Authors:
Gustavo Ayres,
Fernando Paganini,
Volume: 1, Page 3751 Paper number 1761
Abstract:
A method is presented to impose localization in controller design for
distributed arrays with underlying spatial invariance. The method applies
to problems where the performance objective (e.g., stabilization, H_2
or H-infinity control) can be stated in terms of the search for a suitable
Lyapunov matrix over spatial frequency. By restricting this matrix
to be constant across frequency, controller localization can be naturally
imposed. Thus we obtain sufficient conditions for the existence of
a controller with the desired localization and performance, which take
the form of linear matrix inequalities (LMIs) over spatial frequency.
For one-dimensional arrays, we further show how to convert these conditions
exactly to finite dimensional LMIs by means of the KYP lemma.
Authors:
Dimitry Gorinevsky,
Gunter Stein,
Volume: 1, Page 3757 Paper number 2021
Abstract:
This paper considers one of the fundamental issues in design and analysis
of sampled multidimensional systems - that of uncertainty modeling
and robust stability analysis. This paper extends methods of structured
uncertainty analysis (µ-analysis) towards spatially distributed
system with dynamical and spatial coordinates. The main contribution
with respect to earlier work in this area is in clarification of stability
issues for multidimensional systems with noncausal coordinates. Here
stability is understood in a broad sense and includes decay (localization)
of system response along noncausal spatial coordinates. The presented
framework allows to address such practically important issues as robustness
of dynamical stability and spatial localization of multidimensional
closed-loop feedback system response and boundary effects in a unified
way.
Authors:
Petros G. Voulgaris,
Gianni Bianchini,
Bassam Bamieh,
Volume: 1, Page 3763 Paper number 2087
Abstract:
We consider the problem of optimal H_2 design of semi-decentralized
controllers for a special class of spatially distributed systems. This
class includes spatially invariant and distributed discrete-time systems
with an inherent temporal delay in the interaction of neighbouring
sites. Such a structure arises naturally from spatio-temporal discretizations
of many physical systems described by partial differential equations.
We consider the problem of optimal design of distributed controllers
that have the same information passing delay structure as the plant.
We show how the YJBK parametrization of such stabilizing controllers
yields a convex parametrization for this class. We then show how the
optimal H_2 problem can be solved exactly.
Authors:
Mohammed Aassila,
Marcelo Moreira Cavalcanti,
Juan Amadeo Soriano,
Volume: 1, Page 3769 Paper number 4
Abstract:
We study the asymptotic stability and give the energy decay rates for
solutions of the wave equation with boundary dissipation of memory
type.
Authors:
Fumitoshi Matsuno,
Takashi Ohno,
Volume: 1, Page 3774 Paper number 1624
Abstract:
In this papaer, we propose the exponential stabilizing controller of
the motion of the rigid mode and the vibration of flexible modes for
two flexible beams connected by a spring as a simple example of the
large space structures. The flexible beams and the spring can be regarded
as an element of the structure with the distributed flexibility and
a connective part with lumped flexibility, respectively. As the rigid
mode is unstable, the original open-loop flexible system is not exponential
stable. We propose a direct sensor output feedback control law for
the motion and vibration absorption control. Using the spectral analysis,
the exponential stability of the closed-loop system is proven. As we
don't need an approximated finite-dimensional model at the controller
design phase, the controller based on the original distributed parameter
system is robust and simple. To demonstrate the validity of the proposed
model and effectiveness of the proposed control law experiments have
been carried out.
Authors:
Jun Imai,
Kiyoshi Wada,
Volume: 1, Page 3780 Paper number 2055
Abstract:
A procedure for control-oriented modeling of uncertainty is proposed
for large flexible structures. Techniques on quantification of errors
in modal truncated nominal models are developed for the case where
a finite number of upper and lower bounds of the unknown modal parameters
are given. A feasible set of systems matching the conditions is introduced,
and then error bounds covering the feasible set are established in
the frequency domain. The bounds are easily checked using linear programming
for any user-specified frequency. The feasibility of the proposed scheme
is illustrated by numerical study on an ideal flexible beam example.
Authors:
Shuzhi Sam Ge,
Tong-Heng Lee,
Fan Hong,
Cher Hiang Goh,
Volume: 1, Page 3785 Paper number 2032
Abstract:
This paper presents a class of non-model-based position controllers
for a kind of flexible spacecraft. A very basic system energy relationship
of the flexible spacecraft is involved in the controller design and
stability analysis instead of system dynamics themselves. With the
controllers, one can achieve not only the closed-loop stability of
the original distributed-parameter system, but also the asymptotic
stability of the truncated system, which is obtained through representing
the deflection of the appendage by an arbitrary finite number of flexible
modes. Simulation results carried out on a kind of spacecraft with
one flexible appendage justify the effectiveness of the proposed controller.
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