595 research outputs found
Pulse Shaping, Localization and the Approximate Eigenstructure of LTV Channels
In this article we show the relation between the theory of pulse shaping for
WSSUS channels and the notion of approximate eigenstructure for time-varying
channels. We consider pulse shaping for a general signaling scheme, called
Weyl-Heisenberg signaling, which includes OFDM with cyclic prefix and
OFDM/OQAM. The pulse design problem in the view of optimal WSSUS--averaged SINR
is an interplay between localization and "orthogonality". The localization
problem itself can be expressed in terms of eigenvalues of localization
operators and is intimately connected to the concept of approximate
eigenstructure of LTV channel operators. In fact, on the L_2-level both are
equivalent as we will show. The concept of "orthogonality" in turn can be
related to notion of tight frames. The right balance between these two sides is
still an open problem. However, several statements on achievable values of
certain localization measures and fundamental limits on SINR can already be
made as will be shown in the paper.Comment: 6 pages, 2 figures, invited pape
Ultimate boundedness of droop controlled Microgrids with secondary loops
In this paper we study theoretical properties of inverter-based microgrids
controlled via primary and secondary loops. Stability of these microgrids has
been the subject of a number of recent studies. Conventional approaches based
on standard hierarchical control rely on time-scale separation between primary
and secondary control loops to show local stability of equilibria. In this
paper we show that (i) frequency regulation can be ensured without assuming
time-scale separation and, (ii) ultimate boundedness of the trajectories
starting inside a region of the state space can be guaranteed under a condition
on the inverters power injection errors. The trajectory ultimate bound can be
computed by simple iterations of a nonlinear mapping and provides a certificate
of the overall performance of the controlled microgrid.Comment: 8 pages, 1 figur
Minimal set of generators of controllability space for singular linear dynamical systems
Due to the significant role played by singular systems in the form E ¿ x ( t ) = Ax ( t ) , on mathematical modeling of science and engineering problems; in the last years recent years its interest in the descriptive analysis of its structural and dynamic properties. However, much less effort has been devoted to studying the exact con- trollability by measuring the minimum set of controls needed to direct the entire system E ¿ x ( t ) = Ax ( t ) to any desired state. In this work, we focus the study on obtaining the set of all matrices B with a minimal number of columns, by making the singular system E ¿ x ( t ) = Ax ( t ) + Bu ( t ) controllable.Postprint (author's final draft
Steepest-entropy-ascent quantum thermodynamic modeling of heat and mass diffusion in a far-from-equilibrium system based on a single particle ensemble
This paper presents a nonequilibrium thermodynamic model for the relaxation
of a local, isolated system in nonequilibrium using the principle of steepest
entropy ascent (SEA), which can be expressed as a variational principle in
thermodynamic state space. The model is able to arrive at the Onsager relations
for such a system. Since no assumption of local equilibrium is made, the
conjugate fluxes and forces, which result, are intrinsic to the subspaces of
the system's state space and are defined using the concepts of hypoequilibrium
state and nonequilibrium intensive properties, which describe the non-mutual
equilibrium status between subspaces of the thermodynamic state space. The
Onsager relations are shown to be a thermodynamic kinematic feature of the
system independent of the specific details of the micro-mechanical dynamics.
Two kinds of relaxation processes are studied with different constraints (i.e.,
conservation laws) corresponding to heat and mass diffusion. Linear behavior in
the near-equilibrium region as well as nonlinear behavior in the
far-from-equilibrium region are discussed. Thermodynamic relations in the
equilibrium and near-equilibrium realm, including the Gibbs relation, the
Clausius inequality, and the Onsager relations, are generalized to the
far-from-equilibrium realm. The variational principle in the space spanned by
the intrinsic conjugate fluxes and forces is expressed via the quadratic
dissipation potential. As an application, the model is applied to the heat and
mass diffusion of a system represented by a single particle ensemble, which can
also be applied to a simple system of many particles. Phenomenological
transport coefficients are also derived in near-equilibrium realm.Comment: 15 pages, 4 figure
Increasing eigenstructure assignment design degree of freedom using lifting
This paper presents the exposition of an output-lifting eigenstructure assignment (EA) design framework, wherein the available EA design degrees of freedom (DoF) is significantly increased, and the desired eigenstructure of a single-rate full state feedback solution can be achieved within an output feedback system. A structural mapping is introduced to release the output-lifting causality constraint. Additionally, the available design DoF can be further enlarged via involving the input-lifting into the output-lifting EA framework. The newly induced design DoF can be utilised to calculate a structurally constrained, causal gain matrix which will maintain the same assignment capability. In this paper, the robustification of the output-lifting EA is also proposed, which allows a trade-off between performance and robustness in the presence of structured model uncertainties to be established. A lateral flight control benchmark in the EA literature and a numerical example are used to demonstrate the effectiveness of the design framework
A homoclinic tangle on the edge of shear turbulence
Experiments and simulations lend mounting evidence for the edge state
hypothesis on subcritical transition to turbulence, which asserts that simple
states of fluid motion mediate between laminar and turbulent shear flow as
their stable manifolds separate the two in state space. In this Letter we
describe a flow homoclinic to a time-periodic edge state. Its existence
explains turbulent bursting through the classical Smale-Birkhoff theorem.
During a burst, vortical structures and the associated energy dissipation are
highly localized near the wall, in contrast to the familiar regeneration cycle
Robust control of quasi-linear parameter-varying L2 point formation flying with uncertain parameters
Robust high precision control of spacecraft formation flying is one of the most important techniques required for high-resolution interferometry missions in the complex deep-space environment. The thesis is focussed on the design of an invariant stringent performance controller for the Sun-Earth L2 point formation flying system over a wide range of conditions while maintaining system robust stability in the presence of parametric uncertainties. A Quasi-Linear Parameter-Varying (QLPV) model, generated without approximation from the exact nonlinear model, is developed in this study. With this QLPV form, the model preserves the transparency of linear controller design while reflecting the nonlinearity of the system dynamics. The Polynomial Eigenstructure Assignment (PEA) approach used for Linear Time-Invariant (LTI) and Linear Parameter-Varying (LPV ) models is extended to use the QLPV model to perform a form of dynamic inversion for a broader class of nonlinear systems which guarantees specific system performance. The resulting approach is applied to the formation flying QLPV model to design a PEA controller which ensures that the closed-loop performance is independent of the operating point. Due to variation in system parameters, the performance of most closed-loop systems are subject to model uncertainties. This leads naturally to the need to assess the robust stability of nonlinear and uncertain systems. This thesis presents two approaches to this problem, in the first approach, a polynomial matrix method to analyse the robustness of Multiple-Input and Multiple-Output (MIMO) systems for an intersectingD-region,which can copewith time-invariant uncertain systems is developed. In the second approach, an affine parameterdependent Lyapunov function based Linear Matrix Inequality (LMI) condition is developed to check the robust D-stability of QLPV uncertain systems.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
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