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Nejat Olgac - One of the best experts on this subject based on the ideXlab platform.

  • Differentiability of imaginary spectra and determination of its bounds for multiple-Delay LTI systems
    2016 International Symposium on Flexible Automation (ISFA), 2016
    Co-Authors: Nejat Olgac
    Abstract:

    Several new procedures are presented to assess the stability of linear time invariant (LTI) systems with multiple time Delays. The skeleton of the methods is on a paradigm named the cluster treatment of characteristic roots (CTCR). For such systems, all the imaginary characteristic roots can be determined completely on a finite set of hypersurfaces, called kernel hypersurfaces (KH), in the Delay domain. The entire KH is the mere prerequisite to implement CTCR. However, as the number of Delays increases, it becomes computationally prohibitive to calculate the KH in the entire Delay domain. Alternatively, we explore the 2-D cross-section of these KH in the space of any two of the Delays. First we investigate the bounds of the imaginary spectra as a novelty here. For this, the proof of the differentiability of the crossing-frequency variations is provided. Another novelty of the paper appears at the declaration of the KH. For this we utilize the 3-D “Building Block” and “Spectral Delay Space” concepts. The effectiveness of these procedures is shown over an example case study.

  • Investigation of Local Stability Transitions in the Spectral Delay Space and Delay Space
    Journal of Dynamic Systems Measurement and Control, 2014
    Co-Authors: Qingbin Gao, Umut Zalluhoglu, Nejat Olgac
    Abstract:

    The stability boundaries of LTI time-Delayed systems with respect to the Delays are studied in two different domains: (i) Delay space (DS) and (ii) Spectral Delay space (SDS), which contains pointwise frequency information as well as the Delay. SDS is the preferred domain due to its advantageous boundedness properties and simple construct of stability transition boundaries. These transitions at the mentioned boundaries, however, present some conceptual challenges in SDS. This transition property enables us to extract the corresponding local stability variation properties in the DS, while it does not have any implication in the preferred SDS. The novel aspect of the investigation is to introduce a comparison mechanism between these two domains, DS and SDS, from the stability transition perspective. Interestingly, we are able to prove their equivalency, which provides complementary insight to the parametric stability variations. [DOI: 10.1115/1.4027171]

  • Stability of formation control using a consensus protocol under directed communications with two time Delays and Delay scheduling
    International Journal of Systems Science, 2014
    Co-Authors: Rudy Cepeda-gomez, Nejat Olgac
    Abstract:

    We consider a linear algorithm to achieve formation control in a group of agents which are driven by second-order dynamics and affected by two rationally independent Delays. One of the Delays is in the position and the other in the velocity information channels. These Delays are taken as constant and uniform throughout the system. The communication topology is assumed to be directed and fixed. The formation is attained by adding a supplementary control term to the stabilising consensus protocol. In preparation for the formation control logic, we first study the stability of the consensus, using the recent cluster treatment of characteristic roots CTCR paradigm. This effort results in a unique depiction of the non-conservative stability boundaries in the domain of the Delays. However, CTCR requires the knowledge of the potential stability switching loci exhaustively within this domain. The creation of these loci is done in a new surrogate coordinate system, called the ‘Spectral Delay space SDS’. The relative stability is also investigated, which has to do with the speed of reaching consensus. This step leads to a paradoxical control design concept, called the ‘Delay scheduling’, which highlights the fact that the group behaviour may be enhanced by increasing the Delays. These steps lead to a control strategy to establish a desired group formation that guarantees spacing among the agents. Example case studies are presented to validate the underlying analytical derivations.

  • A test platform for cognitive Delays: target tracking problem with multiple time-Delayed feedback control
    International Journal of Dynamics and Control, 2014
    Co-Authors: Qingbin Gao, Rudy Cepeda-gomez, Nejat Olgac
    Abstract:

    This paper studies a baseline 2-dimensional (2-D) target tracking problem from a new perspective. The dynamics entail two rationally independent time Delays in an otherwise traditional feedback controller. A pursuer tries to track a moving target. When there are no time Delays, capture is enabled using any stable control logic (for instance, LQR). If there are different Delays in the sensing of position and velocity of the target, however, the performance of the pursuit changes dramatically. We explore the stability of the dynamics for a broad range of Delay compositions. An exhaustive and exact determination of those stable Delay combinations is achieved using the recent cluster treatment of characteristic roots (CTCR) paradigm. It declares the complete stability outlook in the domain of the two Delays. This method starts with the determination of all the potential stability switching curves in the domain of the Delays. For this, a recent concept called the “Spectral Delay space (SDS)” is used. As a paradoxical outcome of this work, we show that the stability of the dynamics can be recovered by increasing the Delays. The paper is accompanied by an interactive MATLAB-based game which is also available online.

