Stefan Almér

Hybrid Control Techniques for Switched-Mode DC-DC Converters Part I: The Step-Down Topology

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.

Stability Analysis of a Class of PWM Systems

This note considers stability analysis of a class of pulsewidth modulated (PWM) systems that incorporates several different switched mode dc-dc 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).

Harmonic analysis of pulse-width modulated systems

The paper considers the so-called dynamic phasor model as a basis for harmonic analysis of a class of 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.

LQ optimal control for a class of pulse width modulated systems

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.

Stability analysis of a class of PWM systems using sampled-data modeling

Stability analysis is considered for a class of pulse-width modulated (PWM) systems. A procedure is developed for systematic search for Lyapunov functions. The duty ratios that determine the switching times are used to partition the state space in such a way that stability is verified if a set of coupled linear matrix inequalities (LMIs) is feasible. Global stability as well as the computation of local regions of attraction is considered.

Dynamic Phasor Analysis of Pulse-Modulated Systems

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.

Sampled-Data H ∞ Control Design for a Class of PWM Systems

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.

Dynamic Phasor Analysis of Pulse Modulated Systems

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.

Harmonic Analysis of Pulse-Width Modulated Systems

Abstract The paper considers the so-called dynamic phasor model as a basis for harmonic analysis of a class of switching systems. 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.

LQ optimal control synthesis for a class of pulse modulated systems

Abstract 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.