550 research outputs found
Root locii for systems defined on Hilbert spaces
The root locus is an important tool for analysing the stability and time
constants of linear finite-dimensional systems as a parameter, often the gain,
is varied. However, many systems are modelled by partial differential equations
or delay equations. These systems evolve on an infinite-dimensional space and
their transfer functions are not rational. In this paper a rigorous definition
of the root locus for infinite-dimensional systems is given and it is shown
that the root locus is well-defined for a large class of infinite-dimensional
systems. As for finite-dimensional systems, any limit point of a branch of the
root locus is a zero. However, the asymptotic behaviour can be quite different
from that for finite-dimensional systems. This point is illustrated with a
number of examples. It is shown that the familiar pole-zero interlacing
property for collocated systems with a Hermitian state matrix extends to
infinite-dimensional systems with self-adjoint generator. This interlacing
property is also shown to hold for collocated systems with a skew-adjoint
generator
Turing Instability in Reaction-Diffusion Systems with a Single Diffuser: Characterization Based on Root Locus
Cooperative behaviors arising from bacterial cell-to-cell communication can
be modeled by reaction-diffusion equations having only a single diffusible
component. This paper presents the following three contributions for the
systematic analysis of Turing instability in such reaction-diffusion systems.
(i) We first introduce a unified framework to formulate the reaction-diffusion
system as an interconnected multi-agent dynamical system. (ii) Then, we
mathematically classify biologically plausible and implausible Turing
instabilities and characterize them by the root locus of each agent's dynamics,
or the local reaction dynamics. (iii) Using this characterization, we derive
analytic conditions for biologically plausible Turing instability, which
provide useful guidance for the design and the analysis of biological networks.
These results are demonstrated on an extended Gray-Scott model with a single
diffuser
Zero Dynamics for Port-Hamiltonian Systems
The zero dynamics of infinite-dimensional systems can be difficult to
characterize. The zero dynamics of boundary control systems are particularly
problematic. In this paper the zero dynamics of port-Hamiltonian systems are
studied. A complete characterization of the zero dynamics for a
port-Hamiltonian systems with invertible feedthrough as another
port-Hamiltonian system on the same state space is given. It is shown that the
zero dynamics for any port-Hamiltonian system with commensurate wave speeds are
well-defined, and are also a port-Hamiltonian system. Examples include wave
equations with uniform wave speed on a network. A constructive procedure for
calculation of the zero dynamics, that can be used for very large system order,
is provided.Comment: 17 page
Damping controller design for FACTS devices in power systems using novel control techniques
Power systems are under increasing stress as deregulation introduces several new economic objectives for operation. Since power systems are being operated close to their limits, weak connections, unexpected events, hidden failures in protection system, human errors, and a host of other factors may cause a system to lose stability and even lead to catastrophic failure. Therefore, the need for improved system damping in a wider operating range is gaining more attention. Among the available damping control methods, each approach has advantages and disadvantages in different systems. The effectiveness of damping control depends on the devices chosen, the system modal feature, and the applied controller design method;In the literature, many approaches have been proposed to undertake this task. However, some of these approaches only take a fixed operating point into consideration without describing the changing uncertainty in varying system conditions; computational effort. Furthermore, no systematic comparison of controller design methods has been conducted with regard to different system profiles. Attention has been drawn to the enhanced susceptibility to inter-area oscillations between groups of machines under large others require a great deal of variation of system operating conditions. The linear parameter varying (LPV) approach, which has been widely studied in the literature, provides a potential method for capturing the varying system condition precisely without formulation of system uncertainty. However, in some cases no solution can be achieved if the system variation is too large using the traditional LPV approach. Also, sometimes the system structure imposes limitations in the achievable damping performance. In general, there is a critical need for a cost-effective control strategy applicable to different systems from an economic point of view;In this dissertation, a comprehensive comparison among controller design methods has been conducted to study the damping effectiveness of different FACTS devices. Based on these, a robust regional pole-placement method is applied in a TCSC damping controller design in a 4-machine system; an interpolated LPV approach is proposed and applied to designing a SVC damping controller in the IEEE 50-machine system; finally with the advantage of an additional feedback signal, limitations in achieving satisfactory damping performance can be relieved using a two-input single-output (TISO) damping controller for a TCSC in the IEEE 50-machine system
Coordinated Spatial Pattern Formation in Biomolecular Communication Networks
This paper proposes a control theoretic framework to model and analyze the self-organized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular communication networks, bio-nanomachines, or biological cells, communicate with each other using a cell-to-cell communication mechanism mediated by a diffusible signaling molecule, thereby the dynamics of molecular concentrations are approximately modeled as a reaction-diffusion system with a single diffuser. We first introduce a feedback model representation of the reaction-diffusion system and provide a systematic local stability/instability analysis tool using the root locus of the feedback system. The instability analysis then allows us to analytically derive the conditions for the self-organized spatial pattern formation, or Turing pattern formation, of the bionanomachines. We propose a novel synthetic biocircuit motif called activator-repressor-diffuser system and show that it is one of the minimum biomolecular circuits that admit self-organized patterns over cell population
Automatic control of a liquid nitrogen cooled, closed-circuit, cryogenic pressure tunnel
The control system design, performance analysis, microprocesser based controller software development, and specifications for the Transonic Cryogenic Tunnel (TCT) are discussed. The control laws for the single-input single-output controllers were tested on the TCT simulator, and successfully demonstrated on the TCT
Robustness results in LQG based multivariable control designs
The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Results are derived under a common framework in which the minimum singular value of the return difference transfer matrix is the key quantity. In particular, the LQ and LQG robustness results are discussed
Decentralized pole assignment for interconnected systems
Given a general proper interconnected system,
this paper aims to design a LTI decentralized controller to
place the modes of the closed-loop system at pre-determined
locations. To this end, it is first assumed that the structural
graph of the system is strongly connected. Then, it is shown
applying generic static local controllers to any number of
subsystems will not introduce new decentralized fixed modes
(DFM) in the resultant system, although it has fewer inputoutput
stations compared to the original system. This means
that if there are some subsystems whose control costs are
highly dependent on the complexity of the control law, then
generic static controllers can be applied to such subsystems,
without changing the characteristics of the system in terms of
the fixed modes. As a direct application of this result, in the
case when the system has no DFMs, one can apply generic static
controllers to all but one subsystem, and the resultant system
will be controllable and observable through that subsystem.
Now, a simple observer-based local controller corresponding to
this subsystem can be designed to displace the modes of the
entire system arbitrarily. Similar results can also be attained
for a system whose structural graph is not strongly connected.
It is worth mentioning that similar concepts are deployed in the
literature for the special case of strictly proper systems, but as
noted in the relevant papers, extension of the results to general
proper systems is not trivial. This demonstrates the significance
of the present work
- …