INTEGRATED
P
ROCEDURE FOR
IDENTIFICATION AND
CONTROL OF
MDOF STRUCTURES
1
2
By Vincenzo Gattulli and Francesco Romeo
A
BSTRACT: An integrated procedure based on a direct adaptive control algorithm is applied to structural
systems for both vibration suppression and damage detection. The wider class of noncollocated actuator-sensor
schemes is investigated through parameterized linear functions of the state variables that preserve the minimum
phase property of the system. A larger number of mechanical parameters are shown to be identifiable in non-
collocated configurations. Proper output selection allowing for model reference control and tracking error based
parameters estimation under persistent excitation is described. Using full-state feedback, these capabilities are
effectively exploited for oscillation reduction and health monitoring of uncertain multi-degree-of-freedom
(MDOF) shear-type structures.
INTRODUCTION
and Baz 1996; Ghanem et al. 1997; Sun and Stelson 1997;
Gattulli and Ghanem 1999; Gattulli and Romeo 1999). In par-
ticular, Ghanem et al. (1997) implemented an adaptive control
procedure in a nonlinear single-degree-of-freedom system
modeling a device that relies on an electrorheological fluid for
its force-resisting mechanism. Gattulli and Ghanem (1999)
proposed the use of a direct adaptive procedure to mitigate
hydrodynamic vortex induced oscillations. Experimental vali-
dation of the direct adaptive controller has been pursued for a
large aerospace flexible structure with six collocated actuator/
sensor pairs (Ih et al. 1993a,b).
Recently Ray and Tian (1999) proposed a sensitivity en-
hancing procedure based on feedback control for damage de-
tection pointing out the potential use of feedback for vibration
suppression and health monitoring. According to this point of
view, the present work proposes the use of an integrated pro-
cedure for robust control of oscillations and damage detection
of MDOF linear structural systems. The methodology is
founded on direct model reference adaptive control (MRAC),
highlighting the key role played by the output selection in both
collocated and noncollocated actuator/sensor configurations.
Indeed, a proper output choice assures a linear dependence on
the on-line identifiable mechanical parameters, and it allows
detection of their variations due to damage under persistent
excitation. Moreover, the number of the latter parameters is
shown to be increased in noncollocated configurations. A qual-
itative analysis of the uncontrolled dynamics together with a
Lyapunov-based controller design guarantee overall stability.
It is assumed that the number of actuators is smaller than the
number of sensors, which is the case in a general configuration
for structural control in earthquake engineering applications
The technical science of mechatronics—developing systems
composed by integrated mechanical elements, control logic,
and electronic components—has been fastly evolving during
the last decades. Vibration suppression and health monitoring
of large flexible structures are recent structural engineering
applications of this multidisciplinary field. In this respect, a
structural system equipped with sensors and actuators may be
designed to enable the identification of the relevant structural
parameters and the robust reduction of the oscillations during
a dynamical event. Nevertheless, in most of the investigations
the two aspects have been treated separately according to the
primary objective pursued.
On one hand, on-line identification procedures, developed
in the context of system theory [e.g., Isermann et al. (1974)],
have recently received attention for applications to linear and
nonlinear multi-degree-of-freedom (MDOF) structural systems
[
e.g., Ghanem and Shinozuka (1995)]. Most of these proce-
dures consist of prediction error-based estimators, where the
errors between predicted and measured output are used to up-
date estimates of the parameters. The stability proof, parameter
boundedness, smallness condition for the estimation error and
speed of adaptation delineate the differences in the available
methodologies [e.g., Ioannou and Datta (1991)]. Recently,
some specific studies in the structural context have been car-
ried out for time-dependent degrading structures (Lin et al.
1
990) and for nonlinear chain-like MDOF hysteretic systems
(Smyth et al. 1999). In both cases, a least-squares based pro-
cedure has been implemented. Good accuracy in the stiffness
degradation estimate is obtained in the former, whereas the
use of forgetting factors and the effects of both persistent ex-
citation and under- or overparameterization are some of the
results obtained in the latter.
On the other hand, adaptive control procedures for structural
systems have been investigated with the main goal of bringing
some state variable combinations of an uncertain dynamical
system to track a desired behavior relying on on-line adjust-
ment of control parameters. The use of these methodologies
has been proposed in different engineering applications (Poh
(
Soong 1990; Gattulli et al. 1994). The control strategy is cur-
rently based on full-state feedback (i.e., displacements and ve-
locities). Applications for aseismic protection of an existing
structure could be tackled by modifying the procedure to rely
only on acceleration measurements (Dyke et al. 1996).
The present paper is organized as follows. The governing
relations of a general structural system are reported in the sec-
ond section, and control canonical forms are recalled in the
third section. In particular, such transformations permit one to
separate from the assignable dynamics the internal dynamics
unaffected by the control input. The relevant steps of the con-
trol procedure based on sliding mode and model reference con-
cepts are presented in the fourth section. An on-line identifi-
cation procedure based on the asymptotic convergence to zero
of the tracking errors is delineated in the fifth section. The last
section is devoted to the applications of the procedure to shear-
type structures.
1
Asst. Prof., Dipartimento di Ingegneria delle Strutture, delle Acque e
del Terreno, Universit a` di L’Aquila, 67040 Monteluco Roio, Italy; cor-
2
Res. Asst., Dipartimento di Ingegneria delle Strutture, delle Acque e
del Terreno, Universit a` di L’Aquila, 67040 Monteluco Roio, Italy.
Note. Special Editor: Roger Ghanem. Discussion open until December
1
, 2000. To extend the closing date one month, a written request must
be filed with the ASCE Manager of Journals. The manuscript for this
paper was submitted for review and possible publication on December 6,
GOVERNING RELATIONS
1999. This paper is part of the Journal of Engineering Mechanics, Vol.
126, No. 7, July, 2000. ᭧ASCE, ISSN 0733-9399/00/0007-0730–0737/
$8.00 ϩ $.50 per page. Paper No. 22262.
It is assumed that structural oscillations induced by dynamic
loads are described by a linear discrete model with n
Lagran-
q
730 / JOURNAL OF ENGINEERING MECHANICS / JULY 2000
J. Eng. Mech. 2000.126:730-737.