Design and Implementation of a New Sliding-Mode Observer for Speed-Sensorless Control of Induction Machine

Transcription

1 IEEE RANSACIONS ON INDUSRIAL ELECRONICS, VOL. 49, NO. 5, OCOBER ABLE I ANALYICAL VALUES AND EXPERIMENAL RESULS (IN PARENHSES) WIH RESPEC O k AND C FOR SRAEGY A AND SRAEGY B Design an Implementation of a New Sliing-Moe Observer for Spee-Sensorless Control of Inuction Machine Anan Deriyok, Mustafa K. Güven, Habib-ur Rehman, Nihat Inanc, an Longya Xu Abstract In this letter, a new sliing-moe sensorless control algorithm is propose for the fiel-oriente inuction machine rive. In the propose algorithm, the terms containing flux, spee, an rotor time constant, which are common in both current an flux euations, in the current moel of the inuction machine are estimate by a sliing function. he flux an spee estimation accuracy is guarantee when the error between the actual current an observe current converges to zero. Hence, the fourth-orer system is reuce to two secon-orer systems, an the spee estimation becomes very simple an robust to the parameter uncertainties. he new approach is verifie by simulation an experimental results. Inex erms Inuction motor, fiel-oriente control, sensorless control, sliing moe. an experimental results with respect to k an C for strategy A an strategy B. We can conclue that C an I 0 =I L influence the power factor far less than k oes. his can be explaine from the results shown in able I, that the c current reuire (C I o ) to eliminate the voltage imbalance is usually much smaller than I L. Also, the even harmonics introuce in strategy B is negligible when using a larger k. V. CONCLUSION he voltage imbalance in the split capacitors is a isavantage of the half-brige boost rectifier. In this letter, the imbalance phenomenon an the metho of overcoming it have been iscusse in etail. It is prove that the optimal compensation scheme is to a only a reuire c component in the source current. REFERENCES [] J.. Boys an A. W. Green, Current-force single phase reversible rectifier, Proc. Inst. Elect. Eng., pt. B, vol. 36, no. 5, pp , 989. [2] R. Srinivasan an R. Oruganti, A unity power factor converter using half-brige boost topology, IEEE rans. Power Electron., vol. 3, pp , May 998. [3] J. C. Salmon, Circuit topologies for single-phase voltage-oubler boost rectifier, IEEE rans. Power Electron., vol. 8, pp , July 993. I. INRODUCION A traitional rotor-flux-oriente inuction machine rive offers control performance but often reuires aitional sensors on the machine. his as to the cost an complexity of the rive system. o avoi using sensors on the machine, terminal uantities of the machine are use to estimate the flux an spee of the machine. For the last two ecaes, many researchers attempte to solve this problem, an for this purpose, ifferent algorithms have been propose [] []. For this problem, sliing moe is rarely use, even though sliing-moe theory is one of the prospective control methoologies for inuction machine flux an spee estimation problems because of its orer reuction, isturbance rejection, robustness, an simplicity of implementation. he basics of the sliing-moe control for electromechanical systems are introuce in [2]. A few works have been presente for the spee an flux estimation for the inuction machine using sliing-moe theory [3], [4]. In this letter, a new sliing-moe-base flux an spee estimation techniue for sensorless control of a fiel-oriente inuction machine is propose. he flux estimation accuracy is guarantee through the current observer. he rotor spee is estimate base on the measure an estimate stator currents an estimate rotor flux. he propose algorithm estimates the rotor time constant along with the rotor spee, an problems relate to integration process are solve through a low-pass filter structure. In the propose algorithm the terms containing flux, spee, an rotor time constant, which are common in both current an flux euations of the current moel of the inuction machine, are estimate by a sliing function. his makes - an -axes flux estimation ecouple an, therefore, the flux estimation is merely an integration of the known terms. II. HEOREICAL ASPECS In this section, the inuction machine moel an the theoretical aspects of the propose algorithm are introuce, incluing current observer, flux, spee, an rotor time constant estimation /02$ IEEE Manuscript receive September 5, 2000; revise June 2, Abstract publishe on the Internet July 5, A. Deriyok, H. Rehman, N. Inanc, an L. Xu are with the Department of Electrical Engineering, he Ohio State University, Columbus, OH 4320 USA. M. K. Güven is with echnical Center E-855, Caterpillar Inc., Peoria, IL USA. Publisher Item Ientifier 0.09/IE

