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  • 1.
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Control and Analysis of Pulse-Modulated Systems2008Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. We also introduce the harmonic transfer function and finally we provide a summary of the appended papers.

    The first paper considers stability analysis of a class of pulse-width modulated systems based on a discrete time model. The systems considered typically have periodic solutions. Stability of a periodic solution is equivalent to stability of a fixed point of a discrete time model of the system dynamics.

    Conditions for global and local exponential stability of the discrete time model are derived using quadratic and piecewise quadratic Lyapunov functions. A griding procedure is used to develop a systematic method to search for the Lyapunov functions.

    The second paper considers the dynamic phasor model as a tool for stability analysis of a general class of pulse-modulated systems. The analysis covers both linear time periodic systems and systems where the pulse modulation is controlled by feedback. The dynamic phasor model provides an $\textbf{L}_2$-equivalent description of the system dynamics in terms of an infinite dimensional dynamic system. The infinite dimensional phasor system is approximated via a skew truncation. The truncated system is used to derive a systematic method to compute time periodic quadratic Lyapunov functions.

    The third paper considers the dynamic phasor model as a tool for harmonic analysis of a class of pulse-width modulated systems. The analysis covers both linear time periodic systems and non-periodic systems where the switching is controlled by feedback. As in the second paper of the thesis, we represent the switching system using the L_2-equivalent infinite dimensional system provided by the phasor model. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems. The infinite dimensional phasor system is approximated via a square truncation. We assume that the response of the truncated system to a periodic disturbance is also periodic and we consider the corresponding harmonic balance equations. An approximate solution of these equations is stated in terms of a harmonic transfer function which is analogous to the harmonic transfer function of a linear time periodic system. The aforementioned assumption is proved to hold for small disturbances by proving the existence of a solution to a fixed point equation. The proof implies that for small disturbances, the approximation is good.

    Finally, the fourth paper considers control synthesis for switched mode DC-DC converters. The synthesis is based on a sampled data model of the system dynamics. The sampled data model gives an exact description of the converter state at the switching instances, but also includes a lifted signal which represents the inter-sampling behavior. Within the sampled data framework we consider H-infinity control design to achieve robustness to disturbances and load variations. The suggested controller is applied to two benchmark examples; a step-down and a step-up converter. Performance is verified in both simulations and in experiments.

  • 2.
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sampled data control of DC-DC convertersArticle in journal (Other academic)
  • 3.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Fujioka, Hisaya
    KTH. Kyoto University, Japan.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung Yao
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Patino, D.
    Riedinger, P.
    Geyer, T.
    Beccuti, A.
    Papafotiou, G.
    Morari, M.
    Wernrud, A.
    Rantzer, A.
    Hybrid control techniques for switched-mode DC-DC converters part I: The step-down topology2007In: 2007 American Control Conference, IEEE , 2007, p. 5450-5457Conference paper (Refereed)
    Abstract [en]

    Several recent techniques from hybrid and optimal control are evaluated on a power electronics benchmark problem. The benchmark involves a number of practically interesting operating scenarios for a fixed-frequency synchronous step-down dc-dc converter. The specifications are defined such that good performance only can be obtained if the switched and nonlinear nature of the problem is respected during the design phase.

  • 4.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dynamic phasor analysis of pulse-modulated systems2007In: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14, 2007, p. 3938-3945Conference paper (Refereed)
    Abstract [en]

    The paper considers stability analysis of a general class of pulse modulated systems in a phasor dynamic framework. The dynamic phasor model exploits the cyclic nature of the modulation functions by representing the system dynamics in terms of a Fourier series expansion defined over a moving time-window. The contribution of the paper is to show that a special type of periodic Lyapunov function can be used to analyze the system and that the analysis conditions become tractable for computation after truncation. The approach provides a trade-off between complexity and accuracy that includes standard state space averaged models as a special case.

  • 5.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Harmonic analysis of pulse-width modulated systems2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 4, p. 851-862Article in journal (Refereed)
    Abstract [en]

    The paper considers the so-called dynamic phasor model as a basis for harmonic analysis of a class switching systems. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback. The dynamic phasor model is a powerful tool for exploring cyclic properties of dynamic systems. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems.

  • 6.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Harmonic Lyapunov functions in the analysis of periodically switched systems2006In: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, p. 2759-2764Conference paper (Refereed)
    Abstract [en]

    The dynamic phasor model of a time-periodic system is used to derive a stability test involving a harmonic Lyapunov function. This reveals a new interpretation of the harmonic Lyapunov function with an appealing time-domain representation. Most importantly, it indicates that the ideas behind the harmonic Lyapunov equation can be generalized to include cyclic switching systems that have different pulse form in each period.

  • 7.
    Almér, Stefan
    et al.
    KTH, Superseded Departments, Mathematics.
    Jönsson, Ulf
    KTH, Superseded Departments, Mathematics.
    Kao, Chung-Yao
    KTH, Superseded Departments, Mathematics.
    Mari, Jorge
    Global stability analysis of DC-DC converters using sampled-data modeling2004In: PROCEEDINGS OF THE 2004 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2004, p. 4549-4554Conference paper (Refereed)
    Abstract [en]

    The paper presents stability analysis of a class of pulse-width modulated (PWM) systems which incorporates many different DC-DC converters. Two types of pulse-width modulation (digital and analog control) are considered. A procedure is developed for systematic search for Lyapunov functions. The state space is partitioned in such a way that stability is verified if a set of coupled Linear Matrix Inequalities (LMIs) is feasible. Global stability is considered as well as the computation of local regions of attraction.

