Automatic Intelligent Initialization for a Modified Generalized
Minimum Variance Controller
Marco Antonio Paz Ramos
(1) (2)
, Enrique Quintero-Mármol Márquez
(2)
, José Torres Jiménez
(3)
(1)
Instituto Tecnológico y de Estudios Superiores de Monterrey campus Ciudad de México
Calle del Puente 222, Ejidos de Huipulco, Tlalpan, México D.F, México.
e-mail: marco.paz@itesm.mx
(2)
Centro Nacional de Investigación y Desarrollo Tecnológico
Interior Internando Palmira S/N, 62490, Cuernavaca Morelos, México.
e-mail: eqm@cenidet.edu.mx
(3)
Instituto Tecnológico y de Estudios Superiores de Monterrey campus Cuernavaca
Paseo de la Reforma 182-A Lomas de Cuernavaca, Temixco Morelos, México.
e-mail: jtj@itesm.mx
Abstract
When a self-tuning regulator (STR) is applied, is essential
an adequate initialization. The initialization procedure must
to fix the initial parameters, to select a model structure and
to propose the desired control criterion. If the goal is to
have adaptive control when the knowledge about the
process is scarce or even do not exist, is essential to develop
a tool that can initialize to the adaptive controller in
autonomous way. This paper describes an initialization
approach which is based in heuristic rules and intelligent
procedures. Also is developed a modification to the
generalized minimum variance controller with pole
assignment approach to reduce the number of parameters
that must be initialized and simplify the implementation for
practical cases. Test results are included in the document
with the aim to highlight the characteristics of the proposed
initialization procedure.
PRINCIPAL SYMBOLS
A,B,C Polynomials of order n
a
, n
b
and n
c
corresponding to, respectively, system
output, control input, and disturbance input;
a
0
=c
0
=1.
E
x
{·} expectation operation.
φ(t) Generalized output function.
P,Q,R Costing polynomials of order n
P
, n
Q
and n
R
acting on, respectively, system output, input
and reference.
E General polynomial acting on the reference.
F General polynomial acting on the
perturbation.
G General polynomial acting on the output.
H General polynomial acting on the input.
T Pole assignment polynomial
y(t), u(t), r(t) System output, input and set point,
respectively.
e(t) Uncorrelated zero-mean random
sequence.
k System time delay.
t time measured in sample instants.
1 Introduction
The self-tuning regulator (STR) has been studied
intensively during almost three decades, the original work
presented by Åström and Wittermark in 1973 [1] can be
pointed out as the beginning. The adoption of the
microprocessor in the construction of general purpose
controllers at the end of the decade of 1970 strengthened the
expectations of an increase of the adaptive control in
industrial applications.
Considering a current industrial context, Ender [2] mentions
that almost 30% of the process controllers that work in the
world are operated in manual mode. This operation decision
is usually made by the final user when he found
unsatisfactory control performances which can be caused
for different reasons: flickering in valves, problems in
actuators and transmitters, inadequate designs, addition of
loops which was not considered in the initial development,
dramatic environmental changes and parts aging.
These arbitrary dynamics open an opportunity area for the
adaptive control in the industrial environment, however the
profile of these controllers and its complexity have a
negative impact on the final user acceptation [3], since is
not possible to force to an operator (which is not usually
familiarized with the adaptive control) to make decisions
that determine the performance of an adaptive control
[4][5].
To develop an adaptive controller for a particular process is
an advantageous task, because we can always to obtain a
minimum information which can be used in the control
073-40-3016-9 © 2004 ASCC 1231