Characterization of Limit Cycle Oscillations Induced by Fixed Threshold Samplers

Abstract

In this work, a generalized study of the conditions for the appearance of limit cycle oscillations induced by any kind of sampler with multilevel fixed thresholds is presented. These kinds of samplers, which will be referred to as Fixed Threshold Samplers (FTS), are characterized by a series of parameters, which, when selected properly, allow obtaining some of the most used forms of quantization in Event-Based Control (EBC). Because of some sampler characteristics, the obtained limit cycle oscillations can present a bias, therefore, to characterize them the Dual Input Describing Function (DIDF) method is used. The obtained DIDF is analyzed revealing some interesting properties allowing to simplify the robustness analysis. The analysis takes into account the effect of the disturbance and reference signal influence on the system, generally overlooked in DF analysis. Guidelines about how to perform the robustness analysis are given, showing their application through some study cases.