The dynamic response and bifurcations of a harmonic oscillator with a hysteretic restoring force and sinusoidal excitation are investigated. A multilinear model of hysteresis is presented. A hybrid system approach is used to formulate and study the problem. A novel method for obtaining exact transient and steady state response of the system is discussed. Simple periodic orbits of the system are analyzed using the KBM method and an analytic criterion for existence of bound and unbound resonance is derived. Results of KBM analysis are compared with those from numerical simulations. Stability and bifurcations of higher period orbits are studied using Poincar´e maps. The Poincar´e map for the system is constructed by composing the corresponding maps for the individual subsystems of the hybrid system. The novelty of this work lies in a.) the study of a multilinear model of hysteresis, and, b.) developing a methodology for obtaining the exact transient and steady state response of the system.

Automotive turbochargers (TCs) increase internal combustion engine power and efficiency in passenger and commercial vehicles. TC rotors are usually supported on floating ring bearings (FRBs) or semi-floating ring bearings (SFRBs), both of which are inexpensive to manufacture. However, fluid film bearings are highly nonlinear components of TC units and contribute to the complex behavior (i.e. bifurcations and frequency jumps between a first whirl frequency and a second whirl frequency) of the entire rotor-bearing system (RBS). The frequency jump phenomenon concerns the TC manufacturing industry due to increased levels of noise generation. This thesis presents progress on assessing the effects of some bearing parameters and operating conditions on the RBS dynamic forced performance and the frequency jump phenomenon. A fluid film bearing model is integrated into a finite element rotordynamics computational model for numerical prediction of the TC linear and nonlinear (time transient) forced response. Since automotive TCs operate with variable rotational speed, predictions are conducted with shaft acceleration/deceleration. Over most of its operating speed range, TC rotor nonlinear response predictions display two subsynchronous whirl frequencies w1 and w 2 representing a conical mode and a cylindrical bending mode, respectively. At low shaft speeds w1 is present up to a shaft speed (Omega bifurcation), where there is a frequency jump from w1 to w 2. The second whirl frequency may persist up to the highest shaft speeds (depending on operating conditions). Results show during rotor deceleration the Omega bifurcation may be different from the one during rotor acceleration (hysteresis). Predictions show the following factors delay the Omega bifurcation: increasing oil supply pressure, decreasing oil supply temperature, and increasing shaft acceleration. Also, rotor imbalance distribution greatly affects Omega bifurcation and the shaft amplitude of total motion. Overall, this study shows the sensitivity of bifurcations and frequency jump phenomenon in TC nonlinear response due to various bearing parameters and operating conditions. Further analysis is required to generalize these findings and to assess the effect of other bearing parameters (i.e. clearances, outer film length, ring rotation, etc.) on this phenomenon. In addition further validation of the predictions against test data is required for refinement of the predictive tool.

When excitable cardiac tissue is electrically paced at a sufficiently high rate, the duration of excitation can alternate from beat to beat despite a constant stimulation period. This rhythm, known as alternans, has been identified as an early stage in a sequence of increasingly complex instabilities leading to the lethal arrhythmia ventricular fibrillation (VF). This connection served as as a motivation for research into the control of alternans as a strategy to prevent VF. Control methods that do not use a model of the dynamics have been used for the suppression of alternans. However, these methods possess limitations. In this thesis we study theoretically model-based control techniques with the goal of developing protocols that would overcome the shortcomings of non model-based approaches. We consider one dimensional tissue in two different geometrical configurations: a ring and a fiber with free ends (open fiber). We apply standard control methods for linear time invariant systems to a stroboscopic map of the linearized dynamics around the normal rhythm. We found that, in the ring geometry, model-based control is able to suppress alternans faster and with lower current, thereby reducing the risk of tissue damage, compared with non-model-based control. In the open fiber, model-based control is able to suppress alternans for longer fibers and higher pacing frequencies in comparison with non-model-based control. The methodology presented here can be extended to two- and three-dimensional tissue, and could eventually lead to the suppression of alternans on the entire ventricles.

Boom cranes are one of the most dynamically complicated types of cranes because they possess rotational joints as opposed to the linear tracks of bridge and gantry cranes. In addition, if the boom crane is placed on a mobile base, additional complexity is added to the system. However, mobile boom cranes have huge potential benefits as they can be quickly transported from one location to another. Furthermore, if they utilize their mobile base during lifting operations, then they can have an extremely large workspace. All cranes share the same limiting weakness; the payload oscillates when the crane moves. A command-generation approach is taken to control the payload oscillation. Input shaping is one such command-generation technique that modifies the original reference command by convolving it with a series of impulses. The shaped command produced by the convolution can then move the crane without inducing payload oscillation. Input shaping can accommodate parameter uncertainties, nonlinearities, multiple modes of vibration, and has been shown to be compatible with human operators. This thesis focuses on three aspects of mobile boom cranes: 1) dynamic analysis, 2) input-shaping control, and 3) experimental testing. A majority of the thesis focuses on analyzing and describing the complicated dynamics of mobile boom cranes. Then, various input-shaping controllers are designed and tested, including two-mode shapers for double-pendulum dynamics. In order to experimentally verify the simulation results, a small-scale mobile boom crane has been constructed. The details of the mobile boom crane and its important features are presented and discussed. Details of the software used to control the crane are also presented. Then, several different experimental protocols are introduced and the results presented. In addition, a set of operator performance studies that analyze human operators maneuvering the mobile boom crane through an obstacle course is presented.

