The Experts below are selected from a list of 70059 Experts worldwide ranked by ideXlab platform
Marc Bodson - One of the best experts on this subject based on the ideXlab platform.
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Complex-Based Controller for a Three-Phase Inverter With an LCL Filter Connected to Unbalanced Grids
IEEE Transactions on Power Electronics, 2019Co-Authors: Arnau Doria-cerezo, Federico M. Serra, Marc BodsonAbstract:A new controller for a grid-connected inverter with an LCL filter is proposed in this paper. The system is described by its Complex representation, and the controller is designed using the Complex Root locus method. The Complex representation allows a considerable reduction in the order of the system, simplifying the design task and making it possible to use advanced techniques, such as the Complex Root locus. The new Complex controller adds an extra degree of freedom that makes it possible to move the poles of the systems and to improve the stability and speed of response compared with the conventional controls. This paper includes a detailed discussion of the effect of the gains of the controller on the Root locus. The proposal is validated with simulation and experimental results.
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Design of Controllers for Electrical Power Systems Using a Complex Root Locus Method
IEEE Transactions on Industrial Electronics, 2016Co-Authors: Arnau Doria-cerezo, Marc BodsonAbstract:A large class of three-phase electrical power systems possess symmetry conditions that make it possible to describe their behavior using single-input single-output transfer functions with Complex coefficients. In such cases, an extended Root locus method can be used to design control laws, even though the actual systems are multi-input multi-output. In this paper, the symmetric conditions for a large class of power systems are analyzed. Then, the Root locus method is revisited for systems with Complex coeffcients and used for the analysis and control design of power systems. To demonstrate the benefits of the approach, this paper includes two examples: 1) a doubly fed induction machine and 2) a three-phase LCL inverter.
Chee Yap - One of the best experts on this subject based on the ideXlab platform.
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ICMS - Implementation of a Near-Optimal Complex Root Clustering Algorithm
Mathematical Software – ICMS 2018, 2018Co-Authors: Rémi Imbach, Victor Y. Pan, Chee YapAbstract:We describe Ccluster, a software for computing natural \(\varepsilon \)-clusters of Complex Roots in a given box of the Complex plane. This algorithm from Becker et al. (2016) is near-optimal when applied to the benchmark problem of isolating all Complex Roots of an integer polynomial. It is one of the first implementations of a near-optimal algorithm for Complex Roots. We describe some low level techniques for speeding up the algorithm. Its performance is compared with the well-known MPSolve library and Maple.
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Implementation of a Near-Optimal Complex Root Clustering Algorithm.
arXiv: Mathematical Software, 2018Co-Authors: Rémi Imbach, Victor Y. Pan, Chee YapAbstract:We describe Ccluster, a software for computing natural $\epsilon$-clusters of Complex Roots in a given box of the Complex plane. This algorithm from Becker et al.~(2016) is near-optimal when applied to the benchmark problem of isolating all Complex Roots of an integer polynomial. It is one of the first implementations of a near-optimal algorithm for Complex Roots. We describe some low level techniques for speeding up the algorithm. Its performance is compared with the well-known MPSolve library and Maple.
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a simple but exact and efficient algorithm for Complex Root isolation
International Symposium on Symbolic and Algebraic Computation, 2011Co-Authors: Chee Yap, Michael SagraloffAbstract:We present a new exact subdivision algorithm CEVAL for isolating the Complex Roots of a square-free polynomial in any given box. It is a generalization of a previous real Root isolation algorithm called EVAL. Under suitable conditions, our approach is applicable for general analytic functions. CEVAL is based on the simple Bolzano Principle and is easy to implement exactly. Preliminary experiments have shown its competitiveness. We further show that, for the "benchmark problem" of isolating all Roots of a square-free polynomial with integer coefficients, the asymptotic Complexity of both algorithms EVAL and CEVAL matches (up a logarithmic term) that of more sophisticated real Root isolation methods which are based on Descartes' Rule of Signs, Continued Fraction or Sturm sequence. In particular, we show that the tree size of EVAL matches that of other algorithms. Our analysis is based on a novel technique called Δ-clusters from which we expect to see further applications.
