Simultaneous control of coupled actuators using singular value decomposition and semi-nonnegative matrix factorization
Winck, Ryder Christian
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This thesis considers the application of singular value decomposition (SVD) and semi-nonnegative matrix factorization (SNMF) within feedback control systems, called the SVD System and SNMF System, to control numerous subsystems with a reduced number of control inputs. The subsystems are coupled using a row-column structure to allow mn subsystems to be controlled using m+n inputs. Past techniques for controlling systems in this row-column structure have focused on scheduling procedures that offer limited performance. The SVD and SNMF Systems permit simultaneous control of every subsystem, which increases the convergence rate by an order of magnitude compared with previous methods. In addition to closed loop control, open loop procedures using the SVD and SNMF are compared with previous scheduling procedures, demonstrating significant performance improvements. This thesis presents theoretical results for the controllability of systems using the row-column structure and for the stability and performance of the SVD and SNMF Systems. Practical challenges to the implementation of the SVD and SNMF Systems are also examined. Numerous simulation examples are provided, in particular, a dynamic simulation of a pin array device, called Digital Clay, and two physical demonstrations are used to assess the feasibility of the SVD and SNMF Systems for specific applications.