518 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 2, MARCH 2006

Integrated Design of Speed-Sensorless and AdaptiveSpeed Controller for a Brushless DC Motor

Hsiu-Ping Wang and Yen-Tsan Liu

Abstract—The study develops a design of an integrated newspeed-sensorless approach that involves a torque observer andan adaptive speed controller for a brushless dc motor (BLDCM).The system is based on the vector control drive strategy. Thespeed-sensorless approach first employs a load observer to es-timate the disturbed load torque, and then the estimated loadtorque is substituted into the mechanical dynamic equation todetermine the rotor speed, and thus develop a speed-sensorlessalgorithm. Additionally, the mechanical rotor inertia constant andthe friction coefficient, which are the inputs of the load observer,are estimated using the recursive least-square rule. Therefore,the proposed speed-sensorless approach is unaffected by thetime-variant motor parameters nor is affected by the integratordrift problem. It also has a simpler computing algorithm than theextended Kalman filter for estimating the speed. The modifiedmodel reference adaptive system algorithm, an adaptive controlalgorithm, is adopted as a speed controller of the BLDCM toimprove the performance of the speed-sensorless approach. Sim-ulation and experimental results confirm that the performance ofthe design of a new integrated speed-sensorless approach and theadaptive speed controller is good.

Index Terms—Adaptive speed controller, brushless dc motor(BLDCM), load observer, modified model reference adaptivesystem (MMRAS), speed-sensorless, vector control.

I. INTRODUCTION

RECENT investigations of alternating current (ac) motorcontrols have been based on two motor drive frame-

works—vector control and direct torque control. The former,using axis transformation from the three-phase electric terminalaxis and some control algorithms, controls the motor in a simpleenvironment [1]–[4], and involves more complex computingalgorithms compared than the latter. The latter, without theinner current loop, controls the motor using a switching tableat the desired torque and flux, and exhibits a ripple speedresponse, even though its drive framework is simpler than thatof the former [5], [6]. This study adapts the vector controlmotor drive to develop a new speed-sensorless vector controlfor a brushless dc motor (BLDCM).

The BLDCM is the same as the permanent magnet syn-chronous motor; however, the former name refers to the driving

Manuscript received December 9, 2004; revised August 8, 2005. This workwas supported by the National Science Council of Taiwan, R.O.C. under Con-tract NSC 89-2213-E-262-006.

H.-P. Wang is with the Department of Mechanical Engineering, LunghwaUniversity of Science and Technology, Taoyuan 333, Taiwan, R.O.C. (e-mail:hpwang@mail.lhu.edu.tw).

Y.-T. Liu is with the Department of Electrical Engineering, Chung ChengInstitute of Technology, Taoyuan 335, Taiwan, R.O.C.

Digital Object Identifier 10.1109/TPEL.2005.869772

method, and the latter refers to the structure. The BLDCM hasbeen extensively used in industry because it has high powerdensity, large torque and high efficiency. One of its shortcom-ings is in the need for sensors to support position or speedfeedback control, such as an encoder or resolver. These sensorsadd to the cost and weight of the motor drive and reduce thereliability of the system. Research on speed-sensorless controlof a BLDCM, based on estimating the position or speed of therotor by making measurements at the electric terminal has beenconducted to solve these problems [7]–[13].

Studies in this field can be grouped into three categories:1) back-EMF-based (electromotive force) [7], [8], 2) stateobserver-based [9]–[11], and 3) estimator-based approaches[12], [13]. The approximate flux can be determined usingapproaches based on the back-EMF, by first integrating themeasurable voltage signals, and then using the approximateflux to solve the equation for estimating speed. The estimateis sensitive to both the time-variant motor parameters and theintegrator drift problem that arises in the measurement process.State observer-based approaches are almost the same as theback-EMF-based approaches except in that the states of themotor have the role of the back-EMF. Therefore, this approachsuffers from the same problem as the back-EMF-based ap-proach. The estimator-based approach, which used an estimatorsuch as the extended Kalman filter to estimate the speed,require complex computing algorithms and suffer from theinitial-value problem. Additionally, they can only be applied ifa high-performance PC or DSP is available.

