In this thesis, a novel method for control of over- or under-actuated dynamic systems is developed. The primary control method considered here is Sliding Mode Control which requires an inversion of the control input influence matrix. However on many systems this matrix is non-square, requiring alternate methods in order to the control solution. Some existing solutions for this class of problems include pseudo-inversion such as the Moore-Penrose (which does not allow the design engineer to select the desired state to controlled), dynamic extension (which is difficult to implement on large systems), and pseudo-inverse squaring transform methods. While the squaring transform method solves the key issue in the Moore-Penrose method of not being able to select the desired control state, it still has been limited to systems with only one input. The current effort seeks to extend this squaring transformation method to multiple input systems and demonstrate the control allocation properties of the technique. By extending this method to multiple-input systems the technique becomes applicable to a wider range of real world problems, allowing designers to select and optimally control any desired state on multi-input-multi-output systems. This thesis examines the existing solutions for squaring of input influence matrices such as Moore-Penrose and dynamic extension, the transform method developed in previous work, and derives a multi-input extension to that method and also considers control allocation in the solution process. Simulations are then developed on a two-input, four mass-spring-damper system, and multi-input longitudinal aircraft model to demonstrate the technique and characterize its performance in both sterile and noisy environments.
Library of Congress Subject Headings
Sliding mode control; Airplanes--Motors--Automatic control; Airplanes--Dynamics--Mathematical models; Matrices
Mechanical Engineering (MS)
Department, Program, or Center
Mechanical Engineering (KGCOE)
Marvin, Tim, "Sliding Mode Control of MIMO Non-Square Systems via Squaring Matrix Transforms" (2013). Thesis. Rochester Institute of Technology. Accessed from
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