Closed-Loop Monitoring Systems for Detecting Incipient Instability

Monitoring systems are proposed for the detection of incipientinstability in uncertain nonlinear systems. The work employsgeneric features associated with the response to noise inputsof systems bordering on instability. These features, called "noisy precursors" in the work of Wiesenfeld, also yield information onthe type of bifurcation that would be associated with thepredicted instability. The closed-loop monitoring systems proposedin the paper have several advantages over simple open-loop monitoring.The advantages include the ability to influence the frequencies atwhich the noisy precursors are observed, and the ability tosimultaneously monitor and control the system

Stationary Bifurcation Control for Systems with Uncontrollable Linearization

Stationary bifurcation control is studied under the assumption thatthe critical zero eigenvalue is uncontrollable for thelinearized system. The development facilitates explicit constructionof feedback control laws that render the bifurcation supercritical.Thus, the bifurcated equilibria in the controlled system are guaranteedstable. Bothpitchfork bifurcation and transcritical bifurcation are addressed.The results obtained forpitchfork bifurcations apply to general nonlinear models smoothin the state and the control. For transcritical bifurcations,the results require the system to be affine in the control

Sampled-Data Modeling and Analysis of PWM DC-DC Converters Part I. Closed-Loop Circuits

General block diagram models are proposed for PWM DC-DC convertersin continuous and discontinuous conduction modes withfixed switching frequency.Both current mode control and voltage mode control are addressed inthese models.Based on these models detailed nonlinear and linearized sampled-data dynamics are derived.Asymptotic orbital stability is analyzed.Audio-susceptibility and output impedance are derived. In this approach,discontinuous conduction mode andcurrent mode control can be analyzed systematicallywithout special effort.A companion paper (Part II) addresses the same issuesfor the power stage of a PWM DC-DC converter

Lyapunov-Based Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems

Feedback control of piecewise smooth discrete-time systems that undergo border collision bifurcations is considered. These bifurcations occur when a fixed point or a periodic orbit of a piecewise smooth system crosses or collides with the border between two regions of smooth operation as a system parameter is quasistatically varied. The goal of the control effort in this work is to modify the bifurcation so that the bifurcated steady state is locally attracting and locally unique. To achieve this, Lyapunov-based techniques are used. A sufficient condition for nonbifurcation with persistent stability in piecewise smooth maps of dimension $n$ that depend on a parameter is derived. The derived condition is in terms of linear matrix inequalities. This condition is then used as a basis for the design of feedback controls to eliminate border collision bifurcations in piecewise smooth maps and to produce desirable behavior

Local Bifurcations in PWM DC-DC Converters

A general sampled-data model of PWM DC-DC converters is employed tostudy types of loss of stability of the nominal (periodic)operating condition andtheir connection with local bifurcations.In this work, the nominal solution's periodic natureis accounted for via the sampled-data model.This results in moreaccurate predictions of instability and bifurcation than can be obtained using the averaging approach.The local bifurcations of the nominal operating conditionstudied here are period-doublingbifurcation, saddle-node bifurcation, and Neimark bifurcation.Examples of bifurcations associated with instabilities in PWM DC-DC convertersare given.In particular, input filter instability is shown to be closely related tothe Neimark bifurcation

Sampled-Data Modeling and Analysis of Closed-Loop PWM DC-DC Converters

Sampled-data analysis of converters has been a topic of investigationfor the past two decades. However, this powerful tool is not widelyused in control loop design or in closed-loop performance validation.Instead, averaged models are typically used for control loopdesign, while detailed simulations are used for validatingclosed-loop performance. This paper makes several contributions tothe sampled-data modeling and analysis of closed-loop PWM DC-DC converters,with the aim of increasing appreciation and use of the method. General models are presented in a unified and simple manner, while removingsimplifying approximations present in previous work. These models applyboth for current mode control and voltage mode control.The general models are nonlinear. They are used toobtain {it analytical} linearized models, which are in turn employedto obtain local stability results. Detailed examplesillustrate the modeling and analysis in the paper,and point to situations in which the sampled-data approachgives results superior to alternate methods.For instance, it is shownthat the sampled-data approach will reliablypredict the (local) stability of aconverter for which averaging or simulation predicts instability

Analysis and Control of Period Doubling Bifurcation in Buck Converters Using Harmonic Balance

Period doubling bifurcation in buck convertersis studied by using the harmonic balance method.A simple dynamic model of a buck converter in continuous conduction modeunder voltage mode or current mode controlis derived.This model consists of the feedback connection of a linear system and a nonlinear one.An exact harmonic balance analysis is usedto obtain a necessary and sufficient condition fora period doubling bifurcation to occur.If such a bifurcation occurs,the analysis also provides information on its exact location.Using the condition for bifurcation,a feedforward control is designed thateliminates a period doubling bifurcation.This results in a wider range of allowed source voltage,and also in improved output voltage regulation