Data-Driven Nonlinear Control Design Using Virtual-Reference Feedback Tuning Based on the Block-Oriented Modeling of Nonlinear Systems

Abstract

Process nonlinearities impose difficulties for model identification and control-system design. This paper presents a novel data-driven method for nonlinear control design based on the virtual-reference feedback tuning (VRFT) framework and block-oriented modeling of nonlinear systems. Control-design algorithms for Hammerstein, Wiener, and Hammerstein–Wiener systems were systematically developed. The proposed method can be applied to design a nonlinear controller for an unknown plant directly using one-shot input–output data generated by the plant. In the method, identifying a complete dynamic model of the nonlinear system is not necessary; and only the static non-linearity (or its inverse), represented by the B-spline series, requires estimation. Moreover, in the method, the non-linearity estimation and control design processes are performed simultaneously without the need for nonlinear optimization or iterative procedures. The effectiveness of the proposed control design method is demonstrated herein through several simulation examples, including two benchmark processes (namely, a distillation column and a pH-neutralization process).

Separation identification approach for the Hammerstein‐Wiener nonlinear systems with process noise using correlation analysis

“…The Hammerstein‐Wiener system, which is a linear block with a static nonlinear block at the input and output, respectively, is one of the most common types of block‐oriented systems. A Hammerstein‐Wiener system contains simultaneously Hammerstein system (static nonlinear is followed by linear dynamic block) and Wiener system (linear dynamic block is followed by static nonlinear block), thus its application is widespread and growing, and which has been often implemented to describe the nonlinear dynamics of continuous stirred tank reactor, 3 fermentation bioreactor system, 30 power system 31 and pH neutralization process 32 . Two predominant algorithms have been reported on the Hammerstein‐Wiener systems identification, that is, synchronous identification algorithms 30,33 and separation identification algorithms 3,34,35 .…”

“…A Hammerstein-Wiener system contains simultaneously Hammerstein system (static nonlinear is followed by linear dynamic block) and Wiener system (linear dynamic block is followed by static nonlinear block), thus its application is widespread and growing, and which has been often implemented to describe the nonlinear dynamics of continuous stirred tank reactor, 3 fermentation bioreactor system, 30 power system 31 and pH neutralization process. 32 Two predominant algorithms have been reported on the Hammerstein-Wiener systems identification, that is, synchronous identification algorithms 30,33 and separation identification algorithms. 3,34,35 The synchronous identification algorithms include parameters product term of the static nonlinear block and the linear dynamic block, which leads to many redundant parameters.…”

Data‐driven Learning Algorithm of Neural Fuzzy Based Hammerstein‐Wiener System

“…For this, block-oriented nonlinear models which are composed of linear dynamic block and static nonlinear functions for instance Hammerstein model and Wiener model have been performed on account of their simple structures. The two nonlinear models can approximate nonlinear dynamics of many practical industrial processes applications [1][2][3][4][5][6][7].…”

“…(1) Multisignal theory is designed to employ the Hammerstein-Wiener system to separate parameter learning issues, thereby avoiding redundant parameters (2) The unmeasurable problems of Hammerstein-Wiener system are well settled by using correlation analysis method…”

Modeling and parameter learning method for the Hammerstein–Wiener model with disturbance

“…The Hammerstein and Wiener models represent the most familiar models of the nonlinear block-oriented models. The extension of the Hammerstein and Wiener models is the Hammerstein–Wiener model, which constituted by one dynamic linear block surrounded by two static nonlinear blocks has a great flexibility for describing practical nonlinear systems, such as electric arc furnace system, 19 pH neutralization process, 20,21 continuous stirred tank reactor (CSTR), 22 and fermentation bioreactor system. 23 There is an extensive body of research with regard to various learning algorithms of the Hammerstein–Wiener model, mainly including over-parameterization method, 24 subspace method, 23 blind method, 25 iterative method, 26,27 multi-signal based method, 28 and maximum likelihood method.…”