ADAPTIVE CONTROL FOR THE POSITION OF MAGNETIC PARTICLES USING MAGNETIC TRAPS by

Magnetic traps are an important instrument for analyzing the behavior of systems and biological processes. They manipulate magnetic particles by applying a force under the influence of magnetic fields. Controlling the position of the magnetic particle for single molecule studies is difficult due to the complexity of the instrument because its dynamics can change per experiment. This results in users spending an immense amount of time designing compensators to meet experimental requirements, yielding insufficient time spent concentrating on the experiment. One method to alleviate users of designing compensators is to incorporate adaptive control methods into the design of magnetic traps. Adaptive control is able to adjust the parameters of the compensator to ensure the performance of the instrument meets specific requirements. The magnetic particle constantly moves from the Brownian disturbances acting upon it. These disturbances can be minimized by using an adaptive Q-parametrized compensator structure with LMS to minimize a frequency weighted version of the displacement of the magnetic particle for low frequencies. An adaptive Q-parametrized compensator structure was incorporated into the design of the magnetic trap, resulting in the position of the magnetic particle being stabilized, the effects of the Brownian disturbances being reduced, and the dynamics of the instrument changing into account. The displacement of the magnetic particle due to the Brownian disturbances was suppressed more as the number of FIR weights increased than using the nominal adaptive compensator. 1 Design specifications that the various compensation methods must achieve. . 39 2 Parameters for the functional form of the second order underdamped system. 39 3 Numerical values for the parameters of the magnetic trap transfer function. . 50 4 Numerical values for the function form of the magnetic trap transfer function, the transconductance amplifier, and the overall continuous-time magnetic par-6 The gain used to modify the control signal to use the dynamic range of the dSpace boards using the adaptive Q-parametrized compensation methods. . 102 vii LIST OF FIGURES 1 Schematic of the forces applied to a magnetic particle suspended in a fluid 3 Magnetic fields from each electromagnet for one dimensional analysis where L is the distance between electromagnets, and B 1 and B 2 are the magnitude of 5 Schematic of the optical system to translate the angular intensity of the reflected light: The laser is expanded then enters the optical path of the microscope by a dichroic mirror. The backward scattered light is redirected by …