Dynamic inversion of underactuated systems via squaring transformation matrix

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Title: Dynamic inversion of underactuated systems via squaring transformation matrix
Author: Schkoda, Ryan
Abstract: In this thesis, a novel method for control of non-square dynamical systems using a model following approach is developed. Control methodologies such as dynamic inversion and sliding mode control require an inversion of the input influence matrix. However, if the system input influence matrix is non-square direct inversion is not possible. Pseudo inversion of the input influence matrix may be performed for control allocation. However, pseudo inversion limits the control to states where the controller is directly applied. The pseudoinverse method does not permit the engineer to designate a particular state to control or track. When accurate tracking of states that are not directly controlled (“remaining states”) is required the pseudo inversion method is not useful. Current methods such as dynamic extension can be used to generate a square input influence matrix, essentially, creating an input influence matrix that is invertible. However, this method is tedious for large systems. In this work, a new transformation is applied to the original dynamical system model to develop an input influence matrix that is square. Assuming the system is controllable, the proposed transformation allows for accurate tracking of selectable states. Selection of the new transformation matrix is used to develop accurate tracking of certain states compared to the remaining states. A method based on optimal control theory is used to define the transformation matrix. The new approach is first applied to control a two mass system with simulation results presented showing the advantage of the proposed new control strategy. Finally, simulation results are presented for longitudinal control of an aircraft using one control input.
Record URI: http://hdl.handle.net/1850/5282
Date: 2007-11

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