8/10/2019 An Improved Indirect Field-Oriented Controller for the Induction Motor

http://slidepdf.com/reader/full/an-improved-indirect-field-oriented-controller-for-the-induction-motor 1/5

248 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 2, MARCH 2003

An Improved Indirect Field-Oriented Controller for the Induction Motor

A. Behal, M. Feemster, and D. Dawson

 Abstract—In this paper, the standard indirect field-orientedcontroller (IFOC) commonly used in current-fed induction

motor drives is modified to achieve global   exponential   rotor ve-locity/rotor flux tracking. The modifications to the IFOC scheme,which involve the injection of nonlinear terms into the currentcontrol input and the so-called desired rotor flux angle dynamics,facilitate the construction of a standard Lyapunov stabilityargument. The construction of a standard Lyapunov exponentialstability argument allows one to easily design adaptive controllersto compensate for parametric uncertainty associated with themechanical load. Simulation results are included to illustrate theimprovement in performance over the standard IFOC scheme.

 Index Terms— Adaptive control, exponential stability, field-ori-ented control, induction motor, Lyapunov.

I. INTRODUCTION

AS EVIDENCED by its extensive industrial use, the indi-

rect field-oriented control (IFOC) scheme for the induc-

tion motor [1] provides a solid standard by which many other

algorithms are compared. Over the last ten years, a large amount

of induction motor research, many schemes with an IFOC-like

control strategy at the core of the controller, have been devel-

oped to examine the induction motor control problem from a

nonlinear control perspective as opposed to a more classical

motor control perspective. For example, Espinosa-Perez and Or-

tega [5] presented a singularity-free, velocity tracking controller

which did not require rotor flux measurements; however, the

performance of the controller was limited by the fact that the

convergence rate of the velocity tracking error was restricted bythe natural damping of the motor. Ortega  et al.  [11] improved

upon [5] by utilizing a linear filtering technique to remove the

damping restriction in [5]; furthermore, Ortega et al. illustrated

that for a desired constant velocity, the control algorithm of 

[11] reduced to the indirect field-oriented control scheme [1].

In [2], Dawson et al. modified the control structure and stability

analysis presented in [11] to construct an adaptive rotor posi-

tion tracking controller which can be analyzed using standard

Lyapunov type arguments. In [13], Ortega and Taoutaou illus-

trated global asymptotic stability of the IFOC control scheme

for rotor velocity setpoint applications. In [14], Ortega et al. il-

lustrated how previously designed passivity-based control algo-

rithms [15] can be expressed in the indirect field-oriented no-tation. With this link between the notation, Ortega  et al.   illus-

trated global asymptotic speed regulation for current-fed induc-

tion motors with a constant load torque. In [4], DeWit et al. ana-

Manuscript received February 16, 2001; revised December 21, 2001. Manu-script received in final form August 2, 2002. Recommended by Associate Ed-itor K. Schlacher. This work was supported in part by the U.S. National ScienceFoundationunder Grants DMI-9457967,CMS-9634796, and ECS-9619785,theSquare D Corporation, and the Union Camp Corporation.

The authors are with the Departmentof Electrical and Computer Engineering,Clemson University, Clemson, SC 29634-0915 USA.

Digital Object Identifier 10.1109/TCST.2003.809250

lyzed the effects of varying the rotor resistance parameter in the

IFOC scheme on system stability. In [9], Marino et al. designed

an output-feedback control which achieved global exponential

rotor velocity/rotor flux for the reduced order model of the in-

duction motor (i.e., current-fed induction motor). In addition,

Marino  et al. illustrated how the controller in [9] could be mod-

ified to compensate for parametric uncertainty associated with

the load torque and the rotor resistance parameter; however, the

controller exhibited a singularity at motor start-up (see [10] for

the original adaptive observer design). In [8], Marino et al. re-

moved the restriction in [9] by designing the controller for the

full-order model.

In [13], Ortega and Taoutaou illustrated that the standard

IFOC scheme provides global asymptotic rotor position/rotor

flux regulation (see [14] for the tracking extension). In thispaper, the standard IFOC scheme is modified to yield global

exponential  rotor velocity/rotor flux tracking. The modifica-

tions to the IFOC scheme involve the injection of additional

nonlinear terms into the current control input and the so-called

desired rotor flux angle dynamics. These additional nonlinear

terms facilitate the construction of a standard exponential

stability result via the direct cancellation of mechanical/elec-

trical subsystem coupling terms during the Lyapunov stability

argument. The construction of a standard Lyapunov exponen-

tial stability argument allows one to easily design adaptive

controllers to compensate for parametric uncertainty associated

with the mechanical load. The paper is organized as follows. In

Section II, the reduced order model of a current fed inductionmotor actuating a mechanical subsystem is presented. The

problem formulation and the definition of the various error

signals are presented in Section III. In Section IV, the modified

IFOC control scheme and the closed-loop tracking error sub-

systems for the Lyapunov stability analysis are presented. The

global  exponential  rotor velocity/rotor flux tracking result is

presented in Section V. Section VI presents simulation results

to illustrate the improvement in performance over the standard

IFOC scheme.