2 78 IEEE RANSACIONS ON INDUSRIAL ELECRONICS, VOL. 49, NO. 5, OCOBER 2002 A. Inuction Machine Moel he inuction machine moel is efine by the stator currents an rotor fluxes as state variables in the rotor-flux-oriente stationary reference frame by the following s s s r = r s r +! r s r 0 k i s s + k 2 V s s = r s r 0! r s r 0 k i s + k 2 V s = 0 r s r 0! r s r + Lm r i s s = 0 r s r +! r s r + Lm = 0 L2 m L s L r r = Lr R r k 2 = L s = k 2L m L r k =k 2 R S + L2 m L rr : r i s () r is the rotor time constant,! r is the rotor electrical spee, subscripts an are use for -axis an -axis components, an superscript s represents the stationary reference frame. L m, L r, R r, L s, an R s are mutual inuctance, rotor inuctance an resistance, an stator inuctance an resistance, respectively. B. Current Observer Design he propose spee an rotor time constant estimation structures are base on a sliing-moe current observer. Ensuring the convergence of the current observer, the euivalent control [5] is prouce. hen, it is use in the flux estimation to etermine the flux along an axes. Finally, the rotor spee an rotor time constant are estimate by using estimate flux an the sliing function. For clarity, let () be written as _I =A3 0 k I + k 2V _3 = 0 A3 + Lm I (2) r _I s s _3 r s r I = i s s;i s 3 = s r; s r A =! r 0! r V = V s s;v s : Base on the moel given in (2), the propose current observer structure is _^I = 9 0 k ^I + k 2V (3) _^I s s s ^I = ^i s s;^i s 9 =[9 ; 9 ] V = V s s;v s ^is s an ^i s are the observe stator current components in the stationary reference frame. he sliing functions 9 an 9 are efine as an : 9 = 0 u o sign(s ) 9 = 0 u osign(s) (4) s =^i s s 0 i s s s =^i s 0 i s (5) sign(s )= ; if s > 0 0; if s < 0 an the sliing moe surface is efine as s n =[ss s ] : (6) When the estimation error trajectories reach the sliing surface, i.e., s n =0, then, from (5), it is obvious that observe current will converge to the actual ones, i.e., ^i s s = is s an ^i s = i s. It is important to point out that this sliing surface euation selection guarantees that on the sliing surface the observer will not be aeffecte by any system parameter or any isturbance, i.e., the current observer is invariant [5]. Claim: Consier the sliing surface s n =[s ;s ] efine by (5), an the iscontinuous control law 9 efine by (4), an if u o > i s s = ^i s s 0 i s s I A3 0 k I I i s s + i s i s = ^i s 0 i s then, sliing surface s n is attractive. Proof: Let us consier the Lyapunov function V = 0:5s n s n, its time erivative is _ V = s n _s n. hen, using (2) an (3) _s n can be written as _s n = _ I = (9 0 A3) 0 k I: he sliing-moe surface is attractive if _ V = s n _s n < 0, i.e., that is, I 0u o Sign(I) 0 A3 0 k I I < 0 I A3 0 k I I u o > i s s + i s : (7) By selecting large enough u o, foun by the existence conition given by (7), the sliing moe (s n =0)will occur. o efine the control action, which maintains the motion on the sliing manifol, euivalent control concept is introuce [5]. he euivalent control can be efine as the average of the iscontinuous control on the sliing manifol, which by itself is sufficient to maintain the motion on the manifol. herefore, the euivalent control action can be foun by isolating the continuous term using a low-pass filter, which is implemente as = s + 9

