Silvina I. Biagiola

Wiener and Hammerstein uncertain models identification

Block-oriented models have proved to be useful as simple nonlinear models for a vast number of applications. They are described as a cascade of linear dynamic and nonlinear static blocks. They have emerged as an appealing proposal due to their simplicity and the property of being valid over a larger operating region than a LTI model. In the description of these models, several approaches can be found in the literature to perform the identification process. In this sense, an important improvement is to achieve robust identification of block-oriented models to cope with the presence of uncertainty. In this article, we focus at two special and widely used types of uncertain block-oriented models: Hammerstein and Wiener models. They are assumed to be represented by a parametric representation. The approach herein followed allows to describe the uncertainty as a set of parameters which is found through the solution of an optimization problem. The identification algorithms are illustrated through a set of simple examples.

A high gain nonlinear observer: application to the control of an unstable nonlinear process

State estimation has become an important area of research in the field of process engineering. This is because there are many applications that demand the knowledge of many of the state variables, if not all of them. Among others, the implementation of nonlinear control methods as well as monitoring some relevant process variables can be mentioned. The purpose of this paper is to introduce a nonlinear high gain observer in order to estimate the whole process state variables. Whenever some construction conditions hold, it is possible to obtain estimates that converge asymptotically to the actual values. Moreover, this estimator has robust performance in the presence of model uncertainty and measurement noise. A quantitative analysis is developed to measure the observer robustness. Though the estimated states can be used for many purposes, in this work we aim at using the estimates for output regulation. For this goal, a nonlinear controller based on exact linearization is designed. As a particular application, we consider the open-loop unstable jacketed exothermic chemical reactor. This CSTR is widely recognized as a difficult problem for the purpose of control. In order to achieve the control goal, a simple algorithm lying on exact linearization principle is considered. Finally, computer simulations are developed for showing the performance of the proposed nonlinear observer (NO). The performance of the observer when used for control purpose was also evaluated.

An approach for identification of uncertain Wiener systems

As reported in the literature, Wiener models have arisen as an appealing proposal for nonlinear process representation due to their simplicity and their property of being valid over a larger operating region than a LTI model. These models consist of a cascade connection of a linear time invariant system and a static nonlinearity. In the description of these models, there are several ways to represent the linear and the nonlinear blocks, and several approaches can be found in the literature to perform the identification process. In this article, we provide a parametric description for the Wiener system. This approach allows us to describe the uncertainty as a set of parameters. The proposed algorithm is illustrated through a pH neutralization process.

H ∞ control of a Wiener-type system

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.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.

Robust Model Predictive Control of a Wiener-like System

Abstract In this paper, a robust model predictive control for a Wiener-like system is presented. The proposed system consists of a lineal dynamic block represented by Laguerre or Kautz basis followed by a High Level Piecewise Linear function. The results are evaluated on the basis of a simulation of a distillation column.

State estimation in batch processes using a nonlinear observer

This paper deals with the problem of nonlinear states estimation in batch chemical processes. It presents a reduced-order nonlinear observer approach to perform the estimation. The proposed method allows adjustment of the speed of convergence towards zero of the estimation error. The stability properties of the model-based observer are analytically treated in order to show the conditions under which exponential convergence can be achieved. In addition, the performance of the proposed observer is evaluated on batch processes.

CONSTRUCTIVE MPC OF A CLASS OF EXOTHERMIC CSTRs

Abstract In this paper is addressed the problem of controlling a (possible open-loop unstable) CSTR with flow and temperature measurements, with emphasis on the attainment of control robustness, linearity, decentralization, and model independency features. The combination of constructive and MPC ideas yields: (i) an unconstrained controller that is optimal with respect to a meaningful objective function, does not need to the on-line solution of a two-point boundary value problem (TPBVP), and yields the same behavior than the one of a conventional nonlinear MPC, and (ii) a constructive MPC that handles constraints and is simpler and less model dependent than its nonlinear MPC counterpart. The proposed approach is tested with a representative example through simulations.

Identificación Robusta de Modelos Wiener y Hammerstein

Block oriented models have been useful as nonlinear representations for a vast number of applications. They are described as a cascade of linear dynamic and nonlinear static blocks. The main features of these models are their simplicity and the property of being valid over a larger operating region than a LTI model. This paper deals with the identification process of block oriented models in the presence of uncertainty. We focus at two special and widely used types of uncertain Block oriented models: Hammerstein and Wiener models given as parametric representations. The approach herein followed allows to describe the uncertainty as a set of parameters which are obtained by solving an optimization problem. The identification method is illustrated through various examples.

Robustness analysis of Wiener systems

Abstract As reported in the literature, Wiener models have emerge as an appealing proposal for nonlinear processes representation due to their simplicity and the property of being valid over a larger operating region than a LTI model. In this article, we propose a methodology to analyzed the robustness of a typical control scheme. To perform this analysis, we use a parametric description for the Wiener system. This model allows to describe the uncertainty as a set of parameters for the linear and the nonlinear blocks. Then, the linear block uncertainty is considered as a parameter-affine-dependent model and the nonlinear block uncertainty is studied as a conic-sector. The robustness analysis is then performed using μ -theory.

Robust Control of Wiener Systems: A Case Study

The robustness of a typical control scheme for Wiener systems is analyzed. Wiener systems consist of the cascade connection of a linear time invariant system and a static nonlinearity. Several approaches were reported in the literature in order to control this kind of systems. Most of these control schemes involve a transformation of the measured variable as well as the setpoint by using the inverse of the nonlinear gain. As regards the uncertainty in the Wiener model, it is usually described as a partitioned problem. The linear block is considered as a parameter-affine-dependent model. On the other hand, the nonlinear block uncertainty is analyzed as a conic-sector. The robustness evaluation is performed using mu-theory. The results are interpreted on the basis of a simulation of a pH neutralization process