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UBC Theses and Dissertations

Nanovibration control Greenall, Russ

Abstract

This thesis explores techniques to actively control the position of large masses such as focusing magnets with precision on the order of 1 nm against vibrations. The technique applied (labeled as an "optical anchor") is to actively "stiffen" the support structure using an optical interference method to measure distance to a remote reference point. The magnet is modeled as a mass on a spring, with a piezo electric actuator. In this model, proportional and differential control applied to the piezo allows the mass to be critically damped and the spring coefficient to be arbitrarily increased. A digital implementation with finite sampling rate has a finite stable region in control parameter space. If there are more mechanical degrees of freedom, the stable region and the quality of control can be greatly reduced. An interferometric instrument design for remote distance measurement is discussed and measurement results reflecting an accuracy of 0.2nm RMS are demonstrated. The instrument requires only two light detectors in a Michelson interferometer configuration. The algorithm design is implemented at a 5KHz sample rate using a circa 2000 DSP processor with 4-byte floating point operations running at a 40 MHz clock rate. Control tests on a one degree-of-freedom experimental platform are performed using proportional and differential control. These tests demonstrate active control which significantly damps fundamental mode excitations but are insufficient to stiffen the system. More sophisticated models and algorithms will be necessary. Nevertheless, some insight is gained into techniques which will allow control on the nanometer scale against "standard" ground vibrations. In particular, a successful implementation of coherent ground disturbance modeling provides a three-fold reduction in RMS vibration of our test system over our simple PID control.

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