Abstract
〈Vol.5 No.3(2012.5)〉
Titles
[Contributed Papers]
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■ Asymptotic Mean Square Stability Analysis for a Stochastic Delay Differential
Equation
Peng XUE and Shigeru YAMAMOTO
For a stochastic delay differential equation, a stability condition is
derived in the sense of mean square stability. The condition substantiates
the fact that noise with an appropriate power can reduce the influence
of time delay in the differential equations. It is also illustrated by
a numerical example. To derive the stability condition, the so-called domain
subdivision method and Ito’s formula are adopted.
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■ Input-Output Linearization for Transfer Functions of Input-Affine Meromorphic
Systems
Yu KAWANO and Toshiyuki OHTSUKA
Recently, the concept of transfer functions for meromorphic control systems
has been proposed. These transfer functions have many similar properties
to the transfer functions of linear systems. This paper shows that an input-affine
meromorphic system is input-output linearizable with static state feedback
if and only if its transfer function is not identically zero.
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■ Control of Discrete Event Systems Using Condition/Event Nets and Partial
Languages
Satoru HASHIZUME, Susumu HASHIZUME, Tomoyuki YAJIMA, and Katsuaki ONOGI
In order to construct a rational framework of designing discrete event
control systems, it is necessary to develop the method of modeling concurrent
systems, describing control objectives, and synthesizing controllers based
on the plant models and control objectives. If the control of discrete
events is viewed as the manipulation of event occurrences, the role of
a controller is to enable and inhibit the occurrences of events. This paper
presents a framework for control of discrete event systems so as to achieve
the desired behavior specified as a control objective. For this purpose,
by using condition/event nets (C/E nets) as a modeling tool for discrete
event systems and partial languages as a behavioral description tool for
C/E nets, we formulate a control problem to synthesize a controller which
guarantees that all and only the desired behaviors described by a partial
language is possible. We then present the solvability and solution techniques
of the formulated problem, together with the discussion about the design
of discrete event control systems with uncontrollable and unobservable
events.
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■ Further Results on Sufficient LMI Conditions for H∞ Static Output Feedback
Control of Discrete-Time Systems
Zhi-Yong FENG, Li XU, Shin-ya MATSUSHITA, and Min WU
Further results on sufficient LMI conditions for H∞ static output feedback
(SOF) control of discrete-time systems are presented in this paper, which
provide some new insights into this issue. First, by introducing a slack
variable with block-triangular structure and choosing the coordinate transformation
matrix properly, the conservativeness of one kind of existing sufficient
LMI condition is further reduced. Then, by introducing a slack variable
with linear matrix equality constraint, another kind of sufficient LMI
condition is proposed. Furthermore, the relation of these two kinds of
LMI conditions are revealed for the first time through analyzing the effect
of different choices of coordinate transformation matrices. Finally, a
numerical example is provided to demonstrate the effectiveness and merits
of the proposed methods.
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■ Efficient Wireless Power Transmission Based on Position Sensing Using
Magnetic Resonance Coupling
Sousuke NAKAMURA, Ryo KOMA, and Hideki HASHIMOTO
In recent years, frequency control and impedance control systems have been
studied to realize efficient wireless transmission systems using magnetic
resonance coupling. However, the frequency control system has a problem
that the usable frequency is bounded by the Industry-Science-Medical (ISM)
band, and the impedance control system has a problem that the flexibly
controllable impedance converting circuits are difficult to realize. Therefore,
this paper proposes an efficient wireless power transmission system which
operates at fixed frequency and impedance. In the proposed system, the
relative position of the transmitter to the target antenna was measured
and controlled to achieve high transmission efficiency. The relative position
was measured based on a novel position sensing method also using magnetic
resonance coupling. As a result, the transmission efficiency increases
from 45.0% to 62.4% where the target value was 70.0%, and the effectiveness
of the system on improving the transmission efficiency is experimentally
verified.
