Wavelet-Based Linearization Method in Nonlinear Systems

And submitted in partial fulfillment of the requirement for the degree of Master of Applied science(mechanical engineering) Complies with the regulations of the university and meets the accepted standards with respct to originality and quality. Approved by Chair of department or graduate program director Dean of Faculty Date iii ABSTRACT The mathematical theories for linear systems provide a unified framework for understanding all possible linear system behaviors but no correspondingly general theoretical ones exist for treating non-linear problems. Due to the inherent nonlinearities of almost physical systems, the subject of nonlinear control is an important area of automatic control. Among many methods to deal with a nonlinear system, the most commonly used one is to linearize it which allows taking advantage of mature linear system control techniques to control the nonlinear systems approximately. This thesis introduces a wavelet-based linearization method to estimate the nonlinear system response based on the traditional equivalent linearization technique. The mechanism by which the signal is decomposed and reconstructed using the wavelet transform is investigated. The properties and characteristics of some famous harmonic wavelet transforms are analyzed. Since the wavelet analysis can capture temporal variations in the energy and frequency content, a nonlinear system can be approximated as a time dependent linear system by combining the wavelet analysis technique with well-known traditional equivalent linearization method. The nonlinear systems including Duffing oscillator and bilinear hysteresis system are used as examples to verify the effectiveness of the proposed wavelet-based linearization method. Results from this study demonstrate that the wavelet linearization approach is more accurate and promising tool compared with traditional equivalent linearization methods in nonlinear control systems in the real world. iv ACKNOWLEDGEMENTS