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<p>For a successful design of an engineering system it is essential to pay careful attention to its dynamic response. This is particularly true, in the case of nonlinear systems, since they can exhibit very complex dynamic behaviour, including multiple co-existing stable solutions and chaotic motions, characterized by large sensitivity to initial conditions. In some systems nonlinear characteristics are desired and designed for, but in other cases they are unwanted and can cause fatigue and failure. A type of dynamical system which is highly nonlinear is discontinuous or non-smooth systems. In this work, systems with impacts are primarily investigated, and this is a typical example of a discontinuous system. To enhance or optimize the performance of dynamical systems, some kind of control can be implemented. This thesis concerns implementation of low-cost control strategies for discontinuous systems. Low-cost control means that a minimum amount of energy is used when performing the control actions, which is a desirable situation regardless of the application. The disadvantage of such a method is that the performance might be limited as compared with a control strategy with no restrictions on energy consumption. In this work, the control objective is to enforce a continuous or discontinuous grazing bifurcation of the system, whichever is desirable. In Paper A, the dynamic response and bifurcation behaviour of an impactoscillator with dry friction is investigated. For a one-degree-of-freedom model of the system, analytical solutions are found in separate regions of state space. These are then used to perform a perturbation analysis around a grazing trajectory. Through the analysis, a condition on the parameters of the system is derived, which assures a continuous grazing bifurcation. It is also shown that the result has bearing on the dynamic response of a two-degree-of-freedom model of the system. A low-cost active control strategy for a class of impact oscillators is proposed in Paper B. The idea of the control method is to introduce small adjustments in the position of the impact surface, at discrete moments in time, to assure a continuous bifurcation. A proof is given for what control parameters assures the stabilization. In Paper C, the proposed low-cost control method is implemented in a quarter-car model of a vehicle suspension, in order to minimize impact velocities with the bumpstop in case of high amplitude excitation. It is shown that the control method is effective for harmonic road excitation.</p>

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (leaves 275-293).

A principal goal of neural engineering is to control the activation of neural circuits across space and time. The ability to control neural circuits with surrogate inputs is needed for the development of clinical neural prostheses and the experimental interrogation of connectivity between brain regions. Electrical stimulation provides a clinically viable method for activating neural tissue and the emergence of optogenetic stimulation has redefined the limitations on stimulating neural tissue experimentally. However, it remains poorly understood how these tools activate complex neural circuits. The goal of this proposed project was to gain a greater understanding of how to control the activity of neural circuits in-vivo using a combination of experimental and computational approaches. Voltage sensitive dye imaging was used to observe the spatiotemporal activity within the rodent somatosensory cortex in response to systematically varied patterns of sensory, electrical, and optogenetic stimulation. First, the cortical response to simple patterns of sensory and artificial stimuli was characterized and modeled, revealing distinct neural response properties due to the differing synchrony with which the neural circuit was engaged. Then, we specifically designed artificial stimuli to improve the functional relevance of the resulting downstream neural responses. Finally, through direct optogenetic modulation of thalamic state, we demonstrate control of the nonlinear propagation of neural activity within the thalamocortical circuit. The combined experimental and computational approach described in this thesis provides a comprehensive description of the nonlinear dynamics of the thalamocortical circuit to surrogate stimuli. Together, the characterization, modeling, and overall control of downstream neural activity stands to inform the development of central nervous system sensory prostheses, and more generally provides the initial tools and framework for the control of neural activity in-vivo.

A Lagrangian formalism presented by Hay, Ilinskii, Zabolotskaya, and Hamilton [J. Acoust. Soc. Am. 132, 124--137 (2012)] to calculate the pulsation of a spherical bubble, immersed in liquid and near one or two viscoelastic layers, is extended here to include bubble translation. The method presented here is simplified from that given by Hay et al. in that only a single interface between a liquid and a viscoelastic half-space is considered. In the present approach the force on the bubble due to the presence of the liquid-solid interface is calculated using a Green's function that takes into account elastic waves and viscosity in the layer, and the viscous boundary layer within the liquid near the interface. Previous models and experiments have shown that the direction of bubble translation near a viscoelastic layer is correlated with the direction of a liquid jet often produced by the bubble during collapse. In this dissertation an attempt is made to model the pulsation and translation of a spherical bubble near a liquid-solid interface to infer the direction of bubble translation in reference to material parameters of the liquid and viscoelastic medium, and the standoff distance of the bubble from the interface. The analysis is simplified by demonstrating that the direction of bubble translation can be inferred from the phase of the component of the Green's function associated with the reverberant pressure gradient. For linear bubble pulsation it is shown that the domain of material properties of the viscoelastic medium which generally corresponds to bubble translation away from the interface occurs when the effective stiffness of the viscoelastic medium is greater than the effective damping for both itself and the liquid. The analysis is performed assuming the viscoelastic medium is similar to soft tissue, and its dynamics are described by a Voigt, Kelvin, or Maxwell model. The simulations are compared with existing experimental data. Effects of high-amplitude bubble pulsation are explored in terms of how the simulations differ as the pulsation amplitude increases. At higher pulsation amplitudes, it is shown that bubble translation is still described qualitatively by analyzing the phase of the reverberant pressure gradient. / text

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