Model Reference Adaptive Control for Perforated Mill. Xiu-Chun Zhao, Guo-Kai Xu, TaoZhang and Ping-Shu Ge

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1 nd Internatonal Conference on Electronc & Mechancal Engneerng and Inforaton Technology (EMEIT-) Model Reference Adatve Control for Perforated Mll Xu-Chun Zhao, Guo-Ka Xu, TaoZhang and Png-Shu Ge Deartent of Electroechancal & Inforaton Engneerng, Dalan Natonalte Unverty, Dalan, 66, Chna Keyword: Model reference adatve control, Perforated ll, Dturbance and uncertante Abtract. Th aer addree a odel reference adatve controller whch ha ler tructure, fewer adjutable araeter, eaer oeraton and accurate trackng caablty even n the reence of external dturbance and uncertante. The controller aled nto the erforated ll autoatc eed control yte and ulaton reult llutrate the ractcalty and effectvene. Introducton Snce Maachuett Inttute of Technology frt rooed adatve control technology n the late 95 [], any dfferent for adatve control ethod ha aeared [-5], uch a Dreber and Prce, Pearon, who early rooed the degn ethod [5]. Thee ethod can not guarantee the yte global aytotc tablty. Later, Monool reearched an augented error gnal ethod, whch degn adatve control law by Jacob tablty theory[6]. It can adjut the controller nut and outut araeter to gan the good erforance and avod adotng the dfferental of outut gnal. However, th ethod ha too any control araeter and the tructure colex to leent alcaton. Therefore, reducng the adjutable araeter n the odel reference adatve controller and lfyng the controller tructure the key to the ractcal alcaton of adatve controller [7-9]. Moreover, there a varety of nterference gnal nevtably n actual yte. Whle Irove the yte robutne, enure the yte tablty even n the reence of external dturbance and uncertante have becoe the urgent roble. Electrc drve yte one of the ot ucceful area n odel reference adatve control yte alcaton [-]. For exale, C.Lacu and I.Boldea adot adatve control for otor uly drve yte n the early alcaton []. Model reference adatve controller can degn the reference odel baed on the yte erforance, and the adatve controller can enure the yte trackng and tablty by adjutng the controller araeter even n the reence of external dturbance and uncertante. Perforated ll eed control yte anly focued on controllng the drve electrcal otor eed. Accordng to the dfference between the eaured value of ervo otor and et value, the rece eed control acheved by control ervo otor. Conder above reaon, th aer addree a ractcal odel reference adatve controller for erforated ll eed control yte. The controller obtan the feedback gan fro the flter dervatve of control nut, o the yte ha good control erforance even n the reence of external dturbance and uncertante. The controller ha le tructure and fewer tunng araeter, whch ake the rooed reference odel adatve controller ha the ractcal value. Perforated ll eed control yte Perforated ll generally aled nto eale teel e rollng equent. The eed control lay a vtal role on the roducton effcency and roduct qualty. Perforated ll eed control yte anly focued on controllng the drve electrcal otor eed. Accordng to the dfference between the eaured value of ervo otor and et value, the rece eed control acheved by control ervo otor. The control yte adot drect-current otor and lcon controlled rectfer technology and the otor current loo ued a controlled object. The yte dynac tructure hown n Fg.. The yte dered erforance the overhoot M =%, re tet =, o the reference odel elected a Publhed by Atlant Pre, Par, France. 989

2 nd Internatonal Conference on Electronc & Mechancal Engneerng and Inforaton Technology (EMEIT-) ( ) = r ( ) y () Fg. tructure of erforated ll eed control Notaton: u : Arature voltage; K : Slcon controlled rectfer gan T : The control te of the lcon controlled rectfer; L : Arature Inductance R : Arature retance; : Arature current C φ : Motor torque coeffcent; M : Motor torque M L : Motor load torque; J : Motor oent of nerta Model reference adatve controller degn The Model reference adatve control rncle : Accordng to the lant tructure and control requreent, the reference odel degned to ake outut reone can exre the nut coand exect. Then, the trackng error between the odel outut and the controlled object outut by adjutng controller araeter, o that the trackng error converge to zero. That, for any ecewe contnuou unforly bounded nut functon r (t) and any ntal condton, the object control nut can be found to ake the trackng error between the controlled object and reference odel gradually converge to zero. The yte reference odel equaton dected by nut-outut equaton a: A ( ) Y = B ( ) r( t) () Where, n h n h + = A ( ) = a, B ( ) b n h = =. a, b are Known contant, r andy are the reference odel nut and outut reectvely, h the order dfference between controlled object and reference odel, dfferental oerator n all olynoal, = d / dt. The correondng controlled object dected by nut-outut equaton a: A ( ) Y = B ( ) u (3) n n Where, A ( ) = + α, = B ( ) β, n = = α, β both are uncertan low te-varyng coeffcent, u and Y are the controlled object nut and outut reectvely, B Hurwtz olynoal. The trackng error e = Y Y The tructure of odel reference adatve controller hown a fg.. Publhed by Atlant Pre, Par, France. 99

