Dynamical analysis and application of advanced control techniques to atomic force microscopes and camless engines

In this dissertation, we study the following two dynamical systems with the objective to apply available control machinery in order to achieve better performance: (1) Part I: Dynamics of microcantilevers in atomic force microscopes. (2) Part II: Breathing process in a camless internal combustion engine.; The first part provides a study of the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation. Two models are developed for the interaction between the sample and the cantilever. The first model assumes a long range van der Waals (vdW) attractive potential, while second model includes both a short range repulsive and a long range attractive potentials. The cantilever is vibrated by a sinusoidal input, and its deflection is detected optically. We analyze the forced dynamics using Melnikov method, which reveals the regions in the space of physical parameters where subharmonic or chaotic motions are possible. In addition, using a proportional and derivative controller we compute the Melnikov function in terms of the parameters of the controller. Using this relation it is possible to design controllers that will remove the possibility of chaos, and generate or eliminate subharmonics in the system.; In the second part, we exploit advanced control theory tools to investigate the feasibility of camless engine operation. Availability of fully variable camless actuation presents a great opportunity for substantial improvements in engine operation as well as a great challenge in being able to cope with, and properly use the many new degrees of freedom that become available for engine optimization. To this end, an adaptive nonlinear controller has been designed to coordinate intake valve lift and duration by using conventional engine measurements. The controller design is based on a phenomenological model for unthrottled engine operation. The driver torque demand is satisfied, while primping losses are minimized. Simulations are used to test the developed methodology.