  • 8.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung-Yao
    Univ Melbourne, Dept Elect & Elect Engn.
    Mari, Jorge
    GE Global Res, Elect Energy Syst.
    Stability analysis of a class of PWM systems2007In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 52, no 6, p. 1072-1078Article in journal (Refereed)
    Abstract [en]

    This note considers stability analysis of a class of pulsewidth modulated (PWM) systems that incorporates several different switched mode dc-de- converters. The systems of the class typically have periodic solutions. A sampled data model is developed and used to prove stability of these solutions. Conditions for global and local exponential stability are derived using quadratic and piecewise quadratic Lyapunov functions. The state space is partitioned and the stability conditions are verified by checking a set of coupled linear matrix inequalities (LMIs).

  • 9.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dynamic phasor analysis of a class of PWM systems2015In: 2007 European Control Conference, ECC 2007, 2015, p. 1940-1947Conference paper (Refereed)
    Abstract [en]

    The paper makes use of the so-called dynamic phasor model for stability and performance analysis of a class of PWM systems. The dynamic phasor model allows for the state to be represented in the frequency domain where a harmonic Lyapunov function is defined. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback.

  • 10.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dynamic Phasor Analysis of Periodic Systems2009In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, no 8, p. 2007-2012Article in journal (Refereed)
    Abstract [en]

    The paper considers stability analysis of linear time-periodic (LTP) systems based on the dynamic phasor model (DPM). The DPM exploits the periodicity of the system by expanding the system state in a Fourier series over a moving time window. This results in an L-2-equivalent representation in terms of an infinite-dimensional LTI system which describes the evolution of time varying Fourier coefficients. To prove stability, we consider quadratic time-periodic Lyapunov candidates. Using the DPM, the corresponding time-periodic Lyapunov inequality can be stated as a finite dimensional inequality and the Lyapunov function can be found by solving a linear matrix inequality.

  • 11. Beccuti, A. G.
    et al.
    Papafotiou, G.
    Morari, M.
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Fujioka, Hisaya
    KTH. Kyoto University, Japan.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung Yao
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. University of Melbourne, Australia.
    Wernrud, A.
    Rantzer, A.
    Bâja, M.
    Comierais, H.
    Buisson, J.
    Hybrid control techniques for switched-mode DC-DC converters part II: The step-up topology2007In: 2007 American Control Conference, Vols 1-13, 2007, p. 5464-5471Conference paper (Refereed)
    Abstract [en]

    Several recent techniques from hybrid and optimal control are evaluated on a power electronics benchmark problem. The benchmark involves a number of practically interesting operating scenarios for a fixed-frequency step-up dc-dc converter. The specifications are defined such that good performance can only be obtained if the switched and nonlinear nature of the problem is respected during the design phase.

  • 12. Fujioka, H.
    et al.
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, C. -Y
    Control synthesis for a class of PWM systems for robust tracking and H ∞ performance2006In: Proc IEEE Conf Decis Control, 2006, p. 4861-4866Conference paper (Refereed)
    Abstract [en]

    Robust control with robust tracking is considered for a class of pulse-width modulated systems (PWM) that appear, for example, in power electronics applications. The control objective is to regulate a high frequency ripple signal to robustly track a constant reference signal in an average sense. To achieve this goal, a new H∞ -control problem with integral action and averaged sampling is proposed. The design procedure is verified on a synchronous buck converter.

  • 13. Fujioka, H.
    et al.
    Kao, C. -Y
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    LQ optimal control synthesis for a class of pulse modulated systems2005Conference paper (Refereed)
    Abstract [en]

    We consider linear quadratic optimal control for a class of pulse-width-modulated systems. The problem is motivated from a practical application - digital control of switching power converters. The control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the inter sampling behavior into account.

  • 14. Fujioka, H.
    et al.
    Kao, C. -Y
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sampled-data H∞ control design for a class of PWM systems2005In: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, 2005, p. 4499-4504Conference paper (Refereed)
    Abstract [en]

    Robust control of a class of switched dynamical systems is considered. The switching is controlled by pulse-width modulation (PWM). This idea is used, for example, in power electronics for power conversion. The class of systems considered includes digitally controlled power converters of many different types. The traditional approach to control design for power converters rely on an averaged model that ignores the high frequency behavior and the inherent time delay due to sampling. In contrast, the method presented here is based on a sampled-data model which takes the switched nature of the system into account. The sampled-data model is approximated by a linear quadratic model to which sampled-data H∞ theory can be extended. The approach is applied to a bidirectional boost converter which is subjected to a large load disturbance.

  • 15. Fujioka, Hisaya
    et al.
    Kao, Chung-Yao
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    LQ optimal control for a class of pulse width modulated systems2007In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 43, no 6, p. 1009-1020Article in journal (Refereed)
    Abstract [en]

    We consider linear quadratic optimal control for a class of pulse width modulated systems. The problem is motivated from a practical application-digital control of switching power converters. The control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the intersampling behavior into account.

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