Identification of extended Hammerstein systems for modeling sticky control valves under general types of input signals

This paper is motivated by modeling the control valve stiction phenomena in feedback control loops. An extended Hammerstein system with discretized Preisach model as the input nonlinearity is proposed to capture hysteretic dynamic behaviors of cascading systems consisting of control valves followed by linear dynamic subsystems. An iterative method is presented to identify the extended Hammerstein systems. An informative input needs to have multiple local extreme values in order to ensure the discretized Preisach model identifiable. However, if only a single hysteresis loop of the discretized Preisach model is in active, then an oscillatory input with only two extreme values is shown to be persistently excited for identification. Hence, the proposed identification method for extended Hammerstein systems is applicable to general types of inputs as well as oscillatory ones. Two industrial examples are provided to demonstrate the effectiveness of the proposed identification method for extended Hammerstein systems.