The control theory of nonlinear systems has been receiving increasing attention in recent years, both for its technical importance as well as for its impact in various fields of application. In several key areas, such as aerospace, chemical and petrochemical industries, bioengineering, and robotics, a new practical application for this tool appears every day. System nonlinearity is characterized when at least one component or subsystem is nonlinear. Classical methods used in the study of linear systems, particularly superposition, are not usually applied to the nonlinear systems. It is necessary to use other methods to study the control of these systems. For a wide class of nonlinear systems, a rather important structural feature comes from the strong nonlinearity appearing as coupling between spectrally decoupled parts of the system. Even in the case of low frequencies, where lumped models can still be employed the nonlinear coupling between parts of the system requires specific treatment, using advanced mathematical tools. In this context, an alternative, frequency domain approach is pursued here. In the rest of this work, a specific system form of linearly decoupled but nonlinearly coupled subsystems is examined. The mathematical toolbox of the Hilbert transform is appropriately introduced for obtaining two low-pass subsystems that form an equivalent description of the essential overall system dynamics. The nonlinear coupled dynamics is investigated systematically by partitioning the coupled system state vector in such a way as to fully exploit the low-pass and the band-pass intrinsic features of free dynamics. In particular, by employing the Hilbert Transform, a low-pass equivalent system is derived. Then, a typical case is investigated thoroughly by means of numerical simulation of the original coupled low and band-pass, real-state-variable system and the low-pass-equivalent, complex-state-variable derived one. The nonlinear model equations considered here pave the way for a systematic investigation of nonlinear feedback control options designed to operate mechatronic transducers in energy harvesting, sensing or actuation modes.

Dynamic security limits the power transfer capacity between regions and therefore has an economic impact. The power modulation control of high-voltage direct current (HVDC) links can improve the dynamic security of the power system. Having several HVDC links in a system creates the opportunity to coordinate such control, and coordination also ensures that negative interactions do not occur among the controllable devices. This thesis aims to increase dynamic security by coordinating HVDC links, as an alternative to decreasing the transfer capacity. This thesis contributes four control approaches for increasing the dynamic stability, based on feedforward control, adaptive control, optimal control, and exact-feedback linearization control. Depending on the available measurements, dynamic system model, and system topology, one of the developed methods can be applied. The wide-area measurement system provides the central controller with real-time data and sends control signals to the HVDC links. The feedforward controller applies rapid power dispatch, and the strategy used here is to link the N-1 criterion between two systems. The adaptive controller uses the modal analysis approach; based on forecasted load paths, the controller gains are adaptively adjusted to maximize the damping in the system. The optimal controller is designed based on an estimated reduced-order model; system identification develops the model based on the system response. The exact-feedback linearization approach uses a pre-feedback loop to cancel the nonlinearities; a stabilizing controller is designed for the remaining linear system. The conclusion is that coordinating the HVDC links improves the dynamic stability, which makes it possible to increase the transfer capacity. This conclusion is also supported by simulations of each control approach. / QC 20110302