3 IEEE RANSACIONS ON INDUSRIAL ELECRONICS, VOL. 49, NO. 5, OCOBER Fig.. Block iagram of the simulation an implementation of IFO control inuction machine rive system. Fig. 2. Actual an estimate spees, the spee error, (c) observe an actual currents, an () error between them for trapezoial reference. Fig. 3. Actual an estimate spees an spee error between them. is the time constant of the filter an shoul be sufficiently small to preserve the slow component unistorte but large enough to eliminate the high-freuency components. C. Flux, Spee, an Rotor ime Constant Estimation When the trajectories of the system reach the sliing surface sn =0, the observe currents ^i s an ^i s s match with the actual currents i s an i s s, which means the sliing function will represent the term that is replace by them, i.e., When this is substitute in 9 = A3: (8) = 0 9e 9 e + r Lm from which the rotor flux s r an s r can be foun. Note that to calculate the fluxes, a low-pass filter is use instea of integration. Note that this approach was introuce in [5] an showe that it overcomes the problems of an ieal integration such as the effect of initial conitions. Now, using the flux values an (8), spee an rotor time constant can be foun. For this, let (8) be written as = 0!r!r s r s r i s s i s Fig. 4. them. Actual an observe -axis currents an current error between

4 80 IEEE RANSACIONS ON INDUSRIAL ELECRONICS, VOL. 49, NO. 5, OCOBER 2002 (c) Fig. 5. Actual an estimate spees, sliing function -component, an (c) the same sliing function component zoome. Fig. 7. -axis flux component an measure phase current. (c) Fig. 6. Actual -axis current an observe -axis current. Fig. 8. Actual an observe spees, sliing function -component, an (c) the same sliing function component zoome. which can be reorganize as an = s r s r s r 0 s r! r Finally, from (9),! r an = r are foun as! r = j rj = 0 r j r j s r s r 0 s r + s r : =! r j r j 0 s r 0 s r 0 s r s r j r j = 0( s r) 2 0 ( s r) 2 : (9) III. SIMULAION AND EXPERIMENAL SUDIES In this section, the performance of the propose observer structure is presente via simulation an experimental results. he block iagram of the inirect fiel-oriente inuction machine rive system with observer structure is given in Fig.. In the spee regulation loop, a simple proportional-plus-integral (PI) controller is use. It is assume that the

5 IEEE RANSACIONS ON INDUSRIAL ELECRONICS, VOL. 49, NO. 5, OCOBER Fig. 9. Actual -axis current an observe -axis current. Fig.. Comman an observe spees an observe an measure axis currents. Fig. 0. -axis flux component an measure phase current. performance of the PI controller will be sufficient to present the performance of the observer structure. It is important to point out that the rotor time constant estimation is also presente. Note that a four-pole 5-hp inuction machine was use in this stuy, the parameters of which are Lls = Llr = :9 mh, Lm = 4:2 mh, Rs = 0:6, an Rr = 0:42. A. Simulation Results he valiity of the observer structure is verifie by the simulation, an the results are given in Fig. 2, the estimate spee is use as feeback in the close loop. he first step for the spee estimation is the current observation. he observe an actual axis currents are shown in Fig. 2(c), an the error between them is given in Fig. 2(). It is obvious from these results that current convergence is satisfie. B. Experimental Results he laboratory setup consists of a 5-hp cage rotor inuction machine an a high-performance avance controller for electric Fig. 2. Comman an observe spees an observe an measure axis currents. machines (ACE). he ACE is a very-high-performance, rugge, rapi prototyping tool that implements avance control algorithms an interfaces without any traitional programming. It is important to note that all the experimental results presente in this paper have been collecte using the ata acuisition capability of the ACE controller. he performance of the observer is first analyze in the implementation by operating the observer without using it in the close loop, i.e., in the feeback, the actual spee from the encoer is use an the observer structure works parallel to the overall system without affecting the close-loop system at all. his will be calle free operation. For this case, the close-loop system follows a trapezoial trajectory, an parallel with the close-loop system, the observer operates an estimates the encoer spee. he estimate spee an encoer output are given in Fig. 3 together with the error between them in Fig. 3. In aition, observe an measure currents for the axis, an the error between them, are given in Fig. 4. hese results verify the