  • Second-Order Leaderless Consensus Protocols with Multiple Communication and Input Delays from Stability Perspective
    Delay Systems, 2014
    Co-Authors: Rudy Cepeda-gomez, Nejat Olgac
    Abstract:

    A leaderless consensus control protocol for double integrators with multiple, rationally-independent time Delays is studied in this paper from two intriguing and novel perspectives. First, the crucial stability analysis of time Delayed system is performed using a recent technique known as the Cluster Treatment of Characteristic Roots (CTCR). CTCR method is pursued after a block-diagonalization (mode decoupling) transformation on the system. This treatment produces a unique stability outlook for the dynamics in the space of the Delays. Furthermore they are non-conservative and exhaustive. Secondly, a much different stability display is created using the Spectral Delay Space as an overture to the CTCR for the determination of the needed potential stability crossing (switching) hypersurfaces in the Delay space. Examples are provided to display the effectiveness of this new stability analysis mechanism.

Rudy Cepeda-gomez - One of the best experts on this subject based on the ideXlab platform.

  • Stability of formation control using a consensus protocol under directed communications with two time Delays and Delay scheduling
    International Journal of Systems Science, 2014
    Co-Authors: Rudy Cepeda-gomez, Nejat Olgac
    Abstract:

    We consider a linear algorithm to achieve formation control in a group of agents which are driven by second-order dynamics and affected by two rationally independent Delays. One of the Delays is in the position and the other in the velocity information channels. These Delays are taken as constant and uniform throughout the system. The communication topology is assumed to be directed and fixed. The formation is attained by adding a supplementary control term to the stabilising consensus protocol. In preparation for the formation control logic, we first study the stability of the consensus, using the recent cluster treatment of characteristic roots CTCR paradigm. This effort results in a unique depiction of the non-conservative stability boundaries in the domain of the Delays. However, CTCR requires the knowledge of the potential stability switching loci exhaustively within this domain. The creation of these loci is done in a new surrogate coordinate system, called the ‘Spectral Delay space SDS’. The relative stability is also investigated, which has to do with the speed of reaching consensus. This step leads to a paradoxical control design concept, called the ‘Delay scheduling’, which highlights the fact that the group behaviour may be enhanced by increasing the Delays. These steps lead to a control strategy to establish a desired group formation that guarantees spacing among the agents. Example case studies are presented to validate the underlying analytical derivations.

  • A test platform for cognitive Delays: target tracking problem with multiple time-Delayed feedback control
    International Journal of Dynamics and Control, 2014
    Co-Authors: Qingbin Gao, Rudy Cepeda-gomez, Nejat Olgac
    Abstract:

    This paper studies a baseline 2-dimensional (2-D) target tracking problem from a new perspective. The dynamics entail two rationally independent time Delays in an otherwise traditional feedback controller. A pursuer tries to track a moving target. When there are no time Delays, capture is enabled using any stable control logic (for instance, LQR). If there are different Delays in the sensing of position and velocity of the target, however, the performance of the pursuit changes dramatically. We explore the stability of the dynamics for a broad range of Delay compositions. An exhaustive and exact determination of those stable Delay combinations is achieved using the recent cluster treatment of characteristic roots (CTCR) paradigm. It declares the complete stability outlook in the domain of the two Delays. This method starts with the determination of all the potential stability switching curves in the domain of the Delays. For this, a recent concept called the “Spectral Delay space (SDS)” is used. As a paradoxical outcome of this work, we show that the stability of the dynamics can be recovered by increasing the Delays. The paper is accompanied by an interactive MATLAB-based game which is also available online.

