Nonparametric nonlinear model predictive control

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC

Data filtering-based least squares iterative algorithm for Hammerstein nonlinear systems by using the model