In order for a piezoelectric transducer to be used as a sensor and actuator simultaneously, a direct charge due to the applied voltage must be removed from the total response in order to allow observation of the mechanical response alone. Earlier researchers proposed electronic compensators to remove this term by creating a reference signal which destructively interferes with the direct piezoelectric charge output, leaving only the charge related to the mechanical response signal. This research presents alternative analog LMS adaptive filtering methods which accomplish the same result. The main advantage of the proposed analog compensation scheme is its ability to more closely match the order of the adaptive filter to the assumed dynamics of the piezostructure using an adaptive first-order high-pass filter. Theoretical and experimental results are provided along with a discussion of the difficulties encountered in trying to achieve perfect compensation of the feedthrough capacitive charge on a piezoelectric wafer. / Master of Science

Magnetic Resonance Elastography (MRE) is an emerging method for non-invasive breast cancer screening. It takes the MRI displacement data output and reconstructs the internal stiffness distribution, where cancerous tissue is approximately five to ten times stiffer than healthy breast tissue. Hence, MRE offers a high contrast solution to this diagnostic problem. Current MRE methods for reconstructing stiffness use forward simulation based optimization methods that are highly non-linear, non-convex and very heavy computationally. This research develops integral-based inverse problem solutions that reformulate the underlying differential equations in terms of integrals of MRI measured displacement data, and this transforms the problem into a linear, convex optimization. All derivative terms in the formulation are removed by special choice of integration limits, so no smoothing or filtering of the input data is required. The resulting equations can easily be solved by linear least squares requiring very minimal computation. 1D inverse algorithms were developed to provide a proof of concept of the integral-based method. Initially, the complete compressible 2D Navier's equations were used to develop the 2D inverse methods. Reasonable results were achieved with the algorithm successfully identifying a 1cm by 1cm tumour with up to 10% noise, data resolution of 20 measured points per cm and actuation frequencies of 100Hz. However, for the same input data set, a simplified incompressible 2D model was used as the basis for the final proposed inverse algorithm. This approach significantly improved results by removing ill-conditioned terms from the original formulation. For a 1cm by 1 cm tumour, accurate results were obtained with up to 40% noise, a range of actuation frequencies and very low data resolution of the order of 2 measured points per cm. These results thus indicate that more crude and less expensive data measurement systems could be used to obtain good results. The methods developed can be readily extended to 3D by applying a similar incompressible integral formulation to the 3D Navier's equations.

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Indiana University-Purdue University Indianapolis (IUPUI) / Some problems of complex systems are internal to the system whereas other problems exist peripherally; two such problems will be explored in this thesis. First, is the issue of excessive jerk from instantaneous velocity demand changes produced by an adaptive cruise control system. Calculations will be demonstrated and an example control solution will be proposed in Chapter 3. Second, is the issue of a non-perfect plant, called an uncertain or corrupted plant. In initial control analysis, the adaptive cruise control systems are assumed to have a perfect plant; that is to say, the plant always behaves as commanded. In reality, this is seldom the case. Plant corruption may come from a variation in performance through use or misuse, or from noise or imperfections in the sensor signal data. A model for plant corruption is introduced and methods for analysis and compensation are explored in Chapter 4. To facilitate analysis, Chapter 2 discusses the concept of system identification, an order reduction tool which is employed herein. Adaptive cruise control systems are also discussed with special emphasis on the situations most likely to employ jerk limitation.