Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
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Item Stationary Bifurcation Control for Systems with Uncontrollable Linearization(1999) Taihyun Kim; Abed, Eyad H.; ISRStationary 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.
Item Sampled-Data Modeling and Analysis of the Power Stage of PWM DC-DC Converters(1999) Fang, Chung-Chieh; Abed, Eyad H.; Abed, Eyad H.; ISRThe power stage of the PWM DC-DC converter is modeledand analyzed using the sampled-data approach.The work addressescontinuous and discontinuous conduction mode under voltage mode control,and continuous conduction mode under current mode control.For each configuration, nonlinear and linearized sampled-data models andcontrol-to-output transfer function are derived.Using this approach, both current mode control and discontinuous conduction modecan be handled systematically in a unified framework,making the modeling for these cases simpler than with the use of averaging.The results of this paper are similar to the results of Tymerski,but they are presented in a simpler manner tailored to facilitate immediate application to specific circuits.
It is shown howsampling the output at certain instants improves the obtained phase response.Frequency responses obtained from the sampled-data model aremore accurate than those obtained from various averaged models. In addition, a new ("lifted")continuous-time switching frequency-dependent model of the power stage isderived from the sampled-data model. Detailed examples illustrate themodeling tools presented here, and also provide a means of comparingresults obtained from the sampled-data approach with those obtainedfrom averaging.
Item Sampled-Data Modeling and Analysis of Closed-Loop PWM DC-DC Converters(1999) Fang, Chung-Chieh; Abed, Eyad H.; Abed, Eyad H.; ISRSampled-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.
Item Local Bifurcations in PWM DC-DC Converters(1999) Fang, Chung-Chieh; Abed, Eyad H.; Abed, E. H.; ISRA 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.Item Closed-Loop Monitoring Systems for Detecting Incipient Instability(1998) Kim, Taihyun; Abed, Eyad H.; ISRMonitoring 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.Item Feedback Control of Bifurcation and Chaos in Dynamical Systems(1993) Abed, Eyad H.; Wang, H.O.; ISRFeedback control of bifurcation and chaos in nonlinear dynamical systems is discussed. The article summarizes some of the recent work in this area, including both theory and applications. Stabilization of period doubling bifurcations and of the associated route to chaos is considered. Open problems in bifurcation control are noted.Item Local Nonlinear Control of Stall Inception in Axial Flow Compressors(1993) Adomaitis, Raymond A.; Abed, Eyad H.; ISRA combination of theoretical and computational nonlinear analysis techniques are used to study the scenario of bifurcations responsible for the initiation of rotating stall in an axial flow compressor model. It is found that viscosity tends to damp higher-frequency modes and so results in a sequence of bifurcations along the uniform-flow solution branch to stall cells of different mode number. Lower-mode stalled flow solutions are born in subcritical bifurcations, meaning that these equilibria will be unstable for small amplitudes. Secondary bifurcations, however, can render them stable, leading to hysteresis. Using throttle position as a control, we find that while the stall bifurcations are not linearly stabilizable, nonlinear state feedback of the first mode amplitude will reduce the hysteresis. This improves the nonlinear stability of the compression system near the stall margin.Item Bifurcation Analysis of Nonuniform Flow Patterns in Axial-Flow Gas Compressors(1992) Adomaitis, Raymond A.; Abed, Eyad H.; ISRWe study the transition from steady, spatially uniform-flow to nonuniform and time-dependent gas axial velocity profiles in an axial flow compression system. Local bifurcation analysis of the uniform-flow solution reveals a series of bifurcations to traveling waves of different mode number as a function of throttle opening. The number of bifurcating modes is found to depend on the gas viscosity parameter, an effect introduced in this work. Using the local approximations of the bifurcating solutions as starting points of our numerical analysis, we uncover a complicated scenario of secondary bifurcations ultimately resulting in parameter ranges where locally asymptotically stable stalled-flow solutions of different mode number coexist.Item Nonlinear Dynamics of Axial-Flow Compressors: A Parametric Study(1992) Adomaitis, Raymond A.; Liaw, Der-Cherng; Abed, Eyad H.; ISRAnalysis of the post-instability dynamical behavior of an axial- flow compression system model is carried out in a bifurcation- theoretic setting. Using global analysis techniques, we uncover the sequence of bifurcations in parameter space which allows us to rigorously determine whether the compressor stalls or surges when the throttle is slowly closed beyond the instability margin. Using these computational techniques, we also determine the conditions under which stalled and/or surging flow solutions coexist with the desired uniform-flow operating point and quantify the perturbations which destabilize this operating point.Item Bifurcations, Chaos and Crises in Power System Voltage Collapse(1992) Wang, Hua O.; Abed, Eyad H.; Hamdan, Anan M. A.; ISRBifurcations occurring in power system models exhibiting voltage collapse have been the subject of several recent studies. Although such models have been shown to admit a variety of bifurcation phenomena, the view that voltage collapse is triggered by possibly the simplest of these, namely by the (static) saddle node bifurcation of the nominal equilibrium, has been the dominant one. The authors have recently shown that voltage collapse can occur "prior" to the saddle node bifurcation. In the present paper, a new dynamical mechanism for voltage collapse is determined: the boundary crisis of a strange attractor or synonymously a blue sky bifurcation. This determination is reached for an example power system model akin to one studied in several recent papers. The identified mechanism for voltage collapse amounts to the disappearance of a strange attractor through collision with a coexisting saddle equilibrium point. This mechanism results in solution trajectories containing both an oscillatory component (as predicted by recent analytical work), and a sharp, steady drop in voltage (as observed in the field). More generally, blue sky bifurcations (not necessarily chaotic) are identified as important mechanisms deserving further consideration in the study of voltage collapse.