Unwanted Terms Research Articles

Sliding mode control revisited

Controller design for nonlinear systems in its general form is complicated and an open problem. Finding a solution to this problem becomes more complicated when unwanted terms, such as disturbance, are taken into account. To provide a robust design for a subclass of nonlinear systems, sliding mode controllers (SMCs) are used. These controllers have a systematic design procedure and can reject bounded disturbances and at the same time guarantee stability. The guaranteed stability is achieved by separating system states into two parts and assuming that the input to state stability (ISS) condition holds for internal dynamics. This condition restricts the applicability of the SMC and limits the system performance when the controller is designed based on that. In order to remove this restriction and improve the performance, the ISS condition has been relaxed in this study. The relaxation is performed by redesigning SMCs based on suggested Lyapunov functions. The proposed idea insures global asymptotic stability of the closed loop system and is used to revise different well-known SMCs such as conventional SMC, terminal SMC, non-singular terminal SMC, integral SMC, super-twisting SMC, and super-twisting integral SMC. Comparisons between conventional and revised versions are made using simulation to demonstrate excellence of the revisited controllers.

Robustness Analysis of Modified Incremental Nonlinear Dynamic Inversion for Small UAVs

The work presented in this research focuses on the design of a robust nonlinear flight control system for a small fixed-wing UAV against uncertainties and external disturbances. Toward this objective, an integrated UAV waypoints guidance scheme based on Carrot Chasing guidance law (CC) is adopted. The designed attitude angles guidance law is applied to the flight control loop. Nonlinear Dynamic Inversion (NDI) awards the flight control system researchers a straight forward method of deriving control laws for nonlinear systems. The control inputs are used to eliminate unwanted terms in the equations of motion using negative feedback of these terms. However precise dynamic models may not be available and that leads to system instability in the presence of external disturbances or model uncertainties. Therefore a modified incremental dynamic inversion (MINDI) is presented to compensate the model uncertainties and increase robustness and system behavior when compared to incremental NDI. Simulation results showed that the MINDI flight control system is robust against wind disturbances and model mismatch which leads to superior path following performance.

Compensation of polarization-dependent loss using noiseless amplification and attenuation

Polarization dependent loss (PDL) is a serious problem that hinders the transfer of polarization qubits through quantum networks. Recently it has been shown that the detrimental effects of PDL on qubit fidelity can be compensated for with the introduction of an additional passive PDL element that rebalances the polarization modes of the transmitted qubit. This procedure works extremely well when the output of the system is postselected on photon detection. However, in cases where the qubit might be needed for further analysis this procedure introduces unwanted vacuum terms into the state. Here we present procedures for the compensation of the effects of PDL using noiseless amplification and attenuation. Each of these techniques introduces a heralding signal into the correction procedure that significantly reduces the vacuum terms in the final state. When detector inefficiency and dark counts are included in the analysis noiseless amplification remains superior, in terms of the fidelity of the final state, to both noiseless attenuation and passive PDL compensation for detector efficiencies greater than 40%.

Design and Analysis of a Robust UAV Flight Guidance and Control System Based on a Modified Nonlinear Dynamic Inversion

The work presented in this paper focuses on the design of a robust nonlinear flight control system for a small fixed-wing UAV against uncertainties and external disturbances. Toward this objective, an integrated UAV waypoints guidance scheme based on Carrot Chasing guidance law (CC) in comparison with the pure pursuit and line of sight-based path following (PLOS) guidance law is analyzed. For path following based on CC, a Virtual Track Point (VTP) is introduced on the path to let the UAV chase the path. For PLOS, the pure pursuit guidance law directs the UAV to the next waypoint, while the LOS guidance law steers the vehicle toward the line of sight (LOS). Nonlinear Dynamic Inversion (NLDI) awards the flight control system researchers a straight forward method of deriving control laws for nonlinear systems. The control inputs are used to eliminate unwanted terms in the equations of motion using negative feedback of these terms. The two-time scale assumption is adopted here to separate the fast dynamics—three angular rates of aircraft—from the slow dynamics—the angle of attack, sideslip, and bank angles. However, precise dynamic models may not be available, therefore a modification of NLDI is presented to compensate the model uncertainties. Simulation results show that the modified NLDI flight control system is robust against wind disturbances and model mismatch. PLOS path-following technique more accurately follows the desired path than CC and also requires the least control effort.

