Modeling and control of flexible structures

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory

Two-dimensional oscillating airfoil test apparatus

A two dimensional oscillating airfoil test apparatus is presented as a method of measuring unsteady aerodynamic forces on an airfoil or rotor blade section. The oscillating airfoil test rig, which is being built for use in an 11 X 11-foot transonic wind tunnel (speed range M = 0.4 - 1.4), will allow determination of unsteady loadings and detailed pressure distributions on representative airfoil sections undergoing simulated pitching and flapping motions. The design details of the motion generating system and supporting structure are presented. This apparatus is now in the construction phase

Vortex-type elastic structured media and dynamic shielding

The paper addresses a novel model of metamaterial structure. A system of spinners has been embedded into a two-dimensional periodic lattice system. The equations of motion of spinners are used to derive the expression for the chiral term in the equations describing the dynamics of the lattice. Dispersion of elastic waves is shown to possess innovative filtering and polarization properties induced by the vortextype nature of the structured media. The related homogenised effective behavior is obtained analytically and it has been implemented to build a shielding cloak around an obstacle. Analytical work is accompanied by numerical illustrations.Comment: 24 pages, 13 figure

A real-time digital computer program for the simulation of a single rotor helicopter

A computer program was developed for the study of a single-rotor helicopter on the Langley Research Center real-time digital simulation system. Descriptions of helicopter equations and data, program subroutines (including flow charts and listings), real-time simulation system routines, and program operation are included. Program usage is illustrated by standard check cases and a representative flight case

Assembly and force measurement with SPM-like probes in holographic optical tweezers

We report a high fidelity tomographic reconstruction of the quantum state of photon pairs generated by parametric down-conversion with orbital angular momentum (OAM) entanglement. Our tomography method allows us to estimate an upper and lower bound for the entanglement between the down-converted photons. We investigate the two-dimensional state subspace defined by the OAM states ±ℓ and superpositions thereof, with ℓ=1, 2, ..., 30. We find that the reconstructed density matrix, even for OAMs up to around ℓ=20, is close to that of a maximally entangled Bell state with a fidelity in the range between F=0.979 and F=0.814. This demonstrates that, although the single count-rate diminishes with increasing ℓ, entanglement persists in a large dimensional state space

Morphology and thermal conductivity of model organic aerogels

The intersection volume of two independent 2-level cut Gaussian random fields is proposed to model the open-cell microstructure of organic aerogels. The experimentally measured X-ray scattering intensity, surface area and solid thermal conductivity of both polymeric and colloidal organic aerogels can be accounted for by the model.Comment: 5 pages. RevTex with 4 encapsulated figures. Higher resolution figures have been submitted for publication. To be published in Phys. Rev. E (Rapid Comm.). email, [email protected]

Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed

Numerical study of critical properties and hidden orders in dimerized spin ladders

Dimerized antiferromagnetic spin-1/2 ladders are known to exhibit a quantum critical phase transition in the ground state, the existence or absence of which is dependent on the dimerization pattern of the ladder. The gapped phases cannot be distinguished by the conventional Landau long-range order parameter. However, they possess a non-local (hidden) string order parameter, which is non-zero in one phase and vanishes in the other. We use an exact diagonalization technique to calculate ground state energies, energy gaps and string order parameters of dimerized two- and three-leg Heisenberg ladders, as well as a critical scaling analysis to yield estimates of the critical exponents nu and beta.Comment: 7 pages, 14 figures. V.2: Extended version to appear in PR

The optical transmission spectrum of the hot Jupiter HAT-P-32b: clouds explain the absence of broad spectral features?

We report Gemini-North GMOS observations of the inflated hot Jupiter HAT-P-32b during two primary transits. We simultaneously observed two comparison stars and used differential spectro-photometry to produce multi-wavelength light curves. 'White' light curves and 29 'spectral' light curves were extracted for each transit and analysed to refine the system parameters and produce transmission spectra from 520-930nm in ~14nm bins. The light curves contain time-varying white noise as well as time-correlated noise, and we used a Gaussian process model to fit this complex noise model. Common mode corrections derived from the white light curve fits were applied to the spectral light curves which significantly improved our precision, reaching typical uncertainties in the transit depth of ~2x10^-4, corresponding to about half a pressure scale height. The low resolution transmission spectra are consistent with a featureless model, and we can confidently rule out broad features larger than about one scale height. The absence of Na/K wings or prominent TiO/VO features is most easily explained by grey absorption from clouds in the upper atmosphere, masking the spectral features. However, we cannot confidently rule out clear atmosphere models with low abundances (~10^-3 solar) of TiO, VO or even metal hydrides masking the Na and K wings. A smaller scale height or ionisation could also contribute to muted spectral features, but alone are unable to to account for the absence of features reported here.Comment: 17 pages, 11 figures, 2 tables, accepted for publication in MNRA