II. ELECTROMECHANICAL SYSTEM

Following the common assumptions of equal mutual induc-tances and a linear magnetic circuit, the electromechanical

model of a current-fed induction motor driving a mechanical

subsystem in the rotating rotor reference frame [6] can be

written as follows:

(1)

(2)

where and represent the rotor ve-

locity and rotor acceleration, respectively, is the system

inertia (including rotor inertia), represents the coefficient

1063-6536/03$17.00 © 2003 IEEE

8/10/2019 An Improved Indirect Field-Oriented Controller for the Induction Motor

http://slidepdf.com/reader/full/an-improved-indirect-field-oriented-controller-for-the-induction-motor 2/5

8/10/2019 An Improved Indirect Field-Oriented Controller for the Induction Motor

http://slidepdf.com/reader/full/an-improved-indirect-field-oriented-controller-for-the-induction-motor 3/5

250 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 2, MARCH 2003

[and as a consequence the addition of to (13)], it is pos-

sible to formulate a global exponential rotor velocity tracking

result through a standard Lyapunov stability analysis.

In order to examine the stability of the improved IFOC

scheme, the control of (11), (12)–(15) is rewritten into a more

advantageous form. Specifically, a desired rotor flux trajectory

signal, denoted by , , in terms

of of (13) and the desired magnitude of the rotor flux, is defined as follows [11]:

(17)

The structure of (17) is motivated by (6) and the following chain

of equalities:

(18)

where (17) has been used. Since as given by

(18), the rotor flux magnitude tracking error given by (6) can be

written as follows:

(19)

where the rotor flux tracking error, denoted by ,

, is defined as follows:

(20)

From (19), it can be seen that if is exponentially stable

and if both , are bounded, then will be expo-

nentially stable, and hence, the secondary control objective orig-

inally given by (6) will be achieved.To construct the closed-loop rotor flux tracking error system,

the time derivative of (20) is taken and(2) is substituted to obtain

(21)

To complete the closed-loop description given by (21), the con-

trol current of (11) is rewritten as follows:

(22)

which can be further rewritten into the following compact form:

(23)

upon utilization of (4), (14), and (17). Continuing with formu-

lation of the dynamics for , the time derivative of (17) istaken to obtain

(24)

where (4)has been utilized. After utilizing the definition for (17)

and then substituting for from (13), the dynamics for

are obtained as follows:

(25)

After substituting (14) into (23), and then substituting the re-

sulting expression along with (25) into the time derivative of (20), the closed-loop dynamics for   are obtained in the fol-

lowing manner:

(26)

where (20) has been utilized. After canceling common terms

in (26) and noting that is used todenote the identity matrix), the closed-loop rotor flux tracking

error system can be rewritten in the following form:

(27)

which upon applying (23) can be written as

(28)

To formulate the closed-loop tracking error system for the

mechanical subsystem, the time derivative of the rotor velocity

tracking error of (5) is taken, multiplied through by , and the

mechanical system of (1) is substituted to obtain

(29)

where was defined in (16), and the terms ,

have been added and subtracted to the right-hand side of (29).

As an aside, the control input current of (23) is substituted into

the expression to obtain

(30)

where (18) and the fact that have been utilized. After

substituting (15) into (29) and noting that the first bracketed

term in (29) is zero as a result of (30), the closed-loop dynamics

for the rotor velocity tracking error are obtained as follows:

(31)

where (20) has been utilized.

