High Performance Speed Sensor Less

996 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005

High-Performance Speed-Sensorless Control ofan Induction Motor Drive Using a Minimalist

Single-Phase PWM ConverterOlorunfemi Ojo, Senior Member, IEEE, Zhiqiao Wu, Student Member, IEEE, Gan Dong, Student Member, IEEE,

and Sheetal K. Asuri

Abstract—Home appliances and comfort conditioners are yet tobenefit from the recent developments in power electronics becauseof cost constraints. In this paper, a speed-sensorless inductionmotor drive system using converters with reduced device counts(minimalist, sparse converters) and actuated from a single-phasesystem is proposed for such low-cost applications. The analysis,control, dynamic, and steady-state characteristics of the proposeddrive are experimentally illustrated.

Index Terms—Modulation techniques, natural reference framecontroller, single-phase system, sparse (minimalist) converters,speed estimation.

I. INTRODUCTION

HOME appliances and comfort conditioners require rel-atively low electric power between tens of watts and

about 2 kW to drive electric machines generally suppliedfrom single-phase supplies. Hence, most of the existing elec-tric motors used for these applications are various types ofsingle-phase machines such as induction, synchronous reluc-tance, interior permanent-magnet, and universal ac machines. Insome applications, dc motors are also used which are fed fromsingle-phase rectifier-chopper arrangements [1]. Because ofthe limited power densities of single-phase machines and theirrelatively poor input power factors, which result in large VArequirements and relatively higher weight, the functionalitiesof the appliances are somewhat restricted for a given volume.

There have been many proposals to reduce the part counts(especially the switching devices) and evolve novel single andthree-phase converters that transform ac voltages into variablefrequency and variable magnitude voltage sources [2]–[10]. Thenumber of switching devices for the rectifier–inverter system fedfrom a single-phase source is usually eight transistors and eightdiodes if the input supply side is to be fully controllable—unity

Paper IPCSD-05-032, presented at the 2004 Industry Applications SocietyAnnual Meeting, Seattle, WA, October 3–7, and approved for publication inthe IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial DrivesCommittee of the IEEE Industry Applications Society. Manuscript submittedfor review December 25, 2004 and released for publication April 25, 2005. Thiswork was supported by the U.S. Office of Naval Research (ONR) under GrantN000140110909.

O. Ojo, Z. Wu, and G. Dong are with the Department of Electrical andComputer Engineering/Center for Electric Power, Laboratory for ElectricMachines and Power Electronics, Tennessee Technological University,Cookeville, TN 38505 USA (e-mail: [email protected]; [email protected];[email protected]).

S. K. Asuri is with Sierra Atlantic, Inc., Hyderabad 500055, India.Digital Object Identifier 10.1109/TIA.2005.851580

input power factor and bidirectional input power flow. Reduc-tion of active switching devices in minimalist converters natu-rally results in loss of degree of control freedom, lower utiliza-tion of source voltage, higher capacitor rating and, sometimes,higher motor losses [9]. The current rating of the switching de-vices in the rectifier are relatively increased, and the capacitorsused are heavily loaded requiring the use of bigger capacitorswhich increase system cost and may slow down the input sidedynamic response.

Developments at obtaining low-cost drives have been en-hanced by the prospect of using fewer switching devices andsensors, the implementation of advanced control and estimationalgorithms using cheap hardware, and the knowledge thathigh-performance variable-speed operation for existing lowpower multispeed drive systems can improve energy use andsystem performance. Adjustable-speed drives in heating, venti-lating, and air-conditioning appliances and control of flows willdeliver significant advantages in energy efficiency improve-ment, improved startup/shutdown, reduced standby losses, andquieter systems [11]. A three-phase induction motor drivenwith a sparse or minimalist converter with a reduced numberof base drivers and power supplies signposts the feasibilityof an economically viable motor drive for home appliancesand comfort conditioners. Implementation of a sensorlessspeed estimation scheme to eliminate the use of an encoderfurther makes the drive more financially attractive for low-costapplications. Compared with the conventional three-phaseconverter systems, the power of the minimalist converters willbe lower given the single-phase input voltage, however, thepower density and the efficiency of the driven induction motorswill be almost the same.

