal PID control algorthm. he algorthm uses only a set of PID arameters, arameter tunng s more convenent, usng the algorthm to the PMSM control system, can also meet the see, low overshoot an other ynamc roertes for rvng the motor. 533

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