Vehicles and mechanisms which must perform very precise tasks or maneuvers require controllers to compensate for their inherent structural flexibility. Many of these applications involve structures that have time-varying dynamics, or have dynamics that are not considered in the traditional off-line controller design. These types of structures necessitate the use of adaptive control algorithms which can redesign themselves on-line in response to changes in the structural dynamics. This work describes an on-line control algorithm that uses the pole-zero spacings of the collocated control-to-output transfer function to design the optimum Positive Position Feedback (PPF) control law. The PPF control law uses second-order filters to add closed-loop damping to resonant structural modes. An on-line PPF design algorithm was developed based on the theoretical model of the collocated control-to-output transfer function. The optimal PPF filter parameters are shown to be a function of the pole-zero spacing in the collocated transfer function. These parameters were found by solving the pole placement problem using a theoretical model for various pole-zero spacings. The parameters are then stored in a lookup table in the realtime controller, and a frequency sweep algorithm identifies the pole-zero spacing on-line and designs the PPF filters using the parameters in the lookup table. A Phase-Locked Loop (PLL) was also studied as a means for adaptively tuning the PPF filters on-line. The PLL behavior in the presence of random and deterministic signals was characterized. The PLL was used experimentally to tune a PPF filter to a changing modal frequency. Analysis of the theoretical model indicated the amount of closed-loop damping a PPF filter can add monotonically increases with the amount of frequency spacing of the pole/zero pair. Experimental results with the on-line optimal PPF control algorithm proved it to be effective at adding damping to structures and suppressing vibration. The poles and zeros of the control-to-output transfer function were accurately identified by the pole/zero identification routine. However, the closed-loop performance was shown to be very dependent on the correct placement of sensor and actuator pairs. Tests with pointing control problems showed the algorithm to be better suited to vibration suppression rather than vibration isolation. Simulations and experiments with the phase-locked loop showed it to be unable to track a modal frequency of a structure excited by broadband noise. Bandpass prefilters would be necessary to eliminate the frequency content of the other modes, limiting the usefulness of the PLL. / Master of Science

This research thesis aims to achieve the structural analysis and active vibration damping of the Tetraform machining structure. The Tetraform is a space frame made up of four equilateral triangles with spherical masses at the four vertices. This frame was originally developed for grinding of optical lenses and is now being adapted for use in micro-precision milling. The Tetraform is beneficial to the milling process due to its exceptionally high dynamic stiffness characteristics, which increases the machining stability and allows for higher material removal rates and accuracy. However, there are still some modes of vibration that are critical to the milling process and need to be dampened out. Under operating conditions of many structures, resonant modes of vibration can easily be excited which often lead to structural failure or significant reduction in operating performance. For the milling application, resonant frequencies of the machining structure can severely limit the milling process. The goal of the presented research is to increase surface and subsurface integrity with optimal material removal rate and least possible machining vibration, while maintaining accurate precision and surface finish. The vibrations from the machine tool not only affect the quality of the machined part but also the machine tool itself, since the cutting tool is susceptible to break or wear quickly when operating at high vibration modes, thus inevitably decreasing tool life. Vibration control has gained considerable attention in many areas including aerospace, automotive, structural, and manufacturing. Positive Position Feedback (PPF) is a vibration control scheme that is commonly used for its robust stability properties. A PPF controller works as a low pass filter, eliminating instability from unmodeled higher-frequency modes. The PPF controller concept is used in developing an active vibration control scheme to target the critical frequencies of the Tetraform. The controller is implemented with use of piezoelectric actuators and sensors, where the sensors are bonded to the opposing sides of the beams as the actuators, allowing for the assumption of collocation. The sensor/actuator pairs are placed at an optimal location on the Tetraform with high modal displacements for all the critical frequencies. Multiple finite element models are developed in order to analyze the structural dynamics and allow for controller design. A model is developed in the finite element software ANSYS and is used to obtain the Tetraform's dynamic characteristics, which include natural frequencies and mode shapes. This model is also used to visualize the changes in mode shapes due to structural modifications or different material selections. Other models are also developed in Matlab and Simulink. This consists of the creation of a finite element model which is then converted to state space. The piezoelectric transducers are included in this model for the input and output of the state space model. This model can be used for controller design where the goal is to create maximum decibel reduction at critical frequencies while attempting to minimize controller effort.

