Non-singular terminal sliding mode guidance and control with terminal angle constraints for non-maneuvering targets

In this paper guidance laws to intercept stationary and constant velocity targets at a desired impact angle, based on sliding mode control theory, are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight (LOS) angle, is achieved in finite time by selecting the missile's lateral acceleration (latax) to enforce non-singular terminal sliding mode on a switching surface designed using this desired LOS angle and based on non-linear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles.

Common-Mode and Differential-Mode Active Damping for PWM Rectifiers

Modern pulse-width-modulated (PWM) rectifiers use LC L filters that can be applied in both the common mode and differential mode to obtain high-performance filtering. Interaction between the passive L and C components in the filter leads to resonance oscillations. These oscillations need to be damped either by the passive damping or active damping. The passive damping increases power loss and can reduce the effectiveness of the filter. Methods of active damping, using control strategy, are lossless while maintaining the effectiveness of the filters. In this paper, an active damping strategy is proposed to damp the oscillations in both line-to-line and line-to-ground. An approach based on pole placement by the state feedback is used to actively damp both the differential-and common-mode filter oscillations. Analytical expressions for the state-feedback controller gains are derived for both continuous and discrete-time model of the filter. Tradeoff in selection of the active damping gain on the lower order power converter harmonics is analyzed using a weighted admittance function. Experimental results on a 10-kVA laboratory prototype PWM rectifier are presented. The results validate the effectiveness of the active damping method, and the tradeoff in the settings of the damping gain.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe-ion direct correlation function and ion-ion dynamic structure factor. Although the power law decay is reminiscent of Debye-Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.

Nonsingular Terminal Sliding Mode Guidance with Impact Angle Constraints

Guidance laws based on a conventional sliding mode ensures only asymptotic convergence. However, convergence to the desired impact angle within a finite time is important in most practical guidance applications. These finite time convergent guidance laws suffer from singularity leading to control saturation. In this paper, guidance laws to intercept targets at a desired impact angle, from any initial heading angle, without exhibiting any singularity, are presented. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the interceptor's lateral acceleration to enforce nonsingular terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles. Although the guidance laws are designed for constant speed interceptors, its robustness against the time-varying speed of interceptors is also evaluated through extensive simulation results.

A general methodology for calculating mixed mode stress intensity factors and fracture toughness of solder joints with interfacial cracks

Solder joints in electronic packages undergo thermo-mechanical cycling, resulting in nucleation of micro-cracks, especially at the solder/bond-pad interface, which may lead to fracture of the joints. The fracture toughness of a solder joint depends on material properties, process conditions and service history, as well as strain rate and mode-mixity. This paper reports on a methodology for determining the mixed-mode fracture toughness of solder joints with an interfacial starter-crack, using a modified compact mixed mode (CMM) specimen containing an adhesive joint. Expressions for stress intensity factor (K) and strain energy release rate (G) are developed, using a combination of experiments and finite element (FE) analysis. In this methodology, crack length dependent geometry factors to convert for the modified CMM sample are first obtained via the crack-tip opening displacement (CTOD)-based linear extrapolation method to calculate the under far-field mode I and II conditions (f(1a) and f(2a)), (ii) generation of a master-plot to determine a(c), and (iii) computation of K and G to analyze the fracture behavior of joints. The developed methodology was verified using J-integral calculations, and was also used to calculate experimental fracture toughness values of a few lead-free solder-Cu joints. (C) 2014 Elsevier Ltd. All rights reserved.

Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

Sliding Mode Control-Based Autopilots for Leaderless Consensus of Unmanned Aerial Vehicles

In this brief, decentralized sliding mode controllers that enable a connected and leaderless swarm of unmanned aerial vehicles (UAVs) to reach a consensus in altitude and heading angle are presented. In addition, sliding mode control-based autopilot designs to control those states for which consensus is not required are also presented. By equipping each UAV with this combination of controllers, it can autonomously decide on being a member of the swarm or fly independently. The controllers are designed using a coupled nonlinear dynamic model, derived for the YF-22 aircraft, where the aerodynamic forces and moments are linear functions of the states and inputs.