Strong mechanical squeezing in an unresolved-sideband optomechanical system

We study how strong mechanical squeezing (beyond 3 dB) can be achieved through reservoir engineering in an optomechanical system which is far from the resolved-sideband regime. In our proposed setup, the effect of unwanted counter-rotating terms is suppressed by quantum interference from two auxiliary cavities. In the weak coupling regime we develop an analytical treatment based on the effective master equation approach, which allows us to obtain explicitly the condition of maximum squeezing.

Micromachined phase-shifted array-type Mirau interferometer for swept-source OCT imaging: design, microfabrication and experimental validation.

OCT instruments permit fast and non-invasive 3D optical biopsies of biological tissues. However, they are bulky and expensive, making them only affordable at the hospital and thus, not sufficiently used as an early diagnostic tool. Significant reduction of system cost and size is achieved by implementation of MOEMS technologies. We propose an active array of 4x4 Mirau microinterferometers where the reference micro-mirrors are carried by a vertical comb-drive microactuator, enabling the implementation of the phase-shifting technique that improves the sensitivity and eliminates unwanted interferometric terms. We focus on the design of the imaging system, the microfabrication and the assembly of the Mirau microinterferometer, and the swept-source OCT imaging.

Generalized single-sideband three-dimensional computer-generated holography.

The conjugate image and zero-order beam have considerable influences on the optical reconstructions in computer-generated holographic display systems based on the amplitude spatial light modulators. We propose a generalized single-sideband method for suppressing the unwanted terms in computer-generated holography. Computer-generated holograms (CGHs) are calculated based on frequency filtering of the object wave, which redistributes the diffraction wave in spatial frequency domain for spectrum filtering during optical reconstruction. Numerical simulations and optical experiments demonstrate that the proposed method is generally effective for different kinds of CGH algorithms to reconstruct quality three-dimensional scenes that are free of conjugate image and zero-order beam.

Multi-step Knowledge-Aided Iterative Conjugate Gradient Algorithms for DOA Estimation

In this work, we present direction-of-arrival (DoA) estimation algorithms based on the Krylov subspace that effectively exploit prior knowledge of the signals that impinge on a sensor array. The proposed multi-step knowledge-aided iterative conjugate gradient (CG) (MS-KAI-CG) algorithms perform subtraction of the unwanted terms found in the estimated covariance matrix of the sensor data. Furthermore, we develop a version of MS-KAI-CG equipped with forward–backward averaging, called MS-KAI-CG-FB, which is appropriate for scenarios with correlated signals. Unlike current knowledge-aided methods, which take advantage of known DoAs to enhance the estimation of the covariance matrix of the input data, the MS-KAI-CG algorithms take advantage of the knowledge of the structure of the forward–backward smoothed covariance matrix and its disturbance terms. Simulations with both uncorrelated and correlated signals show that the MS-KAI-CG algorithms outperform existing techniques.

Linear seesaw for Dirac neutrinos with A4 flavour symmetry

We propose a linear seesaw model to realise light Dirac neutrinos within the framework of A4 discrete flavour symmetry. The additional fields and their transformations under the flavour symmetries are chosen in such a way that naturally predicts the hierarchies of different elements of the seesaw mass matrix and also keeps the unwanted terms away. For generic choices of flavon alignments, the model predicts normal hierarchical light neutrino masses with the atmospheric mixing angle in the lower octant. Apart from predicting interesting correlations between different neutrino parameters as well as between neutrino and model parameters, the model also predicts the leptonic Dirac CP phase to lie in a specific range −π/2≲δ≲−π/5 and π/5≲δ≲π/2 that includes the currently preferred maximal value. The predictions for the absolute neutrino masses in one specific version of the model can also saturate the cosmological upper bound on sum of absolute neutrino masses.

Linear and Logarithmic Time Compositions of Quantum Many-Body Operators.

We develop a generalized framework for constructing many-body-interaction operations either in linear time or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given for Pauli strings, many-control Toffoli gates, number- and parity-conserving interactions, unitary coupled cluster operations, and sparse matrix generators. We provide a linear time protocol that works by creating a superposition of exponentially many different possible operator strings and then uses dynamical decoupling methodology to undo all the unwanted terms. A logarithmic time protocol overcomes the speed limit of the first by using ancilla registers to condition evolution to the support of the desired many-body interaction before using parallel chaining operations to expand the string length. The two techniques improve substantially on current strategies (reductions in time and space ranging from linear to exponential), are applicable to different physical interaction mechanisms such as cnot, XX, and XX+YY, and generalize to a wide range of many-body operators.

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantify) and discuss experimental signatures.

