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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    Feedback Control of Bifurcation and Chaos in Dynamical Systems
    (1993) Abed, Eyad H.; Wang, H.O.; ISR
    Feedback 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.
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    Local Nonlinear Control of Stall Inception in Axial Flow Compressors
    (1993) Adomaitis, Raymond A.; Abed, Eyad H.; ISR
    A 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.
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    Control of Nonlinear Phenomena at the Inception of Voltage Collapse
    (1993) Wang, H.O.; Abed, Eyad H.; Adomaitis, Raymond A.; Hamdan, Anan M. A.; ISR
    Nonlinear Phenomena, including bifurcations and chaos, occurring in power system models exhibiting voltage collapse have been the subject of several recent studies. These nonlinear phenomena have been determined to be crucial factors in the inception of voltage collapse in these models. In this paper, the problem of controlling voltage collapse in the presence of these nonlinear phenomena is addressed. The work focuses on an example power system model that has been studied in several recent papers. The bifurcation control approach is employed to modify the bifurcations and to suppress chaos. The control law is shown to result in improved performance of the system for a greater range of parameter values.
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    Bifurcation Analysis of Nonuniform Flow Patterns in Axial-Flow Gas Compressors
    (1992) Adomaitis, Raymond A.; Abed, Eyad H.; ISR
    We 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.
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    Active Stabilization of Rotating Stall: A Bifurcation-Theoretic Approach
    (1992) Liaw, Der-Cherng; Abed, Eyad H.; ISR
    Active control of the onset of stall instabilities in axial flow compressors is pursued using bifurcation analysis of a dynamical model proposed by Moore and Greitzer (1986). This model consists of three ordinary differential equations with state variables being the mass flow rate, pressure rise, and the amplitude of the first harmonic mode of the asymmetric component of the flow. The model is found to exhibit a stationary (pitchfork) bifurcation at the inception of stall, resulting in hysteresis. Using throttle opening as a control, analysis of the linearized system at stall shows that the critical mode (zero eigenvalue) is unaffected by linear feedback. Hence, nonlinear tools must be used to achieve stabilization. A quadratic feedback control law using the measurement of asymmetric dynamics is proposed which stabilizes the bifurcation and eliminates the undesirable hysteretic behavior.
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    Nonlinear Dynamics of Axial-Flow Compressors: A Parametric Study
    (1992) Adomaitis, Raymond A.; Liaw, Der-Cherng; Abed, Eyad H.; ISR
    Analysis 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.
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    Bifurcations, Chaos and Crises in Power System Voltage Collapse
    (1992) Wang, Hua O.; Abed, Eyad H.; Hamdan, Anan M. A.; ISR
    Bifurcations 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.
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    Bifurcation Control of chaotic Dynamical Systems
    (1992) Wang, H.O.; Abed, Eyad H.; ISR
    A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems. The first of these ideas is the need for robust control, in the sense that, even with an uncertain dynamic model of the system, the design ensures stabilization without at the same time changing the underlying equilibrium structure of the system. Secondly, the paper shows how focusing on the control of primary bifurcations in the model can result in the taming of chaos. The latter is an example of the 'bifurcation control' approach. When employed along with a dynamic feedback approach to the equilibrium structure preservation issue noted above, this results in a family of robust feedback controllers by which one can achieve various types of 'stability' for the system.
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    Dynamic Bifurcations in a Power System Model Exhibiting Voltage Collapse
    (1992) Abed, Eyad H.; Alexander, James C.; Wang, H.; Hamdan, Anan M. A.; Lee, Hsien-Chiarn; ISR
    Dynamic bifurcations, including Hopf and period-doubling bifurcations, are found to occur in a power system dynamic model recently employed in voltage collapse studies. The occurrence of dynamic bifurcations is ascertained in a region of state and parameter space linked with the onset of voltage collapse. The work focuses on a power system model studied by Dobson and Chiang (1989). The presence of the dynamic bifurcations, and the resulting implications for dynamic behavior, necessitate a re- examination of the role of saddle node bifurcations in the voltage collapse phenomenon. The bifurcation analysis is performed using the reactive power demand at a load bus as the bifurcation parameter. Due to numerical ill-conditioning, a reduced-order model is employed in some of the computations. It is determined that the power system model under consideration exhibits two Hopf bifurcations in the vicinity of the saddle node bifurcation. Between the Hopf bifurcations, i.e., in the "Hopf window," period-doubling bifurcations are found to occur. Simulations are given to illustrate the various types of dynamic behaviors associated with voltage collapse for the model. In particular, it is seen that an oscillatory transient may play a role in the collapse.
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    Families of Liapunov Functions for Nonlinear Systems in Critical Cases
    (1991) Fu, Jyun-Horng; Abed, Eyad H.; ISR
    Liapunov functions are constructed for nonlinear systems of ordinary differential equations whose linearized system at an equilibrium point possesses either a simple zero eigenvalue or a complex conjugate pair of simple, pure imaginary eigenvalues. The construction is explicit, and yields parametrized families of Liapunov functions for such systems. In the case of a zero eigenvalue, the Liapunov functions contain quadratic and cubic terms in the state. Quartic terms appear as well for the case of a pair of pure imaginary eigenvalues. Predictions of local asymptotic stability using these Liapunov functions are shown to coincide with those of pertinent bifurcation-theorectic calculations. The development of the paper is carried out using elementary properties of multilinear functions. The Liapunov function families thus obtained are amenable to symbolic computer coding.