Molecular Dissection of Mycobacterium tuberculosis Integration Host Factor Reveals Novel Insights into the Mode of DNA Binding and Nucleoid Compaction

Background: mIHF belongs to a subfamily of proteins, distinct from E. coli IHF. Results: Functionally important amino acids of mIHF and the mechanism(s) underlying DNA binding, DNA bending, and site-specific recombination are distinct from that of E. coli IHF. Conclusion: mIHF functions could contribute beyond nucleoid compaction. Significance: Because mIHF is essential for growth, the molecular mechanisms identified here can be exploited in drug screening efforts. The annotated whole-genome sequence of Mycobacterium tuberculosis revealed that Rv1388 (Mtihf) is likely to encode for a putative 20-kDa integration host factor (mIHF). However, very little is known about the functional properties of mIHF or the organization of the mycobacterial nucleoid. Molecular modeling of the mIHF three-dimensional structure, based on the cocrystal structure of Streptomyces coelicolor IHF duplex DNA, a bona fide relative of mIHF, revealed the presence of Arg-170, Arg-171, and Arg-173, which might be involved in DNA binding, and a conserved proline (Pro-150) in the tight turn. The phenotypic sensitivity of Escherichia coli ihfA and ihfB strains to UV and methyl methanesulfonate could be complemented with the wild-type Mtihf but not its alleles bearing mutations in the DNA-binding residues. Protein-DNA interaction assays revealed that wild-type mIHF, but not its DNA-binding variants, binds with high affinity to fragments containing attB and attP sites and curved DNA. Strikingly, the functionally important amino acid residues of mIHF and the mechanism(s) underlying its binding to DNA, DNA bending, and site-specific recombination are fundamentally different from that of E. coli IHF. Furthermore, we reveal novel insights into IHF-mediated DNA compaction depending on the placement of its preferred binding sites; mIHF promotes DNA compaction into nucleoid-like or higher order filamentous structures. We therefore propose that mIHF is a distinct member of a subfamily of proteins that serve as essential cofactors in site-specific recombination and nucleoid organization and that these findings represent a significant advance in our understanding of the role(s) of nucleoid-associated proteins.

Wall-mode instability in plane shear flow of viscoelastic fluid over a deformable solid

The linear stability analysis of a plane Couette flow of an Oldroyd-B viscoelastic fluid past a flexible solid medium is carried out to investigate the role of polymer addition in the stability behavior. The system consists of a viscoelastic fluid layer of thickness R, density rho, viscosity eta, relaxation time lambda, and retardation time beta lambda flowing past a linear elastic solid medium of thickness HR, density rho, and shear modulus G. The emphasis is on the high-Reynolds-number wall-mode instability, which has recently been shown in experiments to destabilize the laminar flow of Newtonian fluids in soft-walled tubes and channels at a significantly lower Reynolds number than that for flows in rigid conduits. For Newtonian fluids, the linear stability studies have shown that the wall modes become unstable when flow Reynolds number exceeds a certain critical value Re c which scales as Sigma(3/4), where Reynolds number Re = rho VR/eta, V is the top-plate velocity, and dimensionless parameter Sigma = rho GR(2)/eta(2) characterizes the fluid-solid system. For high-Reynolds-number flow, the addition of polymer tends to decrease the critical Reynolds number in comparison to that for the Newtonian fluid, indicating a destabilizing role for fluid viscoelasticity. Numerical calculations show that the critical Reynolds number could be decreased by up to a factor of 10 by the addition of small amount of polymer. The critical Reynolds number follows the same scaling Re-c similar to Sigma(3/4) as the wall modes for a Newtonian fluid for very high Reynolds number. However, for moderate Reynolds number, there exists a narrow region in beta-H parametric space, corresponding to very dilute polymer solution (0.9 less than or similar to beta < 1) and thin solids (H less than or similar to 1.1), in which the addition of polymer tends to increase the critical Reynolds number in comparison to the Newtonian fluid. Thus, Reynolds number and polymer properties can be tailored to either increase or decrease the critical Reynolds number for unstable modes, thus providing an additional degree of control over the laminar-turbulent transition.