Aircraft and satellite structures are exposed to a wide range of temperatures during normal operation cycles. These fluctuations in temperature may result in significant changes of the structural dynamics. Aircraft, automotive, and satellite structures are also subject to various vibration sources. Passive and active vibration suppression techniques have been developed to minimize acoustic noise and fatigue stress damage. Featuring low weight solutions and high performance, active control techniques are becoming increasingly common. Structures with varying dynamics require more sophisticated active control techniques, such as adaptive control. This research uses a special vibration test rig for evaluating the performance of different vibration suppression systems on a representative aircraft panel. The test panel is clamped rigidly in a frame and can be excited in various frequencies with an electromagnetic shaker. To simulate temperature fluctuations the temperature on the panel can be increased up to 65°C (150°F). Smart material based sensors and actuators are used to interface the mechanical system with the electronic controller. The active controller utilizes three positive position feedback (PPF) filters implemented through a digital signal processor board. This research develops two different adaptation methods to perform vibration suppression in the presence of thermally induced frequency changes of the representative panel. To adjust the PPF filter parameters an open-loop adaptation method and an auto-tuning method are investigated. The open-loop adaptation method uses a measurement of the plate temperature and a look-up table with pre-determined parameters to update the filters accordingly. The auto-tuning methods identifies the frequencies of the poles and zeros in the structure's collocated transfer function. From the knowledge of the pole and zero locations the optimal PPF parameters are calculated online. The results show that both adaptation methods are capable of reducing the vibration levels of the test specimen over the temperature range of interest. Three PPF filters with parameter adaptation through temperature measurement achieve magnitude reductions of the resonance peaks as high as 13.6 decibel. Using the auto-tuning method resonance peak reductions up to 17.4 decibel are possible. The pole/zero identification routine proves to detect the frequencies correctly. The average identification error remained at around one percent even in the presence of external disturbances. / Master of Science

This study evaluates the effectiveness of actively controlled piezoceramics with positive position feedback (PPF) for reducing structural vibrations. A comparison is made between active control with PPF and a parallel resistor-inductor (RLC) shunt technique. The primary objectives of this study are to: 1. Explore the feasibility of using smart materials and fiber optics for simultaneous health monitoring and active damping of a representative aircraft panel. 2. Determine how optical fiber sensors may be used to detect vibration modes of an aircraft panel by investigating their use on a representative test article. 3. Determine how piezoelectric patches may be used to detect and counteract fundamental resonances of a representative test article. 4. Determine a control algorithm and hardware system to increase substantially the damping in the fundamental mode of the representative test article over a wide temperature range. 5. Develop a health-monitoring algorithm based on fiber optic sensors to detect impedance changes in a representative test article. 6. Make a comparison between active control with PPF and an RLC shunt technique. To achieve the objectives of this study, a special test rig was used to evaluate the performance of piezoelectric materials (PZTs) for vibration suppression. The test rig was used to rigidly clamp a flat 20-guage steel plate, and then excite the plate in various frequency ranges with an electromagnetic shaker. For each test, a data acquisition system was used to acquire the data to evaluate the performance of each PPF controller. Once the data was obtained, a comparison was made between active damping with PPF and passive damping with the RLC shunt technique. The active damping technique used for this study combined piezoelectric actuators with fiber optic sensors to achieve simultaneous active control and health monitoring of a test plate. The results of the active damping tests show that piezoelectric materials can provide substantial narrowband and broadband frequency reductions, while at the same time detecting damage on the test plate. More specifically, the test results indicate that smart damping materials can decrease the fundamental mode of vibration of the test plate by 23 dB and detect damage such as a loose bolt in the clamping frame, with the addition of only 0.04 lb of PZT on the test plate. The active damping technique reduced the plate vibrations at each mode within the frequency range of interest, with only one-third the amount of piezoelectric material needed for an RLC shunt circuit technique. / Master of Science