While published works focus on innovative sparse converterstructures and have tended to emphasize and experimentallydemonstrate the open-loop induction motor converter perfor-mance, the possibility of achieving input supply unity powerfactor and the synthesis of motor waveforms, this paper exploresthe determination of the carrier-based pulsewidth-modulation(PWM) method required for the converter operation and thespeed-sensorless control strategy of the three-phase inductionmotor drive when fed with two known sparse converter topolo-gies. These topics—the approach for the determination of thecarrier-based modulation signals required for PWM pulse gen-eration, the dynamic rectifier–inverter–motor drive control forhigh-performance operation when using sparse rectifier–con-verters—have not received adequate research attention. In [3],

0093-9994/$20.00 © 2005 IEEE

OJO et al.: HIGH-PERFORMANCE SPEED-SENSORLESS CONTROL OF AN INDUCTION MOTOR DRIVE 997

Fig. 1. Induction motor drive with a single-phase voltage source. (a) Neutral of wye load connected to the source, Drive I. (b) Smoothening inductor at the inputsource circuit, Drive II.

carrier-based PWM modulation signals augmented with a zerovector voltage are used to control the turn on and off of the ac-tive devices in order to achieve unity power factor operation fora three-phase passive load fed with a sparse rectifier–invertersystem using a single-phase voltage source. In an earlier workconcerned mainly with steady-state, open-loop motor drive op-eration using sparse converters, the inverter dc input voltageis controlled by manipulating the phase angle of the modula-tion signals used to turn on and turn off the switching devices[5]. Space-vector modulation schemes determined for certainreduced-order rectifier–converter–motor drive systems with adigital motor current controller are set forth and steady-statemotor current regulation is also experimentally demonstratedin [8]. The carrier-based PWM modulation method for the in-verter side and a hysteresis controller for the rectifier side for avoltage-source inverter (VSI) rectifier–inverter system with onlyfour controllable legs are presented in [10] which ensure bi-di-rectional power flow, unity power factor and dc rectifier voltageregulation. Experimental results showing dc capacitor voltageregulation, sinusoidal input currents during motor starting andload change are given. An adaptive space vector modulation tocompensate dc link voltage ripple and reduce capacitor sizes forfour-switch three-phase VSIs has been proposed and validatedby extensive experimental results in [9].

In Section II, the derivation of the expressions for the modu-lation signals needed for triangle intersection PWM modulationof the converters is set forth. The linearizing and decouplingcontrol of the three-phase induction machine using the princi-ples of indirect field-orientation control with a speed estima-tion scheme is the subject of Section III. The natural referenceframe current control for the single-phase current is the subjectof Section IV. Steady-state and dynamic performance experi-mental results are shown in Section V to validate theory andconcepts. Although attention is focused on two sparse converterstructures, the methodologies set forth for the analysis and con-trol of the drives under investigation can be applied for the studyof carrier-based modulation and control schemes of other min-imalist/sparse converters.

II. RECTIFIER-INVERTER STRUCTURES

The two drive structures considered in this paper are schemat-ically shown in Fig. 1. The input source voltage is connectedto the neutral of the three-phase induction motor while the

other terminal is at the middle of the rectifier leg as shown inFig. 1(a). The stator leakage inductances filter the input sourcecurrent which is superimposed on the normal motor currents.In Fig. 1(b), the single-phase supply is connected through asmoothening inductor to the rectifier leg midpoint and themiddle of a divided capacitor. The input rectifiers in the twocircuits control the single-phase currents to have unity displace-ment power factor and to regulate the dc capacitor voltagesintervening between the rectifier and inverter. The inverter sideof the converter is comprised of the divided capacitor leg andtwo legs which are used to synthesize the load voltages for themotor control.

The converters are controlled by using the carrier-basedtriangle intersection PWM in which the switching pulses(switching function) are generated by comparing modulationsignals with a high-frequency carrier triangle signal. Theswitches on the same leg cannot be turned on at the same timewhile currents paths must always be made available to ensurecurrents flow if the Kirchoff’s current and voltage laws are notto be violated. Hence, for Drive I, the converter voltage andcurrent equations expressed in terms of the switching functions

are defined as

(1)

(2)

(3)

(4)

(5)

(6)

The voltages are the induction motor phase volt-ages and is the voltage between the neutral point of themotor to the lower end of the dc-link capacitor. The motor cur-rents are and the input single-phase supply current is

. If the switching function is defined as ,where and is the modulation signal, simplifi-cation of (1)–(3) yields the following expressions for the mod-ulation signals [12]:

(7)

(8)


The transformation of (4)–(8) to the synchronous refer-ence frame (angle ) gives the following:

(9)

(10)

Similar analysis for Drive II gives the same equations for themodulation signals as those obtained for Drive I except the fol-lowing:

(11)

The smoothening inductor has a resistance and an inductancewhich are and , respectively. The qdo modulation sig-nals are , and , respectively. The motor volt-ages are and the corresponding motor currents are

, and . The capacitor dc voltage is .

