LQ Previewed Tracking for Biproper Systems

Abstract

In linear quadratic previewed control, strictly proper systems are used for tracking performance by the feedforward control proportional to the measurable exogenous input. However, state space models that employ sensors to measure exogenous inputs are sometimes biproper. A classical example for biproper system is a small aircraft regulation in cruise condition where the gust inputs are measured but the ride quality is deteriorated. For such systems, the previewed control with a biproper system is required. In this paper, the procedure for strictly proper system is extended and a modified Riccati matrix differential equation for biproper system is presented.