18-12-2012, 05:14 PM
Simple Derivative-Free Nonlinear State Observer for Sensorless AC Drives
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Abstract
—In this paper, a new Kalman filtering technique, unscented
Kalman filter (UKF), is utilized both experimentally and
theoretically as a state estimation tool in field-oriented control
(FOC) of sensorless ac drives. Using the advantages of this recent
derivative-free nonlinear estimation tool, rotor speed and dq-axis
fluxes of an induction motor are estimated only with the sensed
stator currents and voltages information. In order to compare the
estimation performances of the extended Kalman filter (EKF) and
UKF explicitly, both observers are designed for the same motor
model and run with the same covariance matrices under the same
conditions. In the simulation results, it is shown that UKF, whose
several intrinsic properties suggest its use over EKF in highly nonlinear
systems, has more satisfactory rotor speed and flux estimates,
which are themost critical states for FOC. These simulation results
are supported with experimental results.
INTRODUCTION
IN the previous decade, several different methods [1]–[9]
were proposed for eliminating speed transducers and Hall
effect flux sensors from industrial ac drives in order to reduce
the cost and increase the reliability of the overall system. These
speed sensors require special attention to noise. Furthermore,
Manuscript received October 11, 2004; revised March 14, 2006. Recommended
by Technical Editor R. Rajamani.
B. Akın is with the Department of Electrical and Computer Engineering,
Texas A&MUniversity, College Station, TX 77843 USA, and also with Toshiba
Industrial Division, Toshiba International Corporation, Houston, TX 77041
USA (e-mail: akbilal[at]ee.tamu.edu).
U. Orguner and A. Ersak are with the Department of Electrical and Electronics
Engineering, Middle East Technical University, Ankara 06531, Turkey
(e-mail: umut[at]metu.edu.tr; ayersak[at]metu.edu.tr).
SIMULATION RESULTS
To verify the state estimation performance of UKF, particularly
the speed estimation, a number of simulations were carried
out under different conditions. The simulations were implemented
with Matlab/Simulink software package. It is quite
difficult to implement all the matrix operations and the overall
computation using only Simulink toolbox. S-functions (system
functions) provide a powerful and special calling system that
enables the interaction with Simulink’s equation solver. Thus,
the UKF and EKF modules are developed as S-functions and
then inserted to Simulink in the form of S-function blocks. The
parameters of the motor model are given in the Appendix.
MEASUREMENT NOISE IMMUNITY
The low-pass filter characteristic of the UKF is tested under
noisy conditions. For this purpose, white Gaussian measurement
noise, shown in Fig. 8, is injected into the dq-axis stator currents.
UKF runs with these noisy currents.
As mentioned earlier, to decrease the effect of measurement
noise on the system, the measurement noise covariance is increased
step-by-step. Then, the information coming from the
system model has more significance on the estimates.
The rotor speed is estimated with three different measurement
noise covariances. As shown in Fig. 9(a), detuned covariance
initialization causes highly noisy estimate and remarkable offset
in the steady-state. In Fig. 9(b), larger covariance makes the estimate
better when compared to the previous case. In Fig. 9©, a
most appropriate covariance forces the estimate tomatch the reference
speed at steady-state and filters the noise on the estimate.
This example obviously demonstrates the measurement noise
immunity of the UKF when run with appropriate covariance
initializations.