III. INDUCTION MOTOR CONTROL

The voltage equations of the squirrel-cage inductionmotor expressed in the synchronous reference frame aregiven as [13]

(12)

(13)

(14)

(15)

(16)

whereandtherotorspeedis ,theangular

frequency of the motor voltages is , the - and -axes rotorfluxlinkagesare and ,respectively.Thestator -and -axescurrentsare and ,respectively.Theloadanddevelopedelec-tromagnetic torques are and , respectively. The number ofpoles is and the moment of inertia is .

The speed control is to be achieved through appropriate com-mand of the - and -axes machine voltages by closed-loop con-trollers. Since the model equations of the induction machinegiven in (12)–(16) are nonlinear and coupled, the principles ofnonlinear control of the input–output linearization with decou-pling are used to remove the nonlinearity and coupled termsthereby enabling classical linear system control methodologyto be used to determine the constant gain parameters of thecontrollers. This is possible since the input–output linearizationand decoupling strategy ensure linear relationships between theinput control variables and the controlled variables with eachoutput–input pair decoupled from each other [14]. The control

variables are and while the controlled variables areand the rotor flux linkages and .

Input–output linearization is a three-step process: 1) differ-entiate a controlled variable until an input variable appears; 2)choose the input variables to cancel nonlinear terms and guar-antee tracking convergence; and 3) study the stability of the in-ternal dynamics. The total number of differentiations for all con-trolled variables is called the relative order , while the internaldynamics are composed of states ( is the total numberof the system dynamic states). When operations 1)–3) are per-formed on (12)–(16), the resulting equations are linearized anddecoupled and, hence, the system is input–output linearizable,decoupled with no internal dynamics. Any realistic dynamicscan be imposed by means of linear controllers. Differentiating(16) with respect to time and substituting (12)–(15) gives

(17)

From (14) and (15), the slip frequency and the reference stator-axis current are derived as

(18)

(19)

The command (reference) q and d axis motor stator voltagesfrom (12)–(13) are expressed as:

(20)

(21)

The unknown quantities , and are theoutputs of controllers which are defined from (12)–(15), (17).If the controllers gains are given as defined below (i.e., and

are the controller gains for the - and -axes current loops),then we have

(22)

(23)

(24)

(25)

(26)


Fig. 2. Control scheme.

The final control scheme is shown in Fig. 2. To achieve fieldorientation control, the reference -axis flux linkage is set equalto zero and the -axis flux linkage reference is either fixed orvaried to achieve minimum motor losses while the rotor speedis regulated.

Since motor operation at very low speed is not very stringentfor the home appliances applications, a conventional sensorlessspeed algorithm can be adopted for this drive. The rotor speedcan be estimated using the rotor voltage equations in the sta-tionary reference frame as follows:

(27)

The rotor speed can be extracted from (27) using either one ofthe two equations. The above equations change to (28) when therotor currents are substituted using rotor flux and stator currents

(28)

The rotor fluxes are calculated from the stator flux linkagesand stator currents using (29)

(29)

The stator flux linkages are estimated by integrating the statorback electromotive force (EMF) using a low-pass filter (LPF)and a compensation scheme to eliminate magnitude and phaseerrors

(30)

Fig. 3. Structure of the natural reference frame controller.

where is the cutoff frequency. Simulation results show thatbetter estimation results are obtained using both equations in(28) as in (31)

(31)

IV. CONTROL OF INPUT-SIDE RECTIFIER

The objectives of the control strategy for the front-end recti-fier are to control the dc capacitor voltage to be equal to a refer-ence value and the input displacement power factor of thesingle-phase supply to be close to unity. Using (10) to define thecontrol structure for the dc capacitor, the transfer function of thecapacitor voltage with respect to the reference capacitor voltageis given in (32) and (33)