  • Second-Order Leaderless Consensus Protocols with Multiple Communication and Input Delays from Stability Perspective
    Delay Systems, 2014
    Co-Authors: Rudy Cepeda-gomez, Nejat Olgac
    Abstract:

    A leaderless consensus control protocol for double integrators with multiple, rationally-independent time Delays is studied in this paper from two intriguing and novel perspectives. First, the crucial stability analysis of time Delayed system is performed using a recent technique known as the Cluster Treatment of Characteristic Roots (CTCR). CTCR method is pursued after a block-diagonalization (mode decoupling) transformation on the system. This treatment produces a unique stability outlook for the dynamics in the space of the Delays. Furthermore they are non-conservative and exhaustive. Secondly, a much different stability display is created using the Spectral Delay Space as an overture to the CTCR for the determination of the needed potential stability crossing (switching) hypersurfaces in the Delay space. Examples are provided to display the effectiveness of this new stability analysis mechanism.

  • A Consensus Protocol under Directed Communications with Two Time Delays and Delay Scheduling
    International Journal of Control, 2013
    Co-Authors: Rudy Cepeda-gomez, Nejat Olgac
    Abstract:

    This paper studies a consensus protocol over a group of agents driven by second order dynamics. The communication among members of the group is assumed to be directed and affected by two rationally independent time Delays, one in the position and the other in the velocity information channels. These Delays are unknown but considered to be constant and uniform throughout the system. The stability of the consensus protocol is studied using a simplifying factorization procedure and deploying the Cluster Treatment of Characteristic Roots (CTCR) paradigm. This effort results in a unique depiction of the exact stability boundaries in the domain of the Delays. CTCR requires the knowledge of the potential stability switching loci exhaustively within this domain. The creation of these loci is an important contribution of this work. It is done in a new surrogate coordinate system, called the \emph{Spectral Delay Space (SDS)}. The relative stability, i.e., the speed to reach consensus of the system is also investigated for this class of systems. Based on the outcome of this effort, a paradoxical control design concept is introduced. It is called the \emph{Delay Scheduling}, which is another key contribution of this paper. It reveals that the performance of the system may be improved by increasing the Delays. The amount of increase, however, is only revealed by the CTCR. Example case studies are presented to verify the underlying analytical derivations.

  • Exact stability analysis of second-order leaderless and leader–follower consensus protocols with rationally-independent multiple time Delays☆
    Systems & Control Letters, 2013
    Co-Authors: Rudy Cepeda-gomez, Nejat Olgac
    Abstract:

    Abstract An investigation of double-integrator agents with directed asymmetric consensus protocols and multiple rationally independent time Delays is presented in this paper from two novel perspectives. First, we complement the group consensus literature on crucial stability analysis, using a recent technique called the Cluster Treatment of Characteristic Roots (CTCR) for the first time on this class of time-Delayed systems. The CTCR paradigm is pursued after a block-diagonalization (mode-decoupling) transformation on the system. This treatment produces some unique stability tables for the dynamics in the space of the Delays which are non-conservative and exhaustive. Second, a novel concept of Spectral Delay space is presented, as an overture to the CTCR for the determination of the complete set of stability-crossing (switching) hypersurfaces in the Delay space. Examples are provided to display the strengths and efficiency of this new stability analysis mechanism.

Thomas Wolf - One of the best experts on this subject based on the ideXlab platform.

  • hexamethylcyclopentadiene time resolved photoelectron spectroscopy and ab initio multiple spawning simulations
    Physical Chemistry Chemical Physics, 2014
    Co-Authors: Thomas Wolf, Thomas Scheby Kuhlman, Oliver Schalk, Todd J Martinez, Klaus B Moller, Albert Stolow, Andreasneil Unterreiner
    Abstract:

    Progress in our understanding of ultrafast light-induced processes in molecules is best achieved through a close combination of experimental and theoretical approaches. Direct comparison is obtained if theory is able to directly reproduce experimental observables. Here, we present a joint approach comparing time-resolved photoelectron spectroscopy (TRPES) with ab initio multiple spawning (AIMS) simulations on the MS-MR-CASPT2 level of theory. We disentangle the relationship between two phenomena that dominate the immediate molecular response upon light absorption: a Spectrally dependent Delay of the photoelectron signal and an induction time prior to excited state depopulation in dynamics simulations. As a benchmark molecule, we have chosen hexamethylcyclopentadiene, which shows an unprecedentedly large Spectral Delay of (310 ± 20) fs in TRPES experiments. For the dynamics simulations, methyl groups were replaced by “hydrogen atoms” having mass 15 and TRPES spectra were calculated. These showed an induction time of (108 ± 10) fs which could directly be assigned to progress along a torsional mode leading to the intersection seam with the molecular ground state. In a stepladder-type approach, the close connection between the two phenomena could be elucidated, allowing for a comparison with other polyenes and supporting the general validity of this finding for their excited state dynamics. Thus, the combination of TRPES and AIMS proves to be a powerful tool for a thorough understanding of ultrafast excited state dynamics in polyenes.

