Modelling, Control and Estimation Techniques For Micromachined Electrostatic Actuators Using Macro Magnetic Actuators
Type of DegreePhD Dissertation
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Parallel plate actuators (PPAs) are fundamental devices in micro-electro-mechanical systems. PPAs' main drawback is their limited open loop stable traveling range which is caused by their nonlinear electrostatic force. Thus, feedback control techniques are required in applications which need large and precision motions. However, controlling and analyzing PPAs' behavior could be limited by several factors. The fabrication process of PPAs is expensive; the miniatured dimension of PPAs makes motion detection and experimental setup difficult. This dissertation proposes an alternative approach to prototype analysis, control and estimation techniques for PPAs by investigating PPAs' dual systems, which are macro magnetic type solenoids. Solenoids have the similar kinematics and their stable traveling range is affected by the nonlinear magnetic force. As a test component, the advantages of solenoids include the low cost and macro size which is convenient to package and detection. An iterative solution method is developed to study the behaviors of the actuators in circuity environment. First, the expressions of the time-variant capacitor in a PPA, AC source and their derivatives with respect to time are determined. An approximated solution combining the initial solution and its iteratively derived higher-order terms is reached. Then, the time-variant inductor in a solenoid with a restrained condition that the circuit is powered by DC sources is modeled. The iterative solution using a small signal theorem is also employed to obtain an approximate closed form solution for the time variant inductor. The simulation and experimental study further demonstrated that: (i) this iterative solution can effectively analyze the dynamics of the square law devices with a time-variant capacitor or inductor; and (ii) computing additional higher-order terms derived from the initial solution can further improve the solution’s accuracy. A practical disturbance controller is developed to extend stable range of solenoids, which could be also extended to PPAs. The input–output linearization control method is an effective technique to extend the stable range. But in practice, however, the time-delay effect from both measurement and actuation can make the system less damped and therefore more sensitive to disturbances. This effect was analyzed and a digital proportional and integrator controller plus extended state observer (ESO) is proposed to enhance the performance of the electromagnetic actuator. Simulation and experimental tests show that this combined proportional and integral and ESO technique can extend the stable range of motion to 77.6 \% of full stroke with less sensitivity to external disturbances. The feasibility of transplanting self sensing from solenoids to PPAs is investigated. The observability improvement of PPA design is investigated. This study proposes an alternative approach of designing an estimator using the measured voltage across the PPA without additional sensing structures and distortions. This novel method can improve the performance and reduce the device's footprint with full state (displacement and velocity) feedback information, using a series resistor. A system model using this configuration is investigated. The observability of this self-sensing technique is analyzed using a small signal model. Then, a singular value decomposition (SVD) is applied to examine how to further improve the observability by choosing appropriate parameters. Simulation and numerical studies were performed which validate this method.