VIBRATION CONTROL OF DISTRIBUTED PARAMETER SYSTEMS AND FLUIDIC FLEXIBLE MATRIX COMPOSITES
Open Access
- Author:
- Lotfi Gaskarimahalle, Amir
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- July 01, 2009
- Committee Members:
- Christopher Rahn, Dissertation Advisor/Co-Advisor
Christopher Rahn, Committee Chair/Co-Chair
Alok Sinha, Committee Member
Qian Wang, Committee Member
George A Lesieutre, Committee Member - Keywords:
- Semi-active Control
Tuned Vibration Absorbers
Variable Stiffness Systems
Input Shaping
Vibration Control - Abstract:
- Vibration degrades the performance of many mechanical systems, reducing the quality of manufactured products, producing noise, introducing fatigue in mechanical compo- nents, and generating an uncomfortable environment for passengers. Vibration control is categorized as: active, passive, semi-active or hybrid, based on the power consumption of the control system and feedback or feedforward based on whether sensing is used to control vibration. In this thesis, we study input shaping control of Distributed Parame- ter 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 distrib- uted 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 in…nite 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 condi- tions (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 sti¤ness structures is studied in the third chapter. The apparent sti¤ness of F2MC tubes can be changed using a variable ori…ce valve. With …ber 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 sti¤ness does not change. When the valve is closed, the high bulk modulus liquid is con…ned, which resists the volume change and causes the apparent sti¤ness 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) Sti¤ness Shaping technique is introduced to suppress the vibration in …nite time. A sensitivity analysis of the ZV Sti¤ness Shaper studies the robustness to parametric uncertainties. We also investigate passive and semi-active vibration control using F2MC tubes. F2MC tubes …lled with ‡uid and connected to an accumulator through a …xed ori…ce can provide damping forces in response to axial strain. If the ori…ce is actively con- trolled, the sti¤ness of F2MC tubes can be dynamically switched from soft to sti¤. 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 moti- vates the development of a ZV feedback control law, that suppresses vibration in …nite time. Coupling of a ‡uid-…lled F2MC tube to a pressurized accumulator through a …xed ori…ce is shown to provide signi…cant passive damping. The open valve ori…ce size is op- timized for optimal passive, Skyhook, and ZV controllers by minimizing the ITAE cost function. Simulation results show that the optimal open valve ori…ce provides a damping ratio of 0:35 compared to no damping in closed valve case. The optimal ZV controller outperforms optimal passive and Skyhook controllers by 32:9% and 34:2% for impulse and 34:7% and 60% for step response, respectively. Theoretical results are con…rmed by experiments that demonstrate the improved damping provided by optimal passive control F2MC and fast transient response provided by semi-active ZV control. Finally, we develop a novel Tuned Vibration Absorber (TVA) using F2MC. Coupling of a ‡uid-…lled F2MC tube through a ‡uid 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 ‡uid 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, ori…ce ‡ow coe¢ cient, and the tube parameters. A small viscous damping in the ori…ce increases the isolation bandwidth. With a fully closed ori…ce, 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.