Qingbin Gao - One of the best experts on this subject based on the ideXlab platform.

  • Delay Impact Kernel and Multiple Delay Coupling Mechanism during the Interaction of Coordinated DC Microgrids
    2019 IEEE 4th International Future Energy Electronics Conference (IFEEC), 2019
    Co-Authors: Qian Xiao, Qingbin Gao, Xingwu Yang, Chaoyu Dong, Chi Jin, Zhe Zhang, Hongjie Jia
    Abstract:

    With the increasing industrial usage of DC microgrids, this work concerns the time-Delay issue during the microgrid interaction, which invariably takes time during operations. During the coordination of DC microgrids, time Delays widely exist in the processes of information exchange. For the theoretical investigation, the time-Delay model is firstly derived for such coordinated microgrid. Due to the infinite dimensionality incurred by the Delays, the Spectral Delay space (SDS), as a preparatory step for the stability analysis tool, is employed to extract the critical Delay spectra and their moving behaviors for the microgrid system. It is shown that the time-Delay impact during the interaction is imposed through a closed kernel destroying the microgrid stability. To closely check the property of the Delay impact kernel, especially the direction of the crossing behavior for purely imaginary roots, the concept of root tendency (RT) is profoundly analyzed and proved, which reveals the coupling mechanism of multiple Delays. Over a testing system consisting of three DC microgrids, the proposed model and analysis are effectively implemented and verified. It is found that the Delay impact kernel is periodical and bounded. Besides, the kernel can be divided into different areas according to the RTs, which indicates only partial kernel area will cause the unstable crossings due to the coupling of multiple Delays.

  • Time-Delay stability switching boundary determination for DC microgrid clusters with the distributed control framework
    Applied Energy, 2018
    Co-Authors: Chaoyu Dong, Qingbin Gao, Qian Xiao, Libor Pekař, Hongjie Jia
    Abstract:

    Abstract In a DC microgrid cluster, distributed DC microgrids are integrated to manage diverse and distributed energy resources. Without the reliance on a management center, the distributed control framework is capable of the cluster deployment by only adjacent collaborations. However, the communication among microgrids and the formation of dispatch signals inevitably lead to time Delays, which might cause the system disorder and multiple-Delay couplings. Considering these unstable effects, the lack of time-Delay study challenges the cluster stability and burdens the energy application. The key contributions of this paper are the definition and detection of the time-Delay stability switching boundary for the DC microgrid cluster with the distributed control framework, which reveals time Delays switching the system stability and proves the Delay-induced oscillation. Through the established time-Delay model and the proposed method based on the cluster treatment of characteristic roots, the explicit time-Delay stability switching boundary is detected in the Delay space, which forms a determination flow of five stages: (1) system initialization: according to the cluster parameter values, the established time-Delay model is initialized; (2) space transformation: applying the space mapping and the rationalization, the Sylvester resultant is constructed in the Spectral Delay space; (3) Spectral boundary sketch: in uniformly divided blocks, Spectral boundaries are found from the resultant; (4) crossing root calculation: with the Spectral boundaries, crossing roots are calculated solving the characteristic equation; (5) boundary determination: back-mapping the Spectral boundaries with the crossing roots, the overall boundary is presented. Comprehensive case studies are performed to study the time-Delay stability switching boundary and to validate the proposed approach. The boundary existence and feature demonstrate the time-Delay effect. Furthermore, the classified stable areas are revealed as well as the relevant strategies for the stability enhancement.