The torque observer in [14] was employed to compensate forthe feedforward of the position controller. The torque observerwas derived from the mechanical dynamic equation with esti-mated parameters – the mechanical-rotor inertia constant andthe friction coefficient. Based on this approach, this study pro-poses a new speed-sensorless approach, which has a simplercomputing algorithm than the estimator-based approaches andis uninfluenced by the time-variant motor parameters or the in-tegrator drift problem, which difficulties are associated with theback-EMF-based and state observer-based approaches.

In [15], the present authors reported that the performance ofthe speed controller influenced the performance of the speed-sensorless approach. Therefore, the modified model referenceadaptive system (MMRAS) [16], an adaptive control algorithm,is used herein in the speed controller of the BLDCM to improvethe performance of the speed-sensorless approach. The PI speedcontroller is used initially and the parameters tuned using theZiegler–Nichols method [17]–[19] to evaluate the performanceof the MMRAS speed controller.

0885-8993/$20.00 © 2006 IEEE

WANG AND LIU: INTEGRATED DESIGN OF SPEED-SENSORLESS AND ADAPTIVE SPEED CONTROLLER 519

Fig. 1. Block diagram of speed control loop.

Simulation results and experimental results reveal that the de-sign of an integrated speed-sensorless and adaptive speed con-troller for a brushless dc motor is effective.

II. NEW SPEED-SENSORLESS TECHNIQUE

The extensively employed synchronously rotational refer-ence frame ( - axis) of the vector control drive is adoptedherein in this study to analyze the BLDCM. The state equationis given by

(1)where is ; is the armature winding resistance; isthe armature winding inductance; and are the -axis and-axis armature voltages; and are the -axis and -axis

armature currents, and is the EMF induced bythe permanent magnet. The mechanical dynamic equation is

(2)

where represents the electrically developed torque; is theload torque; is the mechanical-rotor inertia constant, and isthe friction coefficient.

The second row of (1), the -axis differential equation, and (2)are combined, and the block diagram of the speed control loopassociated with the vector control drive [5], [6] is presented inFig. 1. The following discussion refers to this control loop.

The novel speed-sensorless approach comprises the fol-lowing two steps.

A. Step 1

Both and are parameters in the transfer function, whichis the mechanical dynamic equation in Fig. 1. They may varywith the environmental conditions and uncertainties. The recur-sive least-square (RLS) rule [19], [20] is applied to evaluate theestimated parameters, and . And thus increase the robust-ness of the system.

Equation (2) is rewritten as

(3)

Let

(4)

Fig. 2. Sensorless technique with load observer.

Then, the rules of RLS yield

(5)

(6)

(7)

where is the forgetting factor. The estimated parameters,and , are used in the following torque observer.

B. Step 2

From inputs , and , the torque observer [14] generatesthe estimated load torque ( ), which is substituted into the me-chanical dynamic equation, (3), to be solved for the mechanicalangle rate ( ). Accordingly, a speed-sensorless technique isdeveloped, as presented in Fig. 2.

Therefore, the proposed sensorless technique is stable, evenif the parameters are uncertain and load torque varies. Fig. 3presents the block diagram of the new speed-sensorless vectorcontrol for the BLDCM.

III. MMRAS SPEED CONTROLLER

The MMRAS, an adaptive control algorithm, is used in thespeed controller of the BLDCM, to improve the performance ofthe speed-sensorless technique. Before the MMRAS is consid-ered, the model reference adaptive system (MRAS) [20], [21] isdescribed. In responding to a command signal, the MRAS usesa reference model to generate the desired output, which is com-pared with the actual output of the closed-loop system to yieldthe error signal, as presented in Fig. 4. Adjusting the parametersin the MRAS subsequently minimizes the error signal.

Based on the speed control loop of the BLDCM in Fig. 1, theplant of the closed-loop system is represented as a second ordersystem

(8)

where , , and are constants ( ,; ), and is . The reference

model of the second order system is then defined as

(9)

520 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 2, MARCH 2006

Fig. 3. Sensorless vector control of the BLDCM.

Fig. 4. Model reference adaptive system.

where is the reference model output, is the commandsignal, is the damping ratio, and is the natural frequency.

