Identification and Control of Wiener Processes: a Direct Synthesis Approach

S.I. BIAGIOLA, O.E. AGAMENNONI, J.L. FIGUEROA

Río de Janeiro, Brasil

Congreso; 4to. Congreso de Ingeniería de Procesos del Mercosur; 2005

In the last decades, a considerable amount of research has been carried out on modeling, identification and control of nonlinear processes. Most dynamical systems can be better represented by nonlinear models, which are able to describe the global behavior of the system over the whole operating range. One of the most frequently studied classes of nonlinear models are the so-called block-oriented nonlinear models. One of this classes are the Wiener Models, formed by a linear time invariant (LTI) system H(z) followed by a static (memoryless) nonlinearity N(.). In this article we are interested in the identification and control of the Wiener models. In order to control the process, we follow the principle of the nonlinear regulator as presented by Wigren (1990). This controller is formed by a nonlinear block (the inverse of the nonlinear gain of the process) and a linear compensator.  In our approach, the linear compensator is designed using a direct synthesis approach (Ogunnaike and Ray, 1994) to satisfy the requirements imposed on the closed-loop time response. To simplify the controller structure, the Wiener model is described in terms of the Laguerre polynomials series for the linear block and a Piecewise Linear function for the nonlinear gain. To accomplish the process identification, the approach by Gómez and Baeyens (2004) is followed. This algorithm is based on the least squares estimation (LSE) and the singular value decomposition (SVD) techniques, and its main benefit is that it allows the direct identification of the nonlinear gain inverse. The performance of the proposed direct synthesis approach is tested via simulation. For this purpose, a pH neutralization reactor is considered.