Non-Collocation Problems in Dynamics and Control of Mechanical Systems

Characteristics of mechanical systems with non-collocated sensors and actuators are investigated. Transfer function zeros location as a function of sensor position, zero-pole interlacing, and re-location of zeros are discussed in a context of presented examples. Some of the presented examples involving non-collocation are supported by experimental data. A case study involving a high speed machining spindle is examined. The control problems associated with non-collocation are studied along with the methods to solve the

CHARACTERIZATION AND ENHANCEMENT OF SENSING PROPERTIES OF PIEZOELECTRIC MATERIALS WITH APPLICATIONS TO VIBRATION SUPPRESSION

This thesis undertakes the study of piezoelectric properties of polymer-based fabric and film sensors. An enhancement in piezoelectric properties of such sensors, as noted through earlier work, is observed with increasing weight ratios of nanomaterials dispersed in the polymer matrix. A comprehensive mathematical model using cantilever beams is developed to analyze this enhancement both qualitatively and quantitatively. An experimental setup is also developed to implement the proposed real time signal processing necessary to collect required data towards the characterization. In order to distinguish piezoelectric materials from other materials, study of the frequency response of developed fabric sensors to periodic chirp type actuation signals, is also established. Linear Euler-Bernoulli beam theory is used, to model piezoelectric actuation of cantilever beams. The theory has been extended to integrate piezoelectric sensing with the governing equations of motion to obtain a numerical solution to the governing partial differential equation of motion. All equations are derived using a distributed-parameters model applying the extended Hamilton Principle. Results obtained are compared to base values from literature for known materials. Piezoelectric materials are also known to possess bi-stiffness properties, having a higher modulus of elasticity in their open circuit configuration as compared to that in their short circuit configuration. Through research, it has been observed that the weight ratio of dispersed nanomaterials does not affect the piezoelectric properties alone but also has an effect on the mechanical properties and beyond a threshold, established for every polymer analyzed, the increase in the tensile properties of the fabric developed cannot be ignored. This study is extended to analyze the enhancement in the difference between the two moduli of elasticity for the fabric sensors in their respective configurations. The bi-stiffness elements can be used effectively to suppress vibrations implementing a semi-active vibration damping method known as `Switched Stiffness\u27. This concept is studied in regard to continuous systems, and the underlying principle of switching between two configurations is mathematically modeled. The developed control law for vibration suppression is then integrated using non-contact type measurement of tip deflection to suppress vibrations induced in cantilever beams, using the fabric sensors developed at Clemson University. The damping characteristics have been analyzed to study the enhancement in the difference between the higher and lower stiffness values and qualitative conclusions are drawn. Using the mathematical modeling developed to implement the `Switched Stiffness\u27 concept, a novel method to measure the coupling coefficient, k31, a characteristic constant for piezoelectric materials, is established and validated. The results of this measurement are used to decouple the piezoelectric properties from the mechanical properties and a generalized framework to completely characterize piezoelectric materials towards other constants has been proposed