Modeling and control of Wiener-type processes

We develop a simple relay feedback method to identify Wiener-type nonlinear processes. It separates the identification problem of the nonlinear static function from that of the linear dynamic subsystem to simplify the identification procedure significantly. Owing to the separation, the unmeasurable output of the linear dynamic subsystem can be obtained in a straightforward manner. Then, determining the model structure of the nonlinear static function becomes very simple and the estimates are robust to additive output noises. We can identify the whole activated region of the nonlinear static function as well as the ultimate information of the linear dynamic subsystem from only one relay feedback test. More information on the linear dynamic subsystem can be estimated by well-established linear system identification methods from additional tests. We use a nonlinear control strategy to compensate the nonlinear dynamics of the Wiener process so that the design parameters can be determined by usual tuning rules developed for linear processes and a high control performance can be achievable as in linear processes.