The robust observer design for the online estimation of heat in continuous stirred tank reactors, containing nonstructured uncertainties within its model description as well as noisy temperature measurements, is addressed. The proposed observer contains a sliding-mode term and is designed based on Differential Algebraic technique. The concept of the algebraic observability for a given class of model uncertainty is introduced. It is applied to the uncertainty estimation from noisy temperature measurements providing a simple observer structure which turns out to be robust against output (sensors) noises as well as sustained disturbances. The performance of this observer is shown to be calculated numerically. The obtained results look promising for possible industrial applications.

Issue Section:
Technical Papers
Keywords:
variable structure systems, observers, observability, chemical reactors, heat measurement, temperature measurement, uncertain systems, algebra, chemical variables control, control system synthesis
Topics:
Algebra, Design, Errors, Heat, Noise (Sound), Temperature, Temperature measurement, Uncertainty, Dynamics (Mechanics), Computer simulation, Control systems, Sensors
1.
Ljung, L., 1999, “System for Identification. Theory for the Users,” Second Edition, Prentice Hall PTR, Upper Saddle River, NJ 07458.
2.
Alvarez Ramı´rez, J., and Martı´nez-Guerra, R., 1993, “Practical Stabilization of a Class of Uncertain Chemical Reactors,” Proc. 32nd. IEEE Conference on Decision and Control (CDC) San Antonio, Texas, U.S.A., pp. 3877–3878.
3.
Soroush
,
M.
,
1997
, “
Nonlinear state observer design with application to reactors
,”
Chem. Eng. Sci.
,
52
(
3
), pp.
387
–
404
.
4.
Schuler
,
H.
, and
Schmidt
,
C.
,
1992
, “
Calorimetric-state estimator for chemical reactors diagnosis and control: Review of methods and applications
,”
Chem. Eng. Sci.
,
47
, pp.
899
–
908
.
5.
Krener
,
A. J.
, and
Isidori
,
A.
,
1983
, “
Linearization by output injection and nonlinear observers
,”
Systems & Control Letters
,
3
, pp.
47
–
54
.
6.
Elicabe
,
G. E.
,
Ozdeger
,
E.
, and
Georgakis
,
C.
,
1995
, “
On line estimation of reaction rate in a polymerization process
,”
Ind. Eng. Chem. Res.
,
34
, pp.
1219
–
1227
.
7.
Fliess, M., and Hasler, M., 1990, “Questioning the classical state-space description via circuit example,” Birkhauser, Boston, MA: Mathematical Theory of networks and systems, MTNS-89, Kaashoek MA, Ram ACM, van Shuppen JH (Eds.). Progress in Systems and Control. Boston: Birkha¨user.
8.
Freedman
,
M. I.
, and
Willems
,
J. C.
,
1978
, “
Smooth representation of systems with differentiated inputs
,”
IEEE Transc. Aut. Contr.
,
23
, pp.
16
–
21
.
9.
Hasler, M., and Neirynck, J., 1986, “Nonlinear Circuits,” Boston, MA: Artech House.
10.
Martı´nez-Guerra
,
R.
, and
De Leo´n-Morales
,
J.
,
1996
, “
Nonlinear estimators: a differential algebraic approach
,”
Appl. Math. Lett.
,
9
, pp.
21
–
25
.
11.
Martı´nez-Guerra
,
R.
,
Suarez
,
R.
, and
De Leo´n-Morales
,
J.
,
2001
, “
Asymptotic tracking of a class of nonlinear systems by means of an observer
,”
International Journal of Robust and Nonlinear Control
,
11
, pp.
373
–
391
.
12.
Martı´nez-Guerra
,
R.
, and
De Leo´n-Morales
,
J.
,
1994
, “
Observers for a multi-input multi-output bilinear systems class:a differential algebraic approach
,”
Journal of Mathematics and Computer Modelling
,
20
, pp.
125
–
132
.
13.
Slotine
,
J.
,
Hedricks
,
J.
, and
Misawa
,
E.
,
1987
, “
On sliding observers for nonlinear systems
,”
J. Dyn. Meas. & Control.
,
109
, pp.
245
–
252
.
14.
Aguilar
,
R.
,
Poznyak
,
A.
,
Martinez-Guerra
,
R.
, and
Maya-Yescas
,
R.
,
2002
, “
Temperature control in catalytic cracking reactors via a robust PID controller
,”
Journal of Process Control
,
12
, pp.
695
–
705
.
15.
Fliess
,
M.
,
1990
, “
Generalized controller canonical forms for linear and nonlinear dynamics
,”
IEEE Transc. Aut. Contr.
,
35
, pp.
994
–
1001
.
16.
Ritt, J. F., 1932, “Differential equations from the algebraic standpoint,” New York: American Mathematics Society.
17.
Diop, S., and Fliess, M., 1991, “On nonlinear observability,” Proceedings of the First European Control Conference, Paris Hermes, pp. 152–157.
18.
Martı´nez-Guerra
,
R.
,
Poznyak
,
A.
,
Gortcheva
,
E.
, and
Dı´az-De Leo´n
,
V.
,
2000
, “
Robot angular link velocity estimation in presence of high level mixed uncertainties
,”
International Journal IEE Proce. on Control Theory and Applications
,
147
(
5
), pp.
515
–
522
.
19.
Utkin, V. I. 1978, “Sliding modes and their applications in variable structure systems,” MIR, Moscow.
20.
Drakunov
,
S. V.
,
1984
, “
Adaptive quasi-optimal filters with discontinuous parameters
,”
Automation and Remote Control
,
44
(
9
), pp.
1167
–
1175
.
21.
Drakunov, S. V., and Utkin, V., 1995, “Sliding mode observers, Tutorial,” Proc. 34th IEEE Conference on Decision and Control (CDC), Dec. 13–15, New Orleans, LA, pp. 3376–3378.
22.
De Carlo R., Zak, S., and Drakunov, S., 1996, “Variable structure and sliding mode control,” Chapter in the Control Handbook a volume in the Electrical Engineering Handbook Series, CRC Press, Inc.,
23.
Anulova
,
S. V.
,
1986
, “
Random Disturbances of the Operation of Control Systems in the Sliding Mode
,”
Automation and Remote Control
,
47
(4), Part I, pp.
474
–
479
.
24.
Poznyak, A. S., Sanchez N. N., and Wen Yu, 2001, “Differential Neural Networks for Robust Nonlinear Control: Identification, State estimation and Trajectory Tracking,” World Scientific Publisher, New Jersey-London-Singapore-Hong Kong.
Copyright © 2004
 by ASME
You do not currently have access to this content.