103,683 research outputs found
Reduced-order modeling and dynamics of nonlinear acoustic waves in a combustion chamber
For understanding the fundamental properties of unsteady motions in combustion chambers, and for applications of active feedback control, reduced-order models occupy a uniquely important position. A framework exists for transforming the representation of general behavior by a set of infinite-dimensional partial differential equations to a finite set of nonlinear second-order ordinary
differential equations in time. The procedure rests on an expansion of the pressure and velocity fields in modal or basis functions, followed by spatial averaging to give the set of second-order equations in time. Nonlinear gasdynamics
is accounted for explicitly, but all other contributing processes require modeling. Reduced-order models of the global behavior of the chamber dynamics, most importantly of the pressure, are obtained simply by truncating the
modal expansion to the desired number of terms. Central to the procedures is a criterion for deciding how many modes must be retained to give accurate results. Addressing that problem is the principal purpose of this paper. Our
analysis shows that, in case of longitudinal modes, a first mode instability problem requires a minimum of four modes in the modal truncation whereas, for a second mode instability, one needs to retain at least the first eight modes. A second important problem concerns the conditions under which a linearly stable system becomes unstable to sufficiently large disturbances. Previous work has given a partial answer, suggesting that nonlinear gasdynamics alone cannot produce pulsed or 'triggered' true nonlinear instabilities; that suggestion is now theoretically established. Also, a certain form of the nonlinear energy
addition by combustion processes is known to lead to stable limit cycles in a linearly stable system. A second form of nonlinear combustion dynamics with a new velocity coupling function that naturally displays a threshold character
is shown here also to produce triggered limit cycle behavior
Robust Stability Under Mixed Time Varying, Time Invariant and Parametric Uncertainty
Robustness analysis is considered for systems with structured uncertainty involving a combination of linear time-invariant and linear time-varying perturbations, and parametric uncertainty. A necessary and sufficient condition for robust stability in terms of the structured singular value μ is obtained, based on a finite augmentation of the original problem. The augmentation corresponds to considering the system at a fixed number of frequencies. Sufficient conditions based on scaled small-gain are also considered and characterized
Stabilization of systems with asynchronous sensors and controllers
We study the stabilization of networked control systems with asynchronous
sensors and controllers. Offsets between the sensor and controller clocks are
unknown and modeled as parametric uncertainty. First we consider multi-input
linear systems and provide a sufficient condition for the existence of linear
time-invariant controllers that are capable of stabilizing the closed-loop
system for every clock offset in a given range of admissible values. For
first-order systems, we next obtain the maximum length of the offset range for
which the system can be stabilized by a single controller. Finally, this bound
is compared with the offset bounds that would be allowed if we restricted our
attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015
American Control Conference, July 1-3, 2015, the US
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