Common-Mode Injection PWM for Parallel Converters

The ac-side terminal voltages of parallel-connected converters are different if the line reactive drops of the individual converters are different. This could result either from differences in per-phase inductances or from differences in the line currents of the converters. In such cases, the modulating signals are different for the converters. Hence, the common-mode (CM) voltages for the converters, injected by conventional space vector pulsewidth modulation (CSVPWM) to increase dc-bus utilization, are different. Consequently, significant low-frequency zero-sequence circulating currents result. This paper proposes a new modulation method for parallel-connected converters with unequal terminal voltages. This method does not cause low-frequency zero-sequence circulating currents and is comparable with CSVPWM in terms of dc-bus utilization and device power loss. Experimental results are presented at a power level of 150 kVA from a circulating-power test setup, where the differences in converter terminal voltages are quite significant.

Three Dimensional Impact Angle Constrained Guidance Law using Sliding Mode Control

In this paper, three dimensional impact angle control guidance laws are proposed for stationary targets. Unlike the usual approach of decoupling the engagement dynamics into two mutually orthogonal 2-dimensional planes, the guidance laws are derived using the coupled dynamics. These guidance laws are designed using principles of conventional as well as nonsingular terminal sliding mode control theory. The guidance law based on nonsingular terminal sliding mode guarantees finite time convergence of interceptor to the desired impact angle. In order to derive the guidance laws, multi-dimension switching surfaces are used. The stability of the system, with selected switching surfaces, is demonstrated using Lyapunov stability theory. Numerical simulation results are presented to validate the proposed guidance law.

The cold mode: a phenomenological model for the evolution of density perturbations in the intracluster medium

Cool cluster cores are in global thermal equilibrium but are locally thermally unstable. We study a non-linear phenomenological model for the evolution of density perturbations in the intracluster medium (ICM) due to local thermal instability and gravity. We have analysed and extended a model for the evolution of an overdense blob in the ICM. We find two regimes in which the overdense blobs can cool to thermally stable low temperatures. One for large t(cool)/t(ff) (t(cool) is the cooling time and t(ff) is the free-fall time), where a large initial overdensity is required for thermal runaway to occur; this is the regime which was previously analysed in detail. We discover a second regime for t(cool)/t(ff) less than or similar to 1 (in agreement with Cartesian simulations of local thermal instability in an external gravitational field), where runaway cooling happens for arbitrarily small amplitudes. Numerical simulations have shown that cold gas condenses out more easily in a spherical geometry. We extend the analysis to include geometrical compression in weakly stratified atmospheres such as the ICM. With a single parameter, analogous to the mixing length, we are able to reproduce the results from numerical simulations; namely, small density perturbations lead to the condensation of extended cold filaments only if t(cool)/t(ff) less than or similar to 10.

Mixed Mode Analysis of Obliquely Oriented Edge Cracked Semicircular Disk Under Compression

A new mixed-mode compression fracture specimen, obliquely oriented edge cracked semicircular disk (OECSD) is analyzed by extending pure opening mode configuration of edge cracked semicircular disk (ECSD) under Hertzian compression. Photoelastic experiments are conducted on two different specimens of OECSD of same size and different crack lengths and inclinations. Finite element method (FEM) is used to solve a number of cases of the problem varying crack length and crack inclination. FE results show a good match with experiments. Inclination of edge crack in OECSD can be so made as to obtain any mode-mixity ratio between zero and one and beyond for any crack length. The new specimen can be used for fracture testing under compression more conveniently than the existing ones in several ways.

Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies. (c) 2015 AIP Publishing LLC.