A Wiener Neural Network-Based Identification and Adaptive Generalized Predictive Control for Nonlinear SISO Systems

Abstract

In this study, a Wiener-type neural network (WNN) is derived for identification and control of single-input and single-output (SISO) nonlinear systems. The nonlinear system is identified by the WNN, which consists of a linear dynamic block in cascade with a nonlinear static gain. The Lipschitz criteria for model order determination and back propagation for the adjustment of weights in the network are presented. Using the parameters of the Wiener model, the analytical expressions used in the controller, generalized predictive control (GPC) is modified every time step, to handle the nonlinear dynamics of the controlled variable. Finally, the proposed WNN-based GPC algorithm is tested in simulation on several nonlinear plants with different degrees of nonlinearity. Simulation results show that WNN identification approach has better accuracy, in comparison to other neural network identifiers. The WNN-based GPC has better control performance, in comparison to standard GPC. ' INTRODUCTIONWiener and Hammerstein models are the most known and most widely used for modeling of various processes, such as chemical processes, 1À3 separation processes, 4 hydraulic systems, 5 and chaotic systems. 6,7 In Wiener modeling, a linear dynamic block precedes a nonlinear steady-state one, while Hammerstein models contain the same elements in the reverse order . 8 These types of models are called block-oriented nonlinear models. 9 Unlike black-box models, the block-oriented models have a clear physical interpretation: the steady-state part describes the gain of the system. 10 Artificial neural network (ANN) models have been successfully applied to the identification and control of a variety of nonlinear dynamical systems and processes. Many researchers have integrated neural networks with Wiener and Hammerstein model structures, to formulate the system static nonlinearities. proposed an identification model using a hybrid model consisting of a linear autoregressive moving average (ARMA) model in cascade with a multilayer neural network. The multilayer network was used to represent the dynamic linear block and the static nonlinear element of Wiener model, respectively. For identifying a chaotic system, Chen et al. 6 used a simple linear model to represent the dynamic part and a neural network to represent the nonlinear static part. Also, the dynamic linear part was replaced by Laguerre filters and the nonlinear static part was described as a neural network. 4 T€ otterman and Toivonen 12 used support vector regression to identify nonlinear Wiener systems; the linear block is expanded in terms of Laguerre or Kautz filters, and the static nonlinear block is determined using support vector machine regression. This multiple-input and multiple-output (MIMO) Wiener model has been used for identification of the chromatographic separation process. In addition, some researchers tried to formulate the dynamic linear part and nonlinear static part of the Wiener or Hammerstein model, using a multilayer neural network. Janczak 13 designed a neural n...

Nonlinear Model Predictive Control for pH Neutralization Process based on SOMA Algorithm

“…Different forms are used to describe the nonlinear block for Wiener model starting from the simple polynomial form [19], [28] to more complex description Neural network [19], [15], support vector machine [16]. In this work the nonlinear static block of the Wiener model is given by a feed-forward neural network as adpoted in [15].…”

“…In [18], [19], the minimization problem is converted into a linear one in the case of a simple polynomial description of the nonlinear block. In this case, the nonlinearity is removed by considering the inverse of the polynomial function.…”

“…Many structures are used to describe the steady state block : Polynomial, [14], [27], support vector machine [16], neural network [8], [15], [19], cubic spline [18]. In this work, the nonlinear block is represented by a feed forward Neural Network (NN).…”

Nonlinear predictive control of dynamic systems represented by Wiener–Hammerstein models

“…It is also possible to use the linearised model for calculation of the free trajectory [22]. It is necessary to stress the fact that the MPC-NPSL algorithm does not require an inverse model of the nonlinear steady-state part of the model, as it is necessary in the MPC algorithms with on-line model linearisation for cascade Wiener [19][20][21] and Hammerstein [15][16][17] systems, respectively.…”

“…It is also possible to find on-line a linear approximation of the model for current operating conditions and next use the linearised model in MPC [12,18] or find directly a linear approximation of the predicted trajectory [12]. MPC algorithms for the Wiener structure (a linear dynamic block followed by a nonlinear steady-state one) with an inverse of the steady-state part are discussed in [19][20][21], MPC approaches with on-line model linearisation are discussed in [12,22,23], and MPC approaches with on-line trajectory linearisation are discussed in [12,23]. In case of the three-block cascade models of the Hammerstein-Wiener type (a linear dynamic block sandwiched by two nonlinear steady-state ones), MPC algorithms with an inverse of the steady-state parts are detailed in [24,25], and MPC with on-line trajectory linearisation is discussed in [26].…”