Role of spacetime boundaries in a vierbein formulation of gravity

Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle in teleparallelism with the existence of spacetime boundaries and find that the covariant surface term exactly eliminates all the unwanted surface terms reside in the metric formulation of general relativity, as the role of a Gibbons-Hawking-York (GHY) term. The identity of such a covariant GHY term is further confirmed by the recovery of the correct black hole entropy from the free energy due to the spacetime boundary. These results indicate that the vierbein formulation of gravity generally exhibits a well-posed action principle and readily admits the path integral approach to quantization.

Suppressing Ionic Terms with Number-Counting Jastrow Factors in Real Space.

We demonstrate that four-body real-space Jastrow factors are, with the right type of Jastrow basis function, capable of performing successful wave function stenciling to remove unwanted ionic terms from an overabundant Fermionic reference without unduly modifying the remaining components. In addition to greatly improving size consistency (restoring it exactly in the case of a geminal power), real-space wave function stenciling is, unlike its Hilbert-space predecessors, immediately compatible with diffusion Monte Carlo, allowing it to be used in the pursuit of compact, strongly correlated trial functions with reliable nodal surfaces. We demonstrate the efficacy of this approach in the context of a double bond dissociation by using it to extract a qualitatively correct nodal surface despite being paired with a restricted Slater determinant, that, due to ionic term errors, produces a ground state with a qualitatively incorrect nodal surface when used in the absence of the Jastrow.

Optimized Compensation of Unwanted Current Terms by AC Power Converters Under Generic Voltage Conditions

This paper formulates an optimization-based algorithm for the compensation of unwanted current terms by means of distributed electronic power converters, such as active power filters and grid-connected inverters. The compensation goal consists in achieving suitable load conformity factors, defined at the source side and within a feasible power region in terms of the power converter capability. Based on the measured load quantities and on a certain objective function, the algorithm tracks the expected source currents, which are thereupon used to calculate proper scaling coefficients and, therefore, the compensation current references. It improves the power quality at the point of common coupling and enables full exploitation of distributed energy resources, increasing their efficiency. The compensation is based on a decoupled current decomposition and on an optimization-based algorithm. In this paper, the strategy is applied to nonlinear and unbalanced three-phase four-wire circuit, under nonsinusoidal and asymmetrical voltage conditions. The steady-state and dynamic behaviors have been analyzed by theoretical, simulation, and experimental results. Furthermore, the proposed approach is also compared to other compensation strategies showing its effectiveness.

Nonclassical properties of coherent light in a pair of coupled anharmonic oscillators

The Hamiltonian and hence the equations of motion involving the field operators of two anharmonic oscillators coupled through a linear one is framed. It is found that these equations of motion involving the non-commuting field operators are nonlinear and are coupled to each other and hence pose a great problem for getting the solutions. In order to investigate the dynamics and hence the nonclassical properties of the radiation fields, we obtain approximate analytical solutions of these coupled nonlinear differential equations involving the non-commuting field operators up to the second orders in anharmonic and coupling constants. These solutions are found useful for investigating the squeezing of pure and mixed modes, amplitude squared squeezing, principal squeezing, and the photon antibunching of the input coherent radiation field. With the suitable choice of the parameters (photon number in various field modes, anharmonic, and coupling constants, etc.), we calculate the second order variances of field quadratures of various modes and hence the squeezing, amplitude squared, and mixed mode squeezing of the input coherent light. In the absence of anharmonicities, it is found that these nonlinear nonclassical phenomena (squeezing of pure and mixed modes, amplitude squared squeezing and photon antibunching) are completely absent. The percentage of squeezing, mixed mode squeezing, amplitude squared squeezing increase with the increase of photon number and the dimensionless interaction time. The collapse and revival phenomena in squeezing, mixed mode squeezing and amplitude squared squeezing are exhibited. With the increase of the interaction time, the monotonic increasing nature of the squeezing effects reveal the presence of unwanted secular terms. It is established that the mere coupling of two oscillators through a third one does not produces the squeezing effects of input coherent light. However, the pure nonclassical phenomena of antibunching of photons in vacuum field modes are obtained through the mere coupling and hence the transfers of photons from the remaining coupled mode.