The original controller structure in [21] is

(10)

where and are the adjustable parameters to be evaluated.The controller of the MMRAS algorithm [16] is modified as

(11)

where is the error and defined as . The differencebetween (10) and (11) is the feedback signal. Substituting (11)into (8) yields

(12)The loss function is defined as 1 / 2 . Ac-

cording to the MIT rule [20], [21], the parameter adjustmentalgorithm is

(13)

where is the free parameter to be tuned. Partial derivatives ofthe error with respect to and are obtained

(14)

(15)

These formulas cannot be used directly because the equationsare too complex. An approximation must be made. When theoutput reaches a steady-state, the output error is a small value,as is the controller parameter . Therefore, 0 is assumed;then

(16)

from

(17)

From (13), the following equations for updating the controllerparameters are obtained:

(18)

(19)

In these equations, , and the block diagram of theMMRAS controller is presented in Fig. 5.

WANG AND LIU: INTEGRATED DESIGN OF SPEED-SENSORLESS AND ADAPTIVE SPEED CONTROLLER 521

Fig. 5. Block diagram of the MMRAS.

Fig. 6. Simulated estimates of motor parameters that change after 0.5 s: (a)mechanical-rotor inertia constant (J) and (b) friction coefficient (B).

The MMRAS is designed to force the plant output to thedesired output, enhancing the effect of speed control and im-proving the performance of the speed-sensorless technique. ThePI speed controller, parameters of which are tuned according theZiegler–Nichols method [17]–[19], are also used to evaluate theperformance.

IV. SIMULATION RESULTS

The simulation was performed in the MATLAB environment.Fig. 3 presents the simulation block diagram of sensorless vectorcontrol of the BLDCM. The approach employed in this studywas separated into three steps. First, the aim of parameter-esti-mation step is to determine the estimation of the parameters. Themechanical-rotor inertia constant and the friction coefficient areestimated using the RLS rule. The estimated parameters, and

, are used in the torque observer to establish the sensorless al-gorithm. Motor parameters are changed after 0.5 s. is changedfrom 0.000 658 to 0.001 658 and is changed from zero to0.000 358. This variation may not be realistic but it used onlyto study the estimation performance. Fig. 6(a) and (b) representthe results. The average root mean square error (RMSE), whichis the difference between the real (or command) signal and theoutput signal, and the average RMSE are presented at the topof the figures to reveal the performance of simulation. These re-sults indicate that the estimation error is very small.

Second, in the sensor step, the speed controller uses theMMRAS and PI algorithm, respectively, and their perfor-mances are compared. Parameters of PI are tuned using theZiegler–Nichols method. The aim of this step was to reducethe steady-state error of the speed response. Fig. 7(a) and(b) present the results. Table I shows the average RMSE ofthe sensor BLDCM simulation with the various controllers

Fig. 7. Simulated speed response of sensor at 900 rpm under a 0. 0.97-Nmload applied in the middle of the simulation, as determined using (a) MMRASand (b) PI algorithms.

TABLE IAVERAGE RMSE IN THE SENSOR BLDCM SIMULATION WITH THE DIFFERENT

CONTROLLERS UNDER VARIOUS LOAD CONDITIONS

Fig. 8. Simulated speed response of sensorless at 900 rpm under a 0. 0.97-Nmload applied in the middle of the simulation, as determined using (a) MMRASand (b) PI algorithms.

under various load conditions. These results reveal that thesteady-state error in the speed of the MMRAS controller issmaller than that of the PI controller.

The third step is the sensorless step, the aim of which is todemonstrate the effect of sensorless design. Fig. 8(a) and (b)present the results of applying the sensorless algorithm to themotor drive system with the torque observer. Table II shows theaverage RMSE of the sensorless BLDCM simulation under thevarious controllers and load conditions. These results reveal thatthe new sensorless algorithm is effective. It is also shows thatthe MMRAS controller can reduce the steady-state error in thespeed of the sensorless, except at 1800 rpm without a load.

V. EXPERIMENTAL RESULTS

Fig. 9 presents the configuration of the BLDCM experimentalsystem, where the BLDCM incorporates SINANO 7CB30, andthe load is a dc generator. The experimental process has twosteps. First, the sensor step involves the MMRAS speed con-troller and PI speed controller whose parameters are tuned using

522 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 2, MARCH 2006

Fig. 9. Configuration of the BLDCM experimental system.

Fig. 10. Experimental speed response of sensor at 900 rpm with a 0.1788-Nmload applied in the middle of the experiment, as determined using (a) MMRASand (b) PI algorithms.