6 82 IEEE RANSACIONS ON INDUSRIAL ELECRONICS, VOL. 49, NO. 5, OCOBER 2002 an experimental results. It is conclue from the results presente in this letter that the propose scheme performs well for both high an low spee. It is also important that the new algorithm is robust to parameter changes an easy to implement for an off-the-shelf machine.s Fig. 3. Estimation of = for inuction machine use. performance of the observer. Next, the observer is teste when it is replace with the encoer in the close loop, which is calle feeback operation of the observer. For high-spee performance, a 750-r/min suare an trapezoial reference inputs are applie to the close-loop system. In aition, for the low-spee performance, a 40-r/min suare an a 50-r/min trapezoial reference input are applie. In the following cite figures, these results are presente. Specifically, in Figs. 5 0, observe an comman spees, sliing function, actual an observe -axis currents, observe flux, an measure phase current are shown for high spees. In Figs. an 2, the observe an comman spees, an in Figs. an 2, observe an measure -axis currents are presente. It is important to point out that the observe an measure currents are on top of each other. In aition, the rotor time constant is upate an, as seen from Fig. 3, it converges to its actual value in a short perio of time. IV. CONCLUDING REMARKS A new sliing-moe current observer has been propose for flux, spee, an rotor time constant estimations. he rotor time constant upate algorithm will overcome the problem of rotor resistance variation, normally neee for the slip freuency control in inirect fiel-oriente vector control. he propose scheme is valiate through simulation REFERENCES [] P. Jansen an R. Lorenz, A physically insightful approach to the esign an accuracy assessment of flux observers for fiel oriente inuction machine rives, IEEE rans. In. Applicat., vol. 30, pp. 0 0, Jan./Feb [2] C. Schauer, Aaptive spee ientification for vector control of inuction motors without rotational transucers, in Conf. Rec. IEEE-IAS Annu. Meeting, 989, pp [3] M. Elbuluk, N. Langovsky, an D. Kanman, Design an implementation of a close-loop observer an aaptive controller for inuction motor rives, IIEEE rans. In. Applicat., vol. 34, pp , May/June 998. [4] F. Peng an. Fukuo, Robust spee ientification for spee-sensorless vector control of inuction motors, IEEE rans. In. Applicat., vol. 30, pp , Sept./Oct [5] K. Hurst,. Habetler, G. Griva, an F. Profumo, Zero-spee tacholess IM torue control: Simply a matter of stator voltage integration, IEEE rans. In. Applicat., vol. 34, pp , July/Aug [6] M. Shin, D. Hyun, S. Cho, an S. Choe, An improve stator flux estimation for spee sensorless stator control of inuction motors, IEEE rans. In. Applicat., vol. 5, pp , Mar./Apr [7] C. Bonanno, L. Zhen, an L. Xu, A irect fiel oriente inuction machine rive with robust flux estimator for position sensorless control, presente at the IEEE-IAS Annu. Meeting, Lake Buena Vista, FL, 995. [8] H. Kubota, K. Matsuse, an. Nakano, DSP-base spee aaptive flux observer of inuction motor, IEEE rans. In. Applicat., vol. 29, pp , Mar./Apr [9] G. Yang an. Chin, Aaptive-spee ientification scheme for a vector controlle spee sensorless inverter-inuction motor rive, IEEE rans. In. Applicat., vol. 29, pp , July/Aug [0] L. Harnefors an H. Nee, Sensorless control of inuction motors for improve low-spee performance, in Conf. Rec. IEEE-IAS Annu. Meeting, 996, pp [] H. Kubota, Y. Kataoka, H. Ohta, an K. Matsuse, Sensorless vector controlle inuction machine rives with fast stator voltage offset compansation, in Conf. Rec. IEEE-IAS Annu. Meeting, 999, pp [2] V. I. Utkin, Sliing moe control esign principles an applications to electric rives, IEEE rans. In. Electron., vol. 40, pp , Feb [3] S. Doki, S. Sangwongwnich,. Yonemotor, an S. Okuma, Implementation of spee-sensorless fiel-oriente vector control using aaptive sliing observers, in Proc. IEEE IECON 92, 992, pp [4] F. Parasiliti, R. Petrella, an M. ursini, Aaptive sliing-moe observer for spee sensorless control of inuction motors, IEEE rans. In. Applicat., vol. 46, pp , Jan./Feb [5] V. I. Utkin, Sliing in Control an Optimization. Berlin, Germany: Springer-Verlag, 992.