skip to main content


Title: A Frequency Domain Interpretation of Signal Injection Methods for Salient PMSMs
Several heuristic procedures to estimate the rotor position of interior permanent magnet synchronous motors via signal injection have been reported in the applications literature, and are widely used in practice. These methods, based on the use linear time invariant high-pass/low-pass filters, are instrumental for sensorless controllers. To the best of our knowledge, no theoretical analysis has been carried out for them. The objectives of this note, are (i) to invoke some recent work on the application of averaging techniques for injectionbased observer design to develop a theoretical framework to analyze the sensorless methods, and (ii) to propose a new method that, on one hand, ensures an improved accuracy and, on the other hand, can be related with the current filtering technique. An additional advantage of the new method is that it relies on the use of linear operators, implementable with simple computations. The effectiveness of the proposed scheme is assessed by experiments.  more » « less
Award ID(s):
1710944
NSF-PAR ID:
10163267
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
2019 IEEE Conference on Control Technology and Applications (CCTA)
Page Range / eLocation ID:
517 to 522
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    We introduce a model for ant trail formation, building upon previous work on biologically feasible local algorithms that plausibly describe how ants maintain trail networks. The model is a variant of a reinforced random walk on a directed graph, where ants lay pheromone on edges as they traverse them and the next edge to traverse is chosen based on the level of pheromone; this pheromone decays with time. There is a bidirectional flow of ants in the network: the forward flow proceeds along forward edges from source (e.g. the nest) to sink (e.g. a food source), and the backward flow in the opposite direction. Some fraction of ants are lost as they pass through each node (modeling the loss of ants due to exploration observed in the field). We initiate a theoretical study of this model. We note that ant navigation has inspired the field of ant colony optimization, heuristics that have been applied to several combinatorial optimization problems; however the algorithms developed there are considerably more complex and not constrained to being biologically feasible. We first consider the linear decision rule, where the flow divides itself among the next set of edges in proportion to their pheromone level. Here, we show that the process converges to the path with minimum leakage when the forward and backward flows do not change over time. On the other hand, when the forward and backward flows increase over time (caused by positive reinforcement from the discovery of a food source, for example), we show that the process converges to the shortest path. These results are for graphs consisting of two parallel paths (a case that has been investigated before in experiments). Through simulations, we show that these results hold for more general graphs drawn from various random graph models; proving this convergence in the general case is an interesting open problem. Further, to understand the behaviour of other decision rules beyond the linear rule, we consider a general family of decision rules. For this family, we show that there is no advantage of using a non-linear decision rule, if the goal is to find the shortest or the minimum leakage path. We also show that bidirectional flow is necessary for convergence to such paths. Our results provide a plausible explanation for field observations, and open up new avenues for further theoretical and experimental investigation. 
    more » « less
  2. Abstract Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter’s ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models. Significance Statement Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models. 
    more » « less
  3. Segata, Nicola (Ed.)
    The cost of sequencing the genome is dropping at a much faster rate compared to assembling and finishing the genome. The use of lightly sampled genomes (genome-skims) could be transformative for genomic ecology, and results using k -mers have shown the advantage of this approach in identification and phylogenetic placement of eukaryotic species. Here, we revisit the basic question of estimating genomic parameters such as genome length, coverage, and repeat structure, focusing specifically on estimating the k -mer repeat spectrum. We show using a mix of theoretical and empirical analysis that there are fundamental limitations to estimating the k -mer spectra due to ill-conditioned systems, and that has implications for other genomic parameters. We get around this problem using a novel constrained optimization approach (Spline Linear Programming), where the constraints are learned empirically. On reads simulated at 1X coverage from 66 genomes, our method, REPeat SPECTra Estimation (RESPECT), had 2.2% error in length estimation compared to 27% error previously achieved. In shotgun sequenced read samples with contaminants, RESPECT length estimates had median error 4%, in contrast to other methods that had median error 80%. Together, the results suggest that low-pass genomic sequencing can yield reliable estimates of the length and repeat content of the genome. The RESPECT software will be publicly available at https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_shahab-2Dsarmashghi_RESPECT.git&d=DwIGAw&c=-35OiAkTchMrZOngvJPOeA&r=ZozViWvD1E8PorCkfwYKYQMVKFoEcqLFm4Tg49XnPcA&m=f-xS8GMHKckknkc7Xpp8FJYw_ltUwz5frOw1a5pJ81EpdTOK8xhbYmrN4ZxniM96&s=717o8hLR1JmHFpRPSWG6xdUQTikyUjicjkipjFsKG4w&e= . 
    more » « less
  4. SUMMARY

    Combining finite element methods for the incompressible Stokes equations with particle-in-cell methods is an important technique in computational geodynamics that has been widely applied in mantle convection, lithosphere dynamics and crustal-scale modelling. In these applications, particles are used to transport along properties of the medium such as the temperature, chemical compositions or other material properties; the particle methods are therefore used to reduce the advection equation to an ordinary differential equation for each particle, resulting in a problem that is simpler to solve than the original equation for which stabilization techniques are necessary to avoid oscillations.

    On the other hand, replacing field-based descriptions by quantities only defined at the locations of particles introduces numerical errors. These errors have previously been investigated, but a complete understanding from both the theoretical and practical sides was so far lacking. In addition, we are not aware of systematic guidance regarding the question of how many particles one needs to choose per mesh cell to achieve a certain accuracy.

    In this paper we modify two existing instantaneous benchmarks and present two new analytic benchmarks for time-dependent incompressible Stokes flow in order to compare the convergence rate and accuracy of various combinations of finite elements, particle advection and particle interpolation methods. Using these benchmarks, we find that in order to retain the optimal accuracy of the finite element formulation, one needs to use a sufficiently accurate particle interpolation algorithm. Additionally, we observe and explain that for our higher-order finite-element methods it is necessary to increase the number of particles per cell as the mesh resolution increases (i.e. as the grid cell size decreases) to avoid a reduction in convergence order.

    Our methods and results allow designing new particle-in-cell methods with specific convergence rates, and also provide guidance for the choice of common building blocks and parameters such as the number of particles per cell. In addition, our new time-dependent benchmark provides a simple test that can be used to compare different implementations, algorithms and for the assessment of new numerical methods for particle interpolation and advection. We provide a reference implementation of this benchmark in aspect (the ‘Advanced Solver for Problems in Earth’s ConvecTion’), an open source code for geodynamic modelling.

     
    more » « less
  5. The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs. The goal of this benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance. As a specific application of our geometry and benchmark dataset, we explore the question of relative advantages of unstructured (triangular/ tetrahedral) and structured (quadrilateral/hexahedral) discretizations. We observe that for Lagrange-type elements, while linear tetrahedral elements perform poorly, quadratic tetrahedral elements perform equally well or outperform hexahedral elements for our set of problems and currently available mesh generation algorithms. This observation suggests that for common problems in structural analysis, thermal analysis, and low Reynolds number flows, high-quality results can be obtained with unstructured tetrahedral meshes, which can be created robustly and automatically. We release the description of the benchmark problems, meshes, and reference implementation of our testing infrastructure to enable statistically significant comparisons between different FE methods, which we hope will be helpful in the development of new meshing and FEA techniques. 
    more » « less