(32)

(33)

Unity displacement power factor is achieved when the inputphase current is in phase with the single-phase voltage. Substi-tuting (7) and (8) into (10) and (32) and eliminating the noncon-


Fig. 4. Steady-state waveforms of controlled rectifier–inverter induction motor. Reference speed= 600 r/min, load torque= 4 N�m, d-axis rotor flux= 0.45 Wb.(a) Three-phase motor currents. (b) Modulation signals. (c) Input supply voltage and ten times input supply current.

stant terms using an LPF, the peak of the reference input currentis approximated as for Drive I

(34)

The peak of the single-phase voltage is and the peak ofthe zero-sequence motor voltage is . For Drive I, andare, respectively, the stator winding per phase resistance and

leakage inductance. The reference of the input current which isdesired to be in phase with the input supply voltage is obtainedby multiplying the reference peak current obtained from (34)with the stepped-down input single-phase voltage normalizedwith its peak value. The input current is regulated to followthis time-varying reference current. The model equations of theinput circuit for Drive I are given as

(35)

(36)


Since this single-phase current is an ac signal varying withtime, the control technique using classical (PI, IP, PID) con-trollers is not applicable as there will be steady-state amplitudeand phase errors. Hence, a natural reference frame controlleris employed whose structure is explained in the block diagramform shown in Fig. 3. Rather than controlling the stationary ref-erence frame currents as done in three-phase systems, the actualphase current is directly controlled in this case [15], [16]. Thecurrent signals are first transformed to the positive and negativesynchronous references, passed through two PI controllers andthe resulting signals are finally inverse transformed with somedelay angle, i.e.,

(37)

where is the angular frequency of the input voltages; isthe initial reference angle and is the delay angle.

The transfer function of the current control system in Fig. 3(the same PI controllers are placed in the two paths) are ex-pressed as (38), shown at the bottom of the page.

In designing the parameters of the controllers in each of thetransfer functions in (22)–(25), (33), and (38), the PI controllerstructure is adopted and the gain parameters are selected to lo-cate the eigenvalues of the transfer function uniformly in the lefthalf of the s-plane, on a circle of radius , with its center at theorigin. The delay angle is selected to insure a good place-ment of the system zeros to have negative real parts making thesystem be minimum-phase compliant.

V. EXPERIMENTAL RESULTS

The control scheme in Fig. 2 was implemented by meansof a 40-MHz digital signal processor (DSP) TMS320LF2407AEVM board. A prototype of a rectifier–inverter was built andconnected as in Fig. 1(a) and (b) to feed a 1-hp three-phase in-duction machine which has parameters given in the Appendix.For the following experimental results, the reference capacitordc voltage is 100 V. In Fig. 4, steady-state simulation waveformswhen the controlled motor is loaded are displayed. The motorcurrents in Drive I can be observed to carry the supply input cur-rent in each phase in addition to the motor load current whichmakes them to be unbalanced. In Drive II, the load current isreduced and balanced for the same load making it to possess alower stator current loss and hence has a higher efficiency. Themodulation signals for the top devices for the two convertersare shown as also the input supply voltage and input currents.What is evident from these simulation results is the near unitydisplacement power factor requirement is achieved in the twoschemes, Drive I though not requiring a smoothening inductorhas a higher and distorted load current.

Fig. 5 displays the simulation results showing the responseof the drives in which the reference speed, which is changedbetween 1000–500 r/min, is followed by the actual motor speed.

Fig. 5. Dynamic speed response for speed change from 1000 to 500 r/min.

The measured waveforms for these Drives I and II are shownin Fig. 6. The presence of a zero-sequence current in the three-phase motor currents in Drive I results in the modulated exper-imental current waveforms shown in Fig. 6(a). The input dis-placement power factors for the two drives are close to unity asthe input phase voltage and current are in phase. The presenceof the 60-Hz stator phase current component revealed in Fig. 4is evidenced in the waveforms of Drive I.

Fig. 7 shows experimental results of the dynamics of themotor to changing speed for which the reference rotor speedis changed between 1000–500 r/min. It is observed that theestimated rotor speed follows closely the reference speed.

