Isola in a linear one-degree-of-freedom feedback system with actuator rate saturation

This short communication uses numerical continuation to highlight the existence of an isola in a simple 1 degree-of-freedom harmonically-forced feedback system with actuator rate limiting as its only nonlinear element. It was found that the isola (1) contains only rate-limited responses, (2) merges with the main branch when the forcing amplitude is sufficiently large, and (3) includes stable solutions that create a second attractor in regions where rate limiting is not expected. Furthermore, the isola is composed of two solutions for a given forcing frequency. These solutions have the same amplitudes in the state (pitch rate) projection; however, they have distinct phases, and their amplitudes are also distinct when projected onto the integrator state in the controller. The rich dynamics observed in such a simple example underlines the impact of rate limiting on feedback systems. Specifically, the combination of feedback and rate-limiting can create detrimental dynamics that is hard to predict and requires careful analysis.