Shipboard crane control, simulated data generation, and border-collision bifurcations

This dissertation studies three different yet related applications of the non-linear dynamical theories in general, and of the chaos theories in particular. They are the following: shipboard crane control, simulated data generation, and border-collision bifurcations.; There are many situations in which cranes must be operated on a moving platform. One example is unloading cargo ships in an open sea by using cranes mounted on another ship. Because of ship motions, large pendulation of the cargo may be induced causing equipment damage and personnel injury. Current rigging and control implementations do not provide adequate control over the cargo pendulation. We propose a new cable rigging for a ship crane in order to control load pendulation. The "Maryland Rigging" includes the addition of a pulley-brake mechanism to the existing rigging configuration. We show numerically that by applying friction in this new rigging system we are able to reduce pendulation enormously.; In Chapter 2 we introduce a filtering method of generating nonlinear time series whose spectral characteristics are specified. We argue that the commonly used phase-scrambling technique is inadequate to capture the nonlinear properties of the studied system. Our method, however, not only matches the power spectrum of the output signal to the given characteristics, but also describes the basic nonlinear, or intermittent, features of the studied system.; In Chapter 3 we discuss one and two dimensional normal form theories for piecewise smooth maps. We first derive one and two dimensional normal forms from piecewise smooth maps. We then discuss generic bifurcations for the one and two dimensional normal forms. We divide the parameter space into regions where we can predict what types of bifurcations may occur as one of the parameters is varied.; In Chapter 4 we use a feedback controlled buck converter to demonstrate how normal form theories can be applied in practice. We have observed many border collision bifurcations for the buck circuit. Near each border collision bifurcation point, we determine the corresponding normal form numerically. The normal form gives the same bifurcation structure as we have obtained from the circuit. Therefore the study of the normal form enables us to predict local bifurcation structures. This method can be easily applied to many power electronic circuits as well as other piecewise smooth systems.