Use of dimensional analysis to reduce the parametric space for gain-scheduling

Abstract

A simple method is presented to reduce the number of scheduling parameters for gain-scheduled controller implementation. The method is based on careful reformulation of the dynamic representation using dimensionless parameters. Parameter re-scaling is necessary to transform from one unit system to another, and this work utilizes unit transformations carefully to act as an implicit method of gain scheduling. The choice of a dimensionless formulation of the parameters simplifies the system representation because the number of dimensionless parameters will always be less than or equal to that in the classical representation. The resulting dimensionless gain-scheduling problem can greatly reduce the complexity of the classical gain-scheduling formulation, potentially even reducing an LPV problem in the classic domain to a zero-parameter or LTI controller design problem in the dimensionless domain. The dimensionless gain-scheduling method is demonstrated using a gantry system with the objective of minimizing the swing of the load.