Design of Feedback Systems With Plant Input Rate Saturation via QFT Approach

In this paper, a synthesis approach for input rate saturation compensation of feedback systems is presented. Uncertain, stable plants of type greater than or equal to 1 are considered. Based on Horowitz’s original design for input amplitude saturation (Horowitz, I., 1983) and extensions developed in (Wu, W., and Jayasuriya, S., 1999; Wu, W., and Jayasuriya, S., 2001; Wu, W., 2000) an independent loop around the rate saturating element is introduced for saturation compensation by means of the third DOF (degree of freedom) saturation compensator, $H(s)$⁠. First, the structure of the additional loop transmission is constructed to generate the desired response behavior on a systems recovery from saturation. Second, robust stability and robust performance under the addition of $H(s)$ are investigated. The circle criterion, describing function, and nonovershooting conditions are utilized to generate design constraints. In the end, all design constraints involving saturation compensation are expressed as frequency domain bounds, and the synthesis of saturation compensator $H(s)$ follows from loop shaping methods such as QFT. The proposed approach guarantees input/output stability under saturation for the plant class considered.