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ISSAC - A simple but exact and efficient algorithm for Complex Root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11, 2011Co-Authors: Chee Yap, Michael SagraloffAbstract:We present a new exact subdivision algorithm CEVAL for isolating the Complex Roots of a square-free polynomial in any given box. It is a generalization of a previous real Root isolation algorithm called EVAL. Under suitable conditions, our approach is applicable for general analytic functions. CEVAL is based on the simple Bolzano Principle and is easy to implement exactly. Preliminary experiments have shown its competitiveness. We further show that, for the "benchmark problem" of isolating all Roots of a square-free polynomial with integer coefficients, the asymptotic Complexity of both algorithms EVAL and CEVAL matches (up a logarithmic term) that of more sophisticated real Root isolation methods which are based on Descartes' Rule of Signs, Continued Fraction or Sturm sequence. In particular, we show that the tree size of EVAL matches that of other algorithms. Our analysis is based on a novel technique called Δ-clusters from which we expect to see further applications.
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SNC - Empirical study of an evaluation-based subdivision algorithm for Complex Root isolation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - SNC '11, 2011Co-Authors: Narayan Kamath, Irina Voiculescu, Chee YapAbstract:We provide an empirical study of subdivision algorithms for isolating the simple Roots of a polynomial in any desired box region B0 of the Complex plane. One such class of algorithms is based on Newton-like interval methods (Moore, Krawczyk, Hansen-Sengupta). Another class of subdivision algorithms is based on function evaluation. Here, Yakoubsohn discussed a method that is purely based on an exclusion predicate. Recently, Sagraloff and Yap introduced another algorithm of this type, called Ceval. We describe the first implementation of Ceval in Core Library. We compare its performance to the above mentioned algorithms, and also to the well-known MPSolve software from Bini and Florentino. Our results suggest that certified evaluation-based methods such as Ceval are encouraging and deserve further exploration.
Piotr Kowalczyk - One of the best experts on this subject based on the ideXlab platform.
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Evaluation of propagation parameters of open guiding structures with the use of Complex Root finding algorithms
2017 IEEE MTT-S International Microwave Workshop Series on Advanced Materials and Processes for RF and THz Applications (IMWS-AMP), 2017Co-Authors: Malgorzata Warecka, Piotr Kowalczyk, Rafal LechAbstract:An efficient Complex Root tracing algorithm is utilized for the investigation of electromagnetic wave propagation in open guiding structures. The dispersion characteristics of propagated and leaky waves are calculated for a couple of chosen waveguides. The efficiency of the Root tracing algorithm is discuses and compared to a global Root finding algorithm.
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Efficient Complex Root Tracing Algorithm for Propagation and Radiation Problems
IEEE Transactions on Antennas and Propagation, 2017Co-Authors: Piotr Kowalczyk, Wojciech MarynowskiAbstract:An efficient Complex Root tracing algorithm for propagation and radiation problems is presented. The proposed approach is based on a discretization of Cauchy’s Argument Principle and its generalization to the $\mathbb {C}\times \mathbb {R}$ space. Moreover, an engagement of the tracing process with a global Root finding algorithm recently presented in the literature is performed. In order to confirm a validity and efficiency of the proposed technique, a few different types of structures have been analyzed.
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Efficient Complex Root finding algorithm for microwave and optical propagation problems
2016 21st International Conference on Microwave Radar and Wireless Communications (MIKON), 2016Co-Authors: Piotr KowalczykAbstract:Article relates to the use of innovative Root finding algorithm (on a Complex plane) to study propagation properties of microwave and optical waveguides. Problems of this type occur not only in the analysis of lossy structures, but also in the study of Complex and leaky modes (radiation phenomena). The proposed algorithm is simple to implement and can be applied for functions with singularities and branch cuts in the Complex plane (frequently occurring in these types of issues).
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Innovative Root finding and tracing algorithms in Complex domain for treatment of lossy transmission lines
2016 International Symposium on Antennas and Propagation (ISAP), 2016Co-Authors: Wojciech Marynowski, Piotr KowalczykAbstract:Innovative Complex Root finding and tracing algorithms are applied to the analysis of losses in transmission line containing a thin graphene layer deposited on a silicone substrate. An equivalent transmission-line model of TM modes, which involves spatial dispersion of the graphene is considered. The Root tracing scheme is modified to work effectively in Complex space.
