- O'Connor, William

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# O'Connor, William

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- PublicationTravelling waves in boundary-controlled, non-uniform, cascaded lumped systemsA companion paper considers travelling and standing waves in cascaded, lumped, mass-spring systems, controlled by two boundary actuators, one at each end, when the system is uniform. It first proposes definitions of waves in finite lumped systems. It then shows how to control the actuators to establish desired waves from rest, and to maintain them despite disturbances. The present paper extends this work to the more general, non-uniform case, when mass and spring values can be arbitrary. A special Â¿bi-uniformÂ¿ case is first studied, consisting of two different uniform cascaded systems in series, with an obvious, uncontrolled, impedance mismatch where they meet. The paper shows how boundary actuator control systems can be designed to establish, and robustly maintain, apparently pure travelling waves of constant amplitude in either the first or the second uniform section, in each case with an appropriate, partial, standing wave pattern in the other section. Then a more general non-uniform case is studied. A definition of a Â¿pure travelling waveÂ¿ in non-uniform systems is proposed. Curiously, it does not imply constant amplitude motion. It does however yield maximum power transfer between boundary actuators. The definition, and its implementation in a control system, involves extending the notions of Â¿pureÂ¿ travelling waves, of standing waves, and of input and output impedances of sources and loads, when applied to non-uniform lumped systems. Practical, robust control strategies are presented for all cases.
414 - PublicationBoundary-controlled travelling and standing waves in cascaded lumped systemsThis paper describes how pure travelling waves in cascaded, lumped, uniform, mass-spring systems can be defined, established, and maintained, by controlling two boundary actuators, one at each end. In most cases the control system for each actuator requires identifying and measuring notional component waves, propagating in opposite directions, through the actuator-system interfaces. These measured component waves are then used to form the control inputs to the actuators. The paper also shows how the boundaries can be actively controlled to establish and maintain standing waves of arbitrary standing wave ratio, including those corresponding to classical modes of vibration with textbook boundary conditions. The proposed control systems are also robust to system disturbances: they react quickly to overcome external transient disturbances to re-establish the desired steady motion.
576ScopusÂ© Citations 12 - PublicationTravelling waves in boundary-controlled, non-uniform, cascaded lumped systemsA companion paper in this conference considers travelling and standing waves in cascaded, lumped, mass-spring systems, controlled by two boundary actuators, one at each end, when the system is uniform. It first proposes definitions of waves in finite lumped systems. It then shows how to control the actuators to establish desired waves from rest, and maintain them despite disturbances. The present paper extends this work to the more general, non-uniform case, when mass and spring values are arbitrary. A special "bi-uniform" case is first studied, consisting of two different uniform cascaded systems in series, with an obvious, uncontrolled, impedance mismatch where they meet. The paper shows how boundary actuator control systems can be designed to establish, and robustly maintain, apparently pure travelling waves of constant amplitude in either the first or the second uniform section, in each case with an appropriate standing wave pattern in the other section. Then a more general non-uniform case is studied. A definition of a "pure travelling wave" in non-uniform systems is proposed. Curiously, it does not imply constant amplitude motion. It does however yield maximum power transfer between boundary actuators. The definition, and its implementation in a control system, involves extending the notions of "pure" travelling waves, standing waves, and input and output impedances of sources and loads, when applied to non-uniform lumped systems. Practical, robust control strategies are presented for all cases.
357ScopusÂ© Citations 4 - PublicationWave-like modelling of cascaded, lumped, flexible systems with an arbitrarily moving boundaryThis paper considers cascaded, lumped, flexible systems, which may be short and non-uniform, which are driven by an arbitrarily moving boundary. Such systems exhibit vaguely wavelike behaviour yet defy classical wave analysis. The paper proposes novel ways to analyse and model such systems in terms of waves. It presents two new wave models for non-uniform systems, one series and one shunt, defining their component wave transfer functions, and thereby providing a way to define, identify and measure component waves. Features of the models are compared. The series and shunt configurations are mutually consistent and can be combined into a single composite wave model. The models are exact, but elements within them remain arbitrary to some degree, implying slight differences in the wave decomposition of the system. Some good model choices are proposed and explored. Wave speed and wave impedance are briefly considered, as are ways to measure component waves. Implications are discussed.
1917ScopusÂ© Citations 14 - PublicationA new approach to modal analysis of uniform chain systemsA new method is presented to determine the mode shapes and frequencies of uniform systems consisting of chains of masses and springs of arbitrary number with arbitrary boundary conditions. Instead of the classical eigenproblem approach, the system is analysed in terms of circulating waves and associated phase lags. The phasor conditions for the establishment of standing waves determine the vibration modes. The conditions fully specify their shapes and frequencies, and lead to simple, explicit expressions for the components of the modal vectors and the associated natural frequencies. In addition, the form of the phasor diagrams of the modes gives insight into the modal behaviour. The orthogonality of mode shapes also readily emerges. Examples are presented for different boundary conditions. Although not presented, it is possible to extend the approach to non-uniform lumped systems and to forced frequency responses.
1083ScopusÂ© Citations 7