Closed loop vibrational control: Theory and applications.

This thesis addresses the problem of controlling a plant where conflicting control objectives must be achieved with an insufficient number of actuators. One possible approach is the frequency separation, i.e. the utilization of low and high frequency control signals so that on the average all the control objectives are satisfied. Within this methodology, the resulting equations have control signals entering the open loop dynamics as amplitudes of periodic, zero average functions, and these amplitudes can be chosen to depend on the system's states or the outputs. Such a structure is referred to as closed loop vibrational control. In this thesis, the stabilizability properties of closed loop vibrational control are analyzed and the pole placement capabilities are investigated. The robustness qualities and disturbance rejection capabilities are considered. Synthesis of vibrational controllers to achieve desired specifications is also discussed. Using the idea of closed loop vibrational control, we analyze the helicopter vibration suppression problem with Higher Harmonic Control (HHC). It is well known that for HHC to be effective, not only the amplitude but also the phase of oscillations introduced has to be chosen appropriately, depending on the flight conditions. We show that if the frequency of oscillations used in HHC is much greater than N/rev (N is the number of rotor blades), the phase dependency disappears. To distinguish this approach from HHC, we call it Very High Harmonic Control (VHHC). We present a simple model of the helicopter and a hypothetical explanation of the efficacy of VHHC. Finally, since periodic controllers are known to relocate control loop zeros, we give a solution to the zero placement problem for open and closed loop system and characterize control-theoretic properties of the resulting system. Although the problem of optimal pole placement has received enormous attention during the last 30 years, that of optimal zero placement has been relatively neglected in control systems research. This latter problem could however be of substantial importance not only in the context of vibrational control but also in the placement of actuators and sensors in control systems.PhDElectrical Engineering : SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/103828/1/9409784.pdfDescription of 9409784.pdf : Restricted to UM users only