Explicit mass renormalization and consistent derivation of radiative response of classical electron

The radiative response of the classical electron is commonly described by the Lorentz–Abraham–Dirac (LAD) equation. Dirac’s derivation of this equation is based on energy and momentum conservation laws and on regularization of the field singularities and infinite energies of the point charge by subtraction of certain quantities: “We... shall try to get over difficulties associated with the infinite energy of the process by a process of direct omission or subtraction of unwanted terms”. To substantiate Dirac’s approach and clarify the mass renormalization, we introduce the point charge as a limit of extended charges contracting to a point; the fulfillment of conservation laws follows from the relativistic covariant Lagrangian formulation of the problem. We derive the relativistic point charge dynamics described by the LAD equation from the extended charge dynamics in a localization limit by a method which can be viewed as a refinement of Dirac’s approach in the spirit of Ehrenfest theorem. The model exhibits the mass renormalization as the cancellation of Coulomb energy with the Poincaré cohesive energy. The value of the renormalized mass is not postulated as an arbitrary constant, but is explicitly calculated. The analysis demonstrates that the local energy–momentum conservation laws yield dynamics of a point charge which involves three constants: mass, charge and radiative response coefficient θ. The value of θ depends on the composition of the adjacent potential which generates Poincaré forces. The classical value of the radiative response coefficient is singled out by the global requirement that the adjacent potential does not affect the radiated energy balance and affects only the local energy balance involved in the renormalization.

X-FEM modeling of large plasticity deformation; a convergence study on various blending strategies for weak discontinuities

AbstractIn the extended finite element method (FEM), the transition elements between the enriched and standard elements, which are generally referred as the blending, or partially enriched elements, are often crucial for a good performance of the local partition of unity enrichments. In these elements, the enrichment function cannot be reproduced exactly due to the lack of a partition of unity, and blending elements produce unwanted terms into the approximation that cannot be compensated by the standard final element part of the approximation. In this paper, some optimal X-FEM-type methods reported in literature are employed to study the performance of blending elements in large plastic deformation problems with weak discontinuities. Several numerical examples are solved using the standard X-FEM, the X-FEM with modified enrichment function, the hierarchical X-FEM and the corrected X-FEM technique, and the results are compared with an alternative intrinsic enrichment strategy in large deformation problems.

Non-commutative geometry, non-associative geometry and the standard model of particle physics

Connes’ notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einstein gravity. We suggest a simple reformulation with two key mathematical advantages: (i) it unifies many of the traditional NCG axioms into a single one; and (ii) it immediately generalizes from non-commutative to non-associative geometry. Remarkably, it also resolves a long-standing problem plaguing the NCG construction of the standard model, by precisely eliminating from the action the collection of seven unwanted terms that previously had to be removed by an extra, non-geometric, assumption. With this problem solved, the NCG algorithm for constructing the standard model action is tighter and more explanatory than the traditional one based on effective field theory.

ON SIMULATIONS OF HIGH-DENSITY RATIO FLOWS USING COLOR-GRADIENT MULTIPHASE LATTICE BOLTZMANN MODELS

Originally, the color-gradient model proposed by Rothman and Keller (R–K) was unable to simulate immiscible two-phase flows with different densities. Later, a revised version of the R–K model was proposed by Grunau et al. [D. Grunau, S. Chen and K. Eggert, Phys. Fluids A: Fluid Dyn. 5, 2557 (1993).] and claimed it was able to simulate two-phase flows with high-density contrast. Some studies investigate high-density contrast two-phase flows using this revised R–K model but they are mainly focused on the stationary spherical droplet and bubble cases. Through theoretical analysis of the model, we found that in the recovered Navier–Stokes (N–S) equations which are derived from the R–K model, there are unwanted extra terms. These terms disappear for simulations of two-phase flows with identical densities, so the correct N–S equations are fully recovered. Hence, the R–K model is able to give accurate results for flows with identical densities. However, the unwanted terms may affect the accuracy of simulations significantly when the densities of the two fluids are different. For the simulations of spherical bubbles and droplets immersed in another fluid (where the densities of the two fluids are different), the extra terms may not be important and hence, in terms of surface tension, accurate results can be obtained. However, generally speaking, the unwanted term may be significant in many flows and the R–K model is unable to obtain the correct results due to the effect of the extra terms. Through numerical simulations of parallel two-phase flows in a channel, we confirm that the R–K model is not appropriate for general two-phase flows with different densities. A scheme to eliminate the unwanted terms is also proposed and the scheme works well for cases of density ratios less than 10.

Using a Modified Harmonic Wavelet Transform to Characterize Mechanical Shock

A modified harmonic wavelet transform is used to estimate a time varying spectral density. The resolution of the estimate has an approximate constant time-frequency product. The estimation error is directly related to this time-frequency product. Unwanted cross product terms are effectively minimized. Several examples are given: White random, two sine waves, chirps, impulses, sums of exponentially decaying sinusoids, and a pyroshock. It is also shown how realizations can be generated from the modified harmonic wavelet transform estimate of the time varying spectral density.