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■ Controller Parameter Tuning for Systems with Hysteresis and Its Application
to Shape Memory Alloy Actuators
Yuji WAKASA, Shinji KANAGAWA, Kanya TANAKA, and Yuki NISHIMURA
This paper proposes a simple controller parameter tuning method that can
compensate for hysteresis. The proposed method is based on the so-called
fictitious reference iterative tuning (FRIT) technique which can easily
tune controller parameters such as proportional-integral-derivative gains
using a one-shot closed-loop experimental data. In the proposed framework,
a simple hysteresis model is introduced to a control system, and its inverse
is used as a hysteresis compensator. Since the hysteresis model is characterized
with only three parameters, the related computational burden is moderate
in the parameter tuning process. Also, the proposed FRIT method needs an
only one-shot experiment as in the standard FRIT one, which implies that
the feature of FRIT is well-maintained. In the optimization process, the
so-called covariance matrix adaptation evolution strategy is used for simultaneously
searching hysteresis parameters as well as controller parameters. The proposed
FRIT method is applied to an experimental control system that comprises
a shape memory alloy actuator, and its effectiveness is verified.
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■ Note on Well-Posedness and Separator-Type Robust Stability Theorem of LTI Systems
Tomomichi HAGIWARA
This paper is concerned with the well-posedness (in the classical sense)
and robust stability analysis of linear time-invariant (LTI) systems. Among
approaches to robust stability analysis of LTI systems is the one based
on the separator-type robust stability theorem derived through the topological
separation notion. This paper first shows that the well-posedness assumption
underlying this theorem, which has been considered to be essential in the
discrete-time case, can actually be removed completely. Some arguments
and an example are further provided, suggesting that removing
such an assumption is indeed a nontrivial task. Relevant aspects are also
discussed about well-posedness of uncertain systems through the systematic
arguments underlying the construction of such an example, both in the discrete-time
and continuous-time cases.
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■ State-Space Stabilizing Controllers for Descriptor Systems
Masaki INOUE, Teruyo WADA, Masao IKEDA, and Eiho UEZATO
This paper considers stabilization of linear time-invariant descriptor
systems by dynamic output feedback controllers. We deal with general descriptor
systems including those being irregular or impulsive, and derive statespace
stabilizing controllers. On the derivation process of the state-space controllers,
we first consider descriptor-type controllers. We present a necessary and
sufficient condition for the existence of a descriptor-type controller
which makes the closed-loop descriptor system regular, impulse-free, and
stable. The condition is expressed in terms of linear matrix
inequalities (LMIs), and we show that coefficient matrices of any descriptor-type
stabilizing controller of the same size as the given descriptor system
can be represented by the solution of the LMIs. Then, we present a necessary
and sufficient condition for the descriptor-type controller to be transformable
to an input-output equivalent state-space controller with the dimension
of the dynamic order (the rank of the coefficient matrix for the time-derivative
of the descriptor variable) of the given descriptor system, that is, a
state-space stabilizing controller. The transformability condition is mild
and almost always satisfied by the obtained descriptor-type controller.
Furthermore, even if the transformability condition is not satisfied, a
slightly modified solution of the LMIs, which always exists, gives a descriptor-type
controller being transformable to a state-space controller. The transformation
is carried out analytically, thus the coefficient matrices of any such
state-space stabilizing controller can be expressed by the solution of
the LMIs. We also reveal that if we restrict
the classes of descriptor systems or descriptor-type controllers such that
their transfer functions are strictly proper, the descriptor-type controllers
obtained by the LMI condition are always transformable to state-space controllers.
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■ Application of Interval Methods to Sampled-Data Control of Uncertain Piecewise Affine Systems
Koichi KOBAYASHI and Kunihiko HIRAISHI
In this paper, sampled-data control of piecewise affine (PWA) systems with
parameter uncertainty is addressed based on both the interval method and
the authors’ previously proposed method. First, the optimal sampled-data
control problem of continuous-time PWA systems with parameter uncertainty
is rewritten as an optimal control problem of discrete-time PWA systems
with parameter uncertainty. Since in the obtained problem weighting matrices
of the cost function are also uncertain, this problem is a min-max mixed
integer programming (MIP) problem. Then, by using the interval method and
the authors’ previously proposed method, this problem is approximated
by an MIP problem. Finally, the effectiveness of the proposed method is
shown by a numerical example.
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