Vibration control of distributed parameter systems and fluidic flexible matrix composites

In this thesis, we study input shaping control of Distributed Parameter Systems (DPS) and passive and semi-active vibration control using Fluidic Flexible Matrix Composites (F2MC).;First, we extend input shaping control to one dimensional continua. Unlike discrete systems where the input is shaped only in the temporal domain, temporal and spatial input shaping can produce zero residual vibration in setpoint position control of distributed strings and beams. For collocated and noncollocated boundary control of strings and domain control of strings and pinned beams, the response to step inputs is solved in closed form using delays. For a clamped beam model, a closed form infinite modal series is used. The boundary controlled string can be setpoint regulated using two-pulse Zero Vibration (ZV) and three-pulse Zero Vibration and Derivative (ZVD) shapers but ZVD is not more robust to parameter variations than ZV, a unique characteristic of second-order PDE systems. Noncollocated ZV and ZVD boundary control enables rigid body translation of a string with zero residual vibration. Domain controlled strings and pinned beams with spatial input distributions that satisfy certain orthogonality conditions (e.g. midspan point load or uniformly distributed load) can be setpoint regulated with shaped inputs. For the cantilevered beam, modal shaping of the input distribution and ZV or ZVD temporal shaping drives the tip to the desired position with zero residual vibration.;A command shaping approach in vibration control using F2MC tubes as variable stiffness structures is studied in the third chapter. The apparent stiffness of F2MC tubes can be changed using a variable orifice valve. With fiber reinforcement, the volume inside the tube may change with external load. With an open valve, the liquid is free to move in or out of the tube, so the apparent stiffness does not change. When the valve is closed, the high bulk modulus liquid is confined, which resists the volume change and causes the apparent stiffness of the tube to increase. The equations of motion of an F2MC-mass system is derived using a 3-D elasticity model and the energy method. A reduced order model is then developed for fully-open and fully-closed valves. A Skyhook control that cycles the valve between open and closed, asymptotically decays the vibration. A Zero Vibration (ZV) Stiffness Shaping technique is introduced to suppress the vibration in finite time. A sensitivity analysis of the ZV Stiffness Shaper studies the robustness to parametric uncertainties.;We also investigate passive and semi-active vibration control using F 2MC tubes. F2MC tubes filled with fluid and connected to an accumulator through a fixed orifice can provide damping forces in response to axial strain. If the orifice is actively controlled, the stiffness of F 2MC tubes can be dynamically switched from soft to stiff. The stability of the unforced dynamic system is proven using a Lyapunov approach. The reduced-order model for operation with either a fully-open or fully-closed valve motivates the development of a ZV feedback control law, that suppresses vibration in finite time. Coupling of a fluid-filled F2MC tube to a pressurized accumulator through a fixed orifice is shown to provide significant passive damping. The open valve orifice size is optimized for optimal passive, Skyhook, and ZV controllers by minimizing the ITAE cost function.;Finally, we develop a novel Tuned Vibration Absorber (TVA) using F 2MC. Coupling of a fluid-filled F2MC tube through a fluid port to a pressurized air accumulator can suppress primary mass forced vibration at the tuned absorber frequency. A 3-D elasticity model for the tube and a lumped fluid mass produces a 4th order model of an F2MC-mass system. The model provides a closed-form isolation frequency that depends mainly on the port inertance, orifice flow coefficient, and the tube parameters. A small viscous damping in the orifice increases the isolation bandwidth. With a fully closed orifice, the zero disappears, and the system has a single resonant peak. Variations in the primary mass do not change the isolation frequency, making the F2MC TVA robust to mass variations. Experimental results validate the theoretical predictions in showing a tunable isolation frequency that is insensitive to primary mass variations, and a 94% reduction in forced vibration response relative to the closed valve case. (Abstract shortened by UMI.)...