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Complex Root finding algorithm based on delaunay triangulation
ACM Transactions on Mathematical Software, 2015Co-Authors: Piotr KowalczykAbstract:A simple and flexible algorithm for finding zeros of a Complex function is presented. An arbitrary-shaped search region can be considered and a very wide class of functions can be analyzed, including those containing singular points or even branch cuts. The proposed technique is based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes. As a result, a set of candidate points is created, where the signs of the real and imaginary parts of the function change simultaneously. To verify and refine the results, an iterative algorithm is applied. The validity of the presented technique is supported by the results obtained in numerical tests involving three different types of functions.
Arnau Doria-cerezo - One of the best experts on this subject based on the ideXlab platform.
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Complex-Based Controller for a Three-Phase Inverter With an LCL Filter Connected to Unbalanced Grids
IEEE Transactions on Power Electronics, 2019Co-Authors: Arnau Doria-cerezo, Federico M. Serra, Marc BodsonAbstract:A new controller for a grid-connected inverter with an LCL filter is proposed in this paper. The system is described by its Complex representation, and the controller is designed using the Complex Root locus method. The Complex representation allows a considerable reduction in the order of the system, simplifying the design task and making it possible to use advanced techniques, such as the Complex Root locus. The new Complex controller adds an extra degree of freedom that makes it possible to move the poles of the systems and to improve the stability and speed of response compared with the conventional controls. This paper includes a detailed discussion of the effect of the gains of the controller on the Root locus. The proposal is validated with simulation and experimental results.
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Design of Controllers for Electrical Power Systems Using a Complex Root Locus Method
IEEE Transactions on Industrial Electronics, 2016Co-Authors: Arnau Doria-cerezo, Marc BodsonAbstract:A large class of three-phase electrical power systems possess symmetry conditions that make it possible to describe their behavior using single-input single-output transfer functions with Complex coefficients. In such cases, an extended Root locus method can be used to design control laws, even though the actual systems are multi-input multi-output. In this paper, the symmetric conditions for a large class of power systems are analyzed. Then, the Root locus method is revisited for systems with Complex coeffcients and used for the analysis and control design of power systems. To demonstrate the benefits of the approach, this paper includes two examples: 1) a doubly fed induction machine and 2) a three-phase LCL inverter.
Michael Sagraloff - One of the best experts on this subject based on the ideXlab platform.
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a near optimal subdivision algorithm for Complex Root isolation based on the pellet test and newton iteration
Journal of Symbolic Computation, 2018Co-Authors: Ruben Becker, Michael Sagraloff, Vikram SharmaAbstract:Abstract We describe a subdivision algorithm for isolating the Complex Roots of a polynomial F ∈ C [ x ] . Given an oracle that provides approximations of each of the coefficients of F to any absolute error bound and given an arbitrary square B in the Complex plane containing only simple Roots of F, our algorithm returns disjoint isolating disks for the Roots of F in B . Our Complexity analysis bounds the absolute error to which the coefficients of F have to be provided, the total number of iterations, and the overall bit Complexity. It further shows that the Complexity of our algorithm is controlled by the geometry of the Roots in a near neighborhood of the input square B , namely, the number of Roots, their absolute values and pairwise distances. The number of subdivision steps is near-optimal. For the benchmark problem, namely, to isolate all the Roots of a polynomial of degree n with integer coefficients of bit size less than τ, our algorithm needs O ˜ ( n 3 + n 2 τ ) bit operations, which is comparable to the record bound of Pan (2002) . It is the first time that such a bound has been achieved using subdivision methods, and independent of divide-and-conquer techniques such as Schonhage's splitting circle technique. Our algorithm uses the quadtree construction of Weyl (1924) with two key ingredients: using Pellet's Theorem (1881) combined with Graeffe iteration, we derive a “soft-test” to count the number of Roots in a disk. Using Schroder's modified Newton operator combined with bisection, in a form inspired by the quadratic interval method from Abbot (2006), we achieve quadratic convergence towards Root clusters. Relative to the divide-conquer algorithms, our algorithm is quite simple with the potential of being practical. This paper is self-contained: we provide pseudo-code for all subroutines used by our algorithm.
