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Block-oriented models (BOMs) have shown to be appealing and efficient as nonlinear representations for many applications. They are at the same time valid and simple models in a more extensive region than time-invariant linear models. In this work, Wiener models are considered. They are one of the most diffused BOMs, and their structure consists in a linear dynamics in cascade with a nonlinear static block. Particularly, the problem of control of these systems in the presence of uncertainty is treated. The proposed methodology makes use of a robust identification procedure in order to obtain a robust model to represent the uncertain system. This model is then employed to design a model predictive controller. The mathematical problem involved in the controller design is formulated in the context of the existing linear matrix inequalities (LMI) theory. The main feature of this approach is that it takes advantage of the static nature of the nonlinearity, which allows to solve the control problem by focusing only in the linear dynamics. This formulation results in a simplified design procedure, because the original nonlinear model predictive control (MPC) problem turns into a linear one. [ABSTRACT FROM AUTHOR]

A Wiener system is a system which can be modelled as a linear dynamic followed by a static gain. The goal of this paper is to develop a robust H ∞ compensator for controlling an SISO Wiener system. The controller also takes the form of a Wiener model. The design approach consists of the approximation of the non-linear gain using a piecewise linear (PWL) function and in using a linear controller for each sector obtained from this approximation. Therefore, the general controller structure can be stated as a linear dynamic compensator in series with a PWL static gain. As an illustrative case, a neutralization pH reaction between a strong acid and a strong base in the presence of a buffer agent is dealt with. Computer simulations are developed for showing the performance of the proposed controller. [ABSTRACT FROM AUTHOR]