VI. CONCLUSIONS

This paper has presented the methodology for the analysisand control of a high-performance induction motor drive actu-ated by two controlled rectifier–inverter systems with reducedcount of switching devices. The general approach for deter-mining the modulation signals required for the carrier-basedPWM pulse generation for this class of minimalist converters

(38)


Fig. 6. Steady-state waveforms of the controlled motor. Reference speed= 600 r/min, reference capacitor voltage= 100 V. (a) Stator phase currents (2.5 A/div).(b) Modulation signals for the top devices (0.5/div): (1)M ; (2)M ; (3)M (c) Input supply ac voltage (25 V/div) and input supply current (2 A/div).

has been set forth. The input supply voltage is a single phase andthe input current is controlled using a natural reference framecontroller to operate close to unity displacement power factor.The nature of the modulation signals, the achievable motor dy-namics, and waveforms are clearly lay out in simulation and ex-perimental results.

Compared with the conventional high-performance recti-fier–converter–motor drive system which has eight controllableswitching devices, the converter systems studied in this paperhas the same dynamic performance potential. The Drive Isystem has the limitation of a relatively higher losses due tothe additional zero sequence current flowing through the motor


Fig. 7. Experimental results of the dynamic speed response for speed changefrom 1000 to 500 r/min (278 r/min/div). Top: reference speed; bottom: estimatedspeed.

and the source, a disability that is missing in Drive II. Thereis an input inductor for Drive II which is an additional costand space item. In spite of these limitations, Drives I and IIcan be economically viable for low-power applications wherethe possibility of a high-performance sensorless speed givesfurther performance advantages.

With the advantages of reduced count of switching devices,fewer number of power supplies and base drives, sensorlesshigh-performance speed control, and single-phase supply (suchthat it can be used almost anywhere), Drives I and II should findutility in home appliances and comfort conditioning systems.

APPENDIX

The parameters of the three-phase 230-V four-pole 1-hp in-duction machine used for this experiment are as follows:

stator resistance, ;stator leakage inductance, H;

magnetizing inductance, H;rotor per phase resistance, ;rotor per phase leakage inductance, H;moment of inertia, kg m ;dc capacitor value, F.

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Olorunfemi Ojo (M’87–SM’95) was born in Kabba,Nigeria. He received the Bachelor’s and Master’s de-grees in electrical engineering from Ahmadu BelloUniversity, Zaria, Nigeria, and the Ph.D. degree fromthe University of Wisconsin, Madison.

He is currently a Professor of electrical andcomputer engineering at Tennessee TechnologicalUniversity, Cookeville. His current research interestsspan the areas of electric machine analysis and drivecontrol, switching converter technology, and moderncontrol applications in converter-enhanced power

and distributed energy generation systems.Dr. Ojo is presently the Vice Chairman for Programs of the Industrial Drives

Committee of the IEEE Industry Applications Society. He is also an AssociateEditor of the IEEE TRANSACTIONS ON POWER ELECTRONICS.


Zhiqiao Wu (S’03) was born in Jingzhou, China.He received the B.S. and M.S. degrees in electricalengineering from Huazhong University of Scienceand Technology, Wuhan, China, in 1999 and 2002,respectively. He is currently working toward thePh.D. degree at Tennessee Technological University,Cookeville.

His research interests include power electronics,electrical machines, and motor drives.

Gan Dong (S’02) was born in Hubei, China. Hereceived the B.S. and M.S. degrees in electricalengineering from Huazhong University of Scienceand Technology, Wuhan, China, in 1993 and 1996,respectively. He is currently working toward thePh.D. degree at Tennessee Technological University,Cookeville.

From 1996 to 2001, he was an Electrical Engineerwith the Hubei Electric Power Testing and ResearchInstitute, China. His research interests include powerelectronics and vector control of induction machines.

Sheetal K. Asuri received the Bachelor’s degree inelectrical and electronics engineering from Jawa-harlal Nehru Technological University, Hyderabad,India, and the M.S. degree in electrical engi-neering from Tennessee Technological University,Cookeville, in 2003.

Her research activities during the tenure of herMaster’s degree were in induction motor drivesand their control using sparse matrix converters.She had also done research on different modulationschemes for single-phase inverters. She is currently

a Software Engineer with Sierra Atlantic, Inc., Hyderabad, India.

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High Performance Speed Sensor Less