Fig. 11. Experimental speed response of sensor at 1800 rpm with a 0.459 Nmload applied in the middle of the experiment, as determined using (a) MMRASand (b) PI algorithms.

the Ziegler–Nichols method [17]–[19], respectively, at 900 rpmwith a 0. 1788-Nm load applied in the middle of the experiment.Fig. 10(a) and (b) plot the results, and the average RMSE valueswere 12.78 and 38.51, respectively. Fig. 11(a) and (b) plot theresults obtained at higher speed and under a higher load; theaverage RMSE values were 25.83 and 77.29, respectively. Thespeed error does not keep getting integrated, but try to be inthe bounded range or minimized, by these controllers. The ap-plied load was treated as a disturbance, and the parameters ofthe MMRAS controller are adjusted based on the error, to forcethe system to the desired output. The PI controller has cannotmodify the parameters of the controller so the speed responsecould not represent the desired output after the load is applied.The steady-state error of the PI controller should not be zero, butmay cause an oscillatory response [22]. Clearly, the MMRASspeed controller outperformed the PI speed controller, as re-vealed by the simulation. Therefore, the MMRAS speed con-troller was adopted in the following experiment.

The purpose of the second, sensorless step, step is to study theproposed new speed-sensorless approach. The speed-sensorlessexperiment is performed at 900 rpm without any load. Fig. 12presents the results and the average RMSE of the speed responsewas 16. Fig. 12(c) and (d) reveal that the average RMSE of the

TABLE IIAVERAGE RMSE OF THE SENSORLESS BLDCM SIMULATION WITH DIFFERENT

CONTROLLERS UNDER VARIOUS LOAD CONDITIONS

Fig. 12. Experimental results of sensorless at 900 rpm without any load on theMMRAS speed controller: (a) speed response, (b) estimated load torque, ^T , (c)estimated mechanical rotor inertia constant, ^J , (d) estimated friction coefficient,^B.

Fig. 13. Experimental results obtained for sensorless with a load appliedthroughout the experiment on the MMRAS speed controller: (a) 1500 rpm,with a 0.29-Nm load, (b) 900 rpm, with a 0.1788-Nm load, and (c) 30 rpm,with a 0.0086-Nm load.

WANG AND LIU: INTEGRATED DESIGN OF SPEED-SENSORLESS AND ADAPTIVE SPEED CONTROLLER 523

estimated mechanical rotor inertia constant and friction coeffi-cient were very small, and the load torque in Fig. 12(b), derivedfrom the load observer in the Fig. 2, as accurately estimated. Themethod in chapter 2 was used to obtain information on the speedin the form of a feedback signal, which id used in closed loopcontrol. Therefore, Fig. 12(a) presents favorable sensorless per-formance. Fig. 13 also presents the results obtained under a loadat 1500 rpm, 900 rpm, and 30 rpm. The load is a dc generator,as presented in Fig. 9, so the load is proportional to speed. Theaverage RMSE values of the speed response were 17.93, 21.88,and 16.12, respectively. The range of speeds is from 1500 rpm to30 rpm with or without a load. The reason that the motor cannotoperate in a synchronal speed will be explored in the future.

VI. CONCLUSION

The proposed new speed-sensorless approach, which is basedon the torque observer, was successfully implemented herein inthis study to achieve the speed-sensorless vector control of theBLDCM drive. First, the RLS estimates the uncertain parame-ters of the plant. Then, they are incorporated into the torque ob-server to implement the speed-sensorless approach. Addition-ally, the MMRAS algorithm applies the adaptive function andimproves the performance of the speed control. The effective-ness of the integrated design of the speed-sensorless and adap-tive speed controller of a brushless dc motor, was established bysimulated and experimental results.

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Hsiu-Ping Wang was born in Taiwan, R.O.C., in 1957. He received the B.S.,M.S., and Ph.D. degrees in electrical engineering from National Chung ChengInstitute of Technology, Taoyuan, Taiwan, R.O.C., in 1979, 1983, and 1994,respectively.

He is currently an Associate Professor in the Department of Mechanical En-gineering, Lunghwa University of Science and Technology, Taoyuan. His majorfields of interest are in the areas of motor drive control, adaptive control, and es-timation.

Yen-Tsan Liu was born in Taiwan, R.O.C., in 1970. He received the M.S. degreein electrical engineering from National Chung Cheng Institute of Technology,Taoyuan, Taiwan, R.O.C., in 2000.

He is a Major in the Taiwanese Army specializing in electronic engineering.