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a near optimal subdivision algorithm for Complex Root isolation based on the pellet test and newton iteration
arXiv: Numerical Analysis, 2015Co-Authors: Ruben Becker, Michael Sagraloff, Vikram SharmaAbstract:We describe a subdivision algorithm for isolating the Complex Roots of a polynomial $F\in\mathbb{C}[x]$. Given an oracle that provides approximations of each of the coefficients of $F$ to any absolute error bound and given an arbitrary square $\mathcal{B}$ in the Complex plane containing only simple Roots of $F$, our algorithm returns disjoint isolating disks for the Roots of $F$ in $\mathcal{B}$. Our Complexity analysis bounds the absolute error to which the coefficients of $F$ have to be provided, the total number of iterations, and the overall bit Complexity. It further shows that the Complexity of our algorithm is controlled by the geometry of the Roots in a near neighborhood of the input square $\mathcal{B}$, namely, the number of Roots, their absolute values and pairwise distances. The number of subdivision steps is near-optimal. For the \emph{benchmark problem}, namely, to isolate all the Roots of a polynomial of degree $n$ with integer coefficients of bit size less than $\tau$, our algorithm needs $\tilde O(n^3+n^2\tau)$ bit operations, which is comparable to the record bound of Pan (2002). It is the first time that such a bound has been achieved using subdivision methods, and independent of divide-and-conquer techniques such as Sch\"onhage's splitting circle technique. Our algorithm uses the quadtree construction of Weyl (1924) with two key ingredients: using Pellet's Theorem (1881) combined with Graeffe iteration, we derive a "soft-test" to count the number of Roots in a disk. Using Schr\"oder's modified Newton operator combined with bisection, in a form inspired by the quadratic interval method from Abbot (2006), we achieve quadratic convergence towards Root clusters. Relative to the divide-conquer algorithms, our algorithm is quite simple with the potential of being practical. This paper is self-contained: we provide pseudo-code for all subroutines used by our algorithm.
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a simple but exact and efficient algorithm for Complex Root isolation
International Symposium on Symbolic and Algebraic Computation, 2011Co-Authors: Chee Yap, Michael SagraloffAbstract:We present a new exact subdivision algorithm CEVAL for isolating the Complex Roots of a square-free polynomial in any given box. It is a generalization of a previous real Root isolation algorithm called EVAL. Under suitable conditions, our approach is applicable for general analytic functions. CEVAL is based on the simple Bolzano Principle and is easy to implement exactly. Preliminary experiments have shown its competitiveness. We further show that, for the "benchmark problem" of isolating all Roots of a square-free polynomial with integer coefficients, the asymptotic Complexity of both algorithms EVAL and CEVAL matches (up a logarithmic term) that of more sophisticated real Root isolation methods which are based on Descartes' Rule of Signs, Continued Fraction or Sturm sequence. In particular, we show that the tree size of EVAL matches that of other algorithms. Our analysis is based on a novel technique called Δ-clusters from which we expect to see further applications.
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ISSAC - A simple but exact and efficient algorithm for Complex Root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11, 2011Co-Authors: Chee Yap, Michael SagraloffAbstract:We present a new exact subdivision algorithm CEVAL for isolating the Complex Roots of a square-free polynomial in any given box. It is a generalization of a previous real Root isolation algorithm called EVAL. Under suitable conditions, our approach is applicable for general analytic functions. CEVAL is based on the simple Bolzano Principle and is easy to implement exactly. Preliminary experiments have shown its competitiveness. We further show that, for the "benchmark problem" of isolating all Roots of a square-free polynomial with integer coefficients, the asymptotic Complexity of both algorithms EVAL and CEVAL matches (up a logarithmic term) that of more sophisticated real Root isolation methods which are based on Descartes' Rule of Signs, Continued Fraction or Sturm sequence. In particular, we show that the tree size of EVAL matches that of other algorithms. Our analysis is based on a novel technique called Δ-clusters from which we expect to see further applications.