José L. Figueroa

A nonlinear model predictive control system based on Wiener piecewise linear models

Abstract In this paper a nonlinear model predictive control (NMPC) based on a Wiener model with a piecewise linear gain is presented. This approach retains all the interested properties of the classical linear model predictive control (MPC) and keeps computations easy to solve due to the canonical structure of the nonlinear gain. Some guidelines for the identification of the nominal model as well as the uncertainty bounds are discussed, and two examples that show the possibility of application of this control scheme to real life problems are presented.

Economic impact of disturbances and uncertain parameters in chemical processes—A dynamic back-off analysis

Abstract Optimal operating conditions in chemical plants are characterized by operation on a number of active constraints. The presence of disturbances and model uncertainties can easily cause constraint violations. Thus, it is necessary to move the operating point away from the active constraints into the feasible region (back-off). Recently a strategy for detemining the necessary open-loop steady-state back-off from the nominal optimum has been developed by the authors, which consists of solving a joint steady-state optimization-flexibility problem. This paper extends these ideas to consider dynamic situations, thus leading to a joint dynamic optimization-flexibility problem. Having determined the economic penalty associated with open-loop back-off in dynamic systems, the next step is to estimate the potential recovery of this penalty that various control schemes might provide. The proposed approach also includes the optimization of the controller parameters. Results are given for a simple flowsheet example.

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.

Identification of uncertain MIMO Wiener and Hammerstein models

Abstract Several approaches can be found in the literature to perform the identification of block oriented models (BOMs). In this sense, an important improvement is to achieve robust identification to cope with the presence of uncertainty. In this work, two special and widely used BOMs are considered: Hammerstein and Wiener models. The models herein treated are assumed to be described by parametric representations. The approach introduced in this work for the identification of the multiple input–multiple output (MIMO) uncertain model is performed in a single step. The uncertainty is described as a set of parameters which is found through the solution of an optimization problem. A distillation column simulation model is presented to illustrate the robust identification approach. This process is an interesting benchmark due to its well-known nonlinear dynamics. Both Hammerstein and Wiener models are used to represent this plant in the presence of uncertainty. A comparative study between these models is established.

An algorithm for robust pole assignment via polynomial approach

A computational method for designing controllers which attempt to place the roots of the characteristic polynomial of an uncertain system inside some prescribed regions is presented. The analysis is based on transfer functions of characteristic polynomials, and the problem is formulated as one of semi-infinite programming. An example of an application is given to illustrate this approach. >

Efficient Nonlinear Wiener Model Identification Using a Complex-Valued Simplicial Canonical Piecewise Linear Filter

This paper proposes an efficient adaptive realization of the Wiener model for the identification of complex-valued nonlinear systems. Using a two-dimensional simplicial canonical piecewise linear filter for the complex-valued nonlinear mapping, we derive a realization of the Wiener model requiring fewer parameters than previous approaches. An adaptive implementation of the proposed Wiener model is derived, and local convergence analysis for the updating algorithm is presented. The tradeoff between computational complexity and modeling performance is discussed. Simulations of a system identification example show that the proposed algorithm can provide similar or better performance than other approaches in terms of computational complexity, convergence speed, and final mean-squared error (MSE)

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.

Receiver-side nonlinearities mitigation using an extended iterative decision-based technique

This work presents an iterative receiver cancellation technique for mitigating the inband distortion introduced by a nonlinear wideband transmitter power amplifier (PA). The proposed decision-based technique employs a Wiener-Hammerstein model that accounts for the nonlinear transfer function and memory of the PA as well as for the wireless propagation channel. As such, the mitigation technique can be seen as a generalization of existing iterative decision-based techniques assuming memoryless PA nonlinearities. For successful distortion mitigation, the iterative technique requires an estimate of the nonlinear model that characterizes the PA. We propose to perform this model identification at the receiver, embedded in an iterative decision-based scheme, avoiding the nonideal analog-to-digital feedback loop associated with transmitter-based model identification. A stochastic algorithm is proposed for the model identification providing the necessary PA model parameters required for symbol detection. In addition, we analyze the convergence properties of the proposed technique. Simulation results confirm that the proposed mitigation technique provides distortion cancellation at almost the same level to the case of perfect knowledge of the PA model. These results enable us to employ power amplifiers with more relaxed linearity requirement, moving the operation point to a region with improved power efficiency while reducing the system overall degradation.