Compact LFT-LPV modeling with automated parameterization for efficient LPV controller synthesis

Abstract

A systematic approach to the derivation of Linear Fractional Transformation (LFT)-based Linear Parameter-Varying (LPV) representations for descriptor systems is proposed. Explicit compact rational and affine representations with full non-square parameter blocks are formulated. Based on these, LPV parameterizations of the blocks are then derived automatically via a Principle Component Analysis (PCA)-based algorithm that only requires model coefficients and allows straightforward approximation of LFT-LPV models. A two-stage multiplier approach is employed during controller synthesis, which ensues low synthesis and implementation complexity compared to standard approaches. The methodology is applied to a three-degree of freedom (3-DOF) robotic manipulator, which shows improved performance at lower implementation complexity compared to previously published results.