A QFT design methodology for feedback systems with input rate or amplitude and rate saturation

In this paper, a feedback system design methodology for a plant subject to input rate saturation, or both amplitude and rate saturation is presented. Based on Horowitz´s original 3DOF design (Horowitz, 1983) and extensions developed in (Wu and Jayasuriya, 1999; 2000; Wu, 2000), the structure of the additional loop transmission around the rate saturating element is first proposed for designing the 3rd DOF, H_r (s), using the 3DOF non-interfering loop structure. Robust stability and performance are investigated. The circle criterion, describing function, and non-overshooting conditions are utilized to obtain design constraints. In the case of having both amplitude and rate saturation, approaches developed for amplitude and rate saturation respectively are combined into one method. It results in a 4DOF feedback system with two extra DOFs: H_a(s) and H_r(s). Finally, all these design constraints are expressed as frequency domain bounds and synthesis follows from loop shaping methods such as QFT. This methodology applies to type I or higher stable and neutrally stable plants