  • Investigation of Local Stability Transitions in the Spectral Delay Space and Delay Space
    Journal of Dynamic Systems Measurement and Control, 2014
    Co-Authors: Qingbin Gao, Umut Zalluhoglu, Nejat Olgac
    Abstract:

    The stability boundaries of LTI time-Delayed systems with respect to the Delays are studied in two different domains: (i) Delay space (DS) and (ii) Spectral Delay space (SDS), which contains pointwise frequency information as well as the Delay. SDS is the preferred domain due to its advantageous boundedness properties and simple construct of stability transition boundaries. These transitions at the mentioned boundaries, however, present some conceptual challenges in SDS. This transition property enables us to extract the corresponding local stability variation properties in the DS, while it does not have any implication in the preferred SDS. The novel aspect of the investigation is to introduce a comparison mechanism between these two domains, DS and SDS, from the stability transition perspective. Interestingly, we are able to prove their equivalency, which provides complementary insight to the parametric stability variations. [DOI: 10.1115/1.4027171]

  • A test platform for cognitive Delays: target tracking problem with multiple time-Delayed feedback control
    International Journal of Dynamics and Control, 2014
    Co-Authors: Qingbin Gao, Rudy Cepeda-gomez, Nejat Olgac
    Abstract:

    This paper studies a baseline 2-dimensional (2-D) target tracking problem from a new perspective. The dynamics entail two rationally independent time Delays in an otherwise traditional feedback controller. A pursuer tries to track a moving target. When there are no time Delays, capture is enabled using any stable control logic (for instance, LQR). If there are different Delays in the sensing of position and velocity of the target, however, the performance of the pursuit changes dramatically. We explore the stability of the dynamics for a broad range of Delay compositions. An exhaustive and exact determination of those stable Delay combinations is achieved using the recent cluster treatment of characteristic roots (CTCR) paradigm. It declares the complete stability outlook in the domain of the two Delays. This method starts with the determination of all the potential stability switching curves in the domain of the Delays. For this, a recent concept called the “Spectral Delay space (SDS)” is used. As a paradoxical outcome of this work, we show that the stability of the dynamics can be recovered by increasing the Delays. The paper is accompanied by an interactive MATLAB-based game which is also available online.

  • Equivalency of Stability Transitions Between the SDS (Spectral Delay Space) and DS (Delay Space)
    Volume 2: Control Monitoring and Energy Harvesting of Vibratory Systems; Cooperative and Networked Control; Delay Systems; Dynamical Modeling and Diag, 2013
    Co-Authors: Qingbin Gao, Umut Zalluhoglu, Nejat Olgac
    Abstract:

    It has been shown that the stability of LTI time-Delayed systems with respect to the Delays can be analyzed in two equivalent domains: (i) Delay space (DS) and (ii) Spectral Delay space (SDS). Considering a broad class of linear time-invariant time Delay systems with multiple Delays, the equivalency of the stability transitions along the transition boundaries is studied in both spaces. For this we follow two corresponding radial lines in DS and SDS, and prove for the first time in literature that they are equivalent. This property enables us to extract local stability transition features within the SDS without going back to the DS. The main advantage of remaining in SDS is that, one can avoid a non-linear transition from kernel hypercurves to offspring hypercurves in DS. Instead the potential stability switching curves in SDS are generated simply by stacking a finite dimensional cube called the building block (BB) along the axes. A case study is presented within the report to visualize this property.Copyright © 2013 by ASME

Salvador Balle - One of the best experts on this subject based on the ideXlab platform.

  • Spectral Delay algebraic equation approach forthe modeling of broad area laser diodes
    Conference on Lasers and Electro-Optics, 2015
    Co-Authors: Julien Javaloyes, Antonio Perez Serrano, Salvador Balle
    Abstract:

    The optical power that can be extracted from a semiconductor laser is limited due to catastrophic optical dam- age and one path to circumvent this limit is to increase the volume of the lasing mode. In the simplest case, this is achieved by increasing the lateral dimension. However, the emission profile of Broad-Area Laser Diodes (BALDs) usually presents a low quality and it is prone to instabilities.

  • Spectral Delay Algebraic Equation Approach to Broad Area Laser Diodes
    IEEE Journal of Selected Topics in Quantum Electronics, 2013
    Co-Authors: A. Perez-serrano, Julien Javaloyes, Salvador Balle
    Abstract:

    In this study, we discuss an efficient modeling approach for the simulation of broad-area laser diodes. Our method is based on folding the longitudinal propagation dimension into time Delays which extend to the lateral dimension and to the influence of diffractive terms the idea of mesh decimation as it is discussed in . We compare the results of the dynamics obtained with our improved model that consists of coupled Delay algebraic equations with the results of a standard traveling wave description in the cases of straight current stripes as well as in the important configuration of high-power tapered antireflection coated devices. We obtain an excellent agreement and an improvement of the integration time between one and two orders of magnitudes which may alleviate in some cases the necessity of using complex parallel codes.