V. STABILITY PROOF

Theorem 1:   The improved IFOC of (11)–(15) ensures expo-

nential rotor velocity/rotor flux tracking in the sense that

(32)

8/10/2019 An Improved Indirect Field-Oriented Controller for the Induction Motor

http://slidepdf.com/reader/full/an-improved-indirect-field-oriented-controller-for-the-induction-motor 4/5

8/10/2019 An Improved Indirect Field-Oriented Controller for the Induction Motor

http://slidepdf.com/reader/full/an-improved-indirect-field-oriented-controller-for-the-induction-motor 5/5

252 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 2, MARCH 2003

Fig. 1. Rotor velocity tracking error: Standard IFOC scheme versus improvedIFOC scheme

Fig. 2. Three-Phase stator currents for the improved IFOC scheme

response. With the introduction of standard Lyapunov-type

arguments in the stability analysis of IFOC-based control

strategies, it can be noted that the desired torque trajectory

can be easily upgraded with standard adaptive update lawsto compensate for parametric uncertainty associated with the

mechanical subsystem (e.g., an unknown, constant load torque).

In addition, the ability to utilize Lyapunov stability techniques

fosters added flexibility in the design of a variety of feedback 

control laws without significantly altering the structure of the

control. That is, it is possible to design numerous control laws

based on proportional (P) feedback, proportional-integral (PI)

feedback, and proportional-derivative (PD) / proportional-inte-

gral-derivative (PID) feedback with a minimum number of al-

terations to the control design/stability proof.

ACKNOWLEDGMENT

The authors would like to thank the reviewers for their con-

structive suggestions and a careful review of the manuscript.

REFERENCES

[1] B. Bose,   Power Electronics and AC Drives. Englewood Cliffs, NJ:Prentice-Hall, 1986.

[2] D. Dawson, J. Hu,and P. Vedagarbha, “Anadaptive controllerfor a classof induction motor systems,” in   Proc. IEEE Conf. Decision Control,New Orleans, LA, 1995, pp. 1567–1572.

[3] D. M. Dawson, J. Hu, and T. C. Burg,  Nonlinear Control of Electric Machinery. New York: Marcel Dekker, 1998.

[4] P. De Wit, R. Ortega, and I. Mareels, “Indirect field oriented control of induction motors is robustly globally stable,”   Automatica, vol. 32, no.10, Oct. 1996.

[5] G. Espinoza-Perez and R. Ortega, “State observers are unnecessary forinduction motor control,” Syst. Contr. Lett., vol. 23, no. 5, pp. 315–323,1994.

[6] P. Krause, O. Wasynczuk, and S. Sudhoff,   Analysis of Electric Ma-

chinery. Piscataway, NJ: IEEE Press, 1994.[7] F. L. Lewis, C. T. Abdallah, and D. M. Dawson, Control of Robot Ma-

nipulators. New York: Macmillan, 1993.[8] R. Marino, S. Peresada, and P. Tomei, “Global adaptive output feedback 

control of inductionmotors withuncertainrotor resistance,” IEEE Trans. Automat. Contr., vol. 44, pp. 967–983, May 1999.

[9] , “Output feedback control of current-fed induction motors withunknown rotor resistance,” IEEE Trans. Contr. Syst. Technol., vol. 4, pp.

336–346, July 1996.[10] R. Marino, S. Peresada, and P. Valigi, “Exponentially convergent rotorresistance estimation for induction motors,”  IEEE Trans. Ind. Electron.,vol. 42, no. 5, pp. 508–515, Oct. 1995.

[11] R. Ortega, P. Nicklasson, and G. Espinosa-Perez, “On speed control of induction motors,”  Automatica, vol. 32, no. 3, pp. 455–460, Mar. 1996.

[12] R. Ortega, D. Taoutaou, R. Rabinovici, and J. Vilain, “On field ori-ented and passivity-based control of induction motors: Downward com-patibility,” in  Proc. IFAC NOLCOS Conf., Tahoe City, CA, 1995, pp.672–677.

[13] R. Ortega and D. Taoutaou, “Indirect field oriented speed regulation forinduction motors is globally stable,” IEEE Trans. Ind. Electron., vol. 43,pp. 340–341, Apr. 1996.

[14] R. Ortega, D. Taoutaou, R. Rabinovici, and J. Vilain, “On field ori-ented and passivity-based control of induction motors: Downward com-patibility,” in  Proc. IFAC NOLCOS Conf., Tahoe City, CA, 1995, pp.672–677.

[15] R. Ortega and G. Espinosa, “Torque regulation of induction motors,” Automatica, vol. 29, no. 3, pp. 621–633, May 1993.[16] S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence, and 

 Robustness. Englewood Cliffs, NJ: Prentice-Hall, 1989.[17] J. Slotine and L. Wi, Applied Nonlinear Control. Englewood Cliffs,

NJ: Prentice-Hall, 1991.[18] M. Vidyasagar,   Nonlinear Systems Analysis. Englewood Cliffs, NJ:

Prentice-Hall, 1978.