3 nd Internatonal Conference on Electronc & Mechancal Engneerng and Inforaton Technology (EMEIT-) Fg. tructure of odel reference adatve controller Suoe that: A ( ) = A ( ) + A ( ) A ( )Y (t ) = M ( )u (t ) n = = Where, A ( ) = n + α, M ( ) =, α, (4) both are uncertan low te-varyng coeffcent. Cobnng (4) nto (3), the controlled object can be exreed a follow: A ( )Y (t ) + A ( )Y (t ) = B ( )u (t ) (5) The trackng error e(t ) = Y (t ) Y (t ) ntroduced nto ()-(5), then A ( )e(t ) = B ( )r (t ) B ( )u (t ) + A ( )Y (t ) (6) Contruct controller outut a follow B ( )r (t ) = u (t ) + u (t ), u (t) = H ( )u (t) N f ( ) Where, / N f ( ) tate flter, N f ( ) = n h = (7) h f, H ( ) =, h and f are contant. = Subttutng (7) nto 6, The error functon can be decrbed a, A ( )e f = u (t ) + [ N f ( ) H ( ) B ( ) + M ( )]u f (t ) (8) e, u f = u N f ( ) N f ( ) Subttutng lnear coenator D( ), then Where, e f = v= D( ) {u (t ) + [ N f ( ) H ( ) B ( ) + M ( )]u f (t )} A ( ) (9) Adatve control outut u (t ) can be exreed a u ( t ) = Kˆ ( ) u f ( t ) () Ung () and (9) the generalzed error equaton can be further wrtten a D( ) ˆ v= [ K ( ) + N f ( ) H ( ) B ( ) + M ( )]u f (t ) A ( ) { } Where, Kˆ ( ) = k. = Publhed by Atlant Pre, Par, France. 99 ()

4 nd Internatonal Conference on Electronc & Mechancal Engneerng and Inforaton Technology (EMEIT-) If the arorate adatve udate law for k can be elected and eet the followng condton, we ay ealy rove the convergence of the trackng error to zero and the yte tablty ung Poov hyer-tablty theory. The condton are: Frtly, tranfer functon D( )/ A ( ) trctly otve real, Then the Proortonal-ntegral adatve law defned a d d k = k v u k k v u ) =,,..., n () f ( f dt dt k Where, and k are the gan coeffcent of the adatve control law. Fnally, the yte control nut u n [ ( ) + u = B rf k u f ] H ( ) (3) = Sulaton reult The controlled object erforated ll eed control yte whch tructure hown n fg.. Drve otor araeter are elected a Pe = 5 kw, I e = 7 A, R =. 34 Ω, L =.3 H, J = 547 kg/, K = 5, T =. 67, C φ = 9 N/A, the axu allowable value of the bound 4. In order to verfy the effectvene of the rooed odel reference adatve control, the reference odel elected a two-order functon (). The tructure of odel reference adatve controller hown n fg.. The control gan ued n the ulaton were elected a k = 5, k =., k =.. Alyng Poov hyer-tablty theory and Matlab/ulaton, ulaton reult are hown n Fg.3-4. Fg.3 Outut reone of the reference odel and controlled object Fg.4 Trackng error of the adatve controller Publhed by Atlant Pre, Par, France. 99

5 nd Internatonal Conference on Electronc & Mechancal Engneerng and Inforaton Technology (EMEIT-) Suary A odel reference adatve controller for erforated ll eed control yte reented. The controller obtan the feedback gan fro the flter dervatve of control nut, o the yte ha good control erforance even n the reence of external dturbance and uncertante. Adatve control law baed on the Poov hyer-tablty theory, whch ake the yte have good trackng and tablte. The controller ha le tructure and fewer tunng araeter, whch ake the rooed reference odel adatve controller ha the ractcal value. The effectvene of the rooed controller wa verfed by ulaton. Acknowledgent Th work wa uorted by Fundaental Reearch Fund for the Central Unverte, Foundaton of Laonng Educatonal Cottee (L93). Reference [] Wu hchang, Wu zhongqang: Adatve Control (Bejng: Mechancal Indutry Pre 5) [] J. H. K. Delay and t te-dervatve deendent robut tablty of te delayed lnear yte wth uncertanty, IEEE Tranacton on Autoatc Control, Vol.46, No.5 (), [3] J. Cao, J. Wang. Delay deendent robut tablty of uncertan nonlnear yte wth te delay, Aled Matheatc and Coutaton, Vol.54, No.(4), [4] Y. He, Q. Wang, L. Xe, etal. Further roveent of free-weghtng atrce technque for yte wth te-varyng delay, IEEE Tranacton on Autoatc Control, Vol.5, No.(7), [5] L qngquan. Adatve Control Syte Theory, Degn and Aalcaton(Bejng: Scence Pre 99) [6] Wu zhongqang, Pao chunjun. Overvew of Model reference adatve control theory, Inforaton technology, Vol.5, No.7( ), [7] Zhang engfe, Peng wedong. Control of Inducton Motor Baed on Model Reference Adatve Syte, Modern Electronc Technque, Vol.34, No.(), [8] Xu guoka, Chu zhenyou, WU Shchang. The adatve controller degn of ort yte, Bejng: Chnee technology re, 4. [9] Lu xng, Lu xao. The develoent and alcaton of elf-adatve control yte, Acadec foru, Vol.53, No.9(), [] Zhao xuchun, Xu guoka. Adatve Control of Double Houng Planer, Proceedng of the 7th Chnee control conference, Vol., No.7(8),.-3. [] C.Lacu, I.Boldea, and F.Blaabjerg. A odfed drect torque control for nducton otor enorle drve, IEEE Tran. Ind, No.4(),.-3. [] Mohaed Boukattaya,Tarak Daak, Mohaed Jalloul. Robut Adatve Control for Moble Manulator, Internatonal Journal of Autoaton and Coutng, No.(), Publhed by Atlant Pre, Par, France. 993