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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
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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)
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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.
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