8,369 research outputs found
New Results on Negative Imaginary Systems Theory with Application to Flexible Structures and Nano-Positioning
Flexible structure systems arise in many important applications such as ground and aerospace vehicles, atomic force microscopes, rotating flexible spacecraft, rotary cranes, robotics and flexible link manipulators, hard disk drives and other nano-positioning systems. In control systems design for these flexible systems, it is important to consider the effect of highly resonant modes. Such resonant modes are known to adversely affect the stability and performance of flexible structure control systems, and are often very sensitive to changes in environmental variables. These can lead to vibrational effects which limit the ability of control systems in achieving desired levels of performance. These problems are simplified to some extend by using force actuators combined with colocated measurements of velocity, position, or acceleration. Using force actuators combined with colocated measurements of velocity can be studied using positive real systems theory, which has received a great attention since 1962. Using force actuators combined with colocated measurements of position and acceleration can be studied using negative imaginary (NI) systems theory. In this thesis, we provide a generalization and development of negative imaginary systems theory to include a wider class of systems.
In the generalization of NI systems theory, we provide a new negative imaginary definition that allows for flexible systems with free body motion. Also, we provide a new stability condition for a positive feedback control system where the plant is NI according to the new definition and the controller is strictly negative imaginary (SNI). This general stability result captures all previous NI stability results which have been developed.
This thesis also presents analytical tools for negative imaginary systems theory, which can be useful in the practical applications of the theory. Two methods that can be used for checking the negative imaginary property for a given system are presented. Also, methods for enforcing NI dynamics on mathematical system models to satisfy an NI Property are explored. A systematic method to design controllers for NI systems with guaranteed robust stability also is presented. A practical application of control system design for a three-mirror cavity locking system is presented in the end of the thesis
Parameter-free predictions of the viscoelastic response of glassy polymers from non-affine lattice dynamics
We study the viscoelastic response of amorphous polymers using theory and
simulations. By accounting for internal stresses and considering instantaneous
normal modes (INMs) within athermal non-affine theory, we make parameter-free
predictions of the dynamic viscoelastic moduli obtained in coarse-grained
simulations of polymer glasses at non-zero temperatures. The theoretical
results show very good correspondence with rheology data collected from
molecular dynamics simulations over five orders of magnitude in frequency, with
some instabilities that accumulate in the low-frequency part on approach to the
glass transition. These results provide evidence that the mechanical glass
transition itself is continuous and thus represents a crossover rather than a
true phase transition. The relatively sharp drop of the low-frequency storage
modulus across the glass transition temperature can be explained
mechanistically within the proposed theory: the proliferation of
low-eigenfrequency vibrational excitations (boson peak and nearly-zero energy
excitations) is directly responsible for the rapid growth of a negative
non-affine contribution to the storage modulus.Comment: 10 pages, 7 figure
The role of ongoing dendritic oscillations in single-neuron dynamics
The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as temporally local, near-instantaneous mappings from the current input of the cell to its current output, brought about by somatic summation of dendritic contributions that are generated in spatially localized functional compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations, and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought
Rotation Prevents Finite-Time Breakdown
We consider a two-dimensional convection model augmented with the rotational
Coriolis forcing, , with a fixed
being the inverse Rossby number. We ask whether the action of dispersive
rotational forcing alone, , prevents the generic finite time breakdown
of the free nonlinear convection. The answer provided in this work is a
conditional yes. Namely, we show that the rotating Euler equations admit global
smooth solutions for a subset of generic initial configurations. With other
configurations, however, finite time breakdown of solutions may and actually
does occur. Thus, global regularity depends on whether the initial
configuration crosses an intrinsic, critical threshold, which
is quantified in terms of the initial vorticity, ,
and the initial spectral gap associated with the initial velocity
gradient, . Specifically, global regularity of the rotational Euler equation is
ensured if and only if . We also prove that the velocity field remains smooth if and
only if it is periodic. We observe yet another remarkable periodic behavior
exhibited by the {\em gradient} of the velocity field. The spectral dynamics of
the Eulerian formulation reveals that the vorticity and the eigenvalues (and
hence the divergence) of the flow evolve with their own path-dependent period.
We conclude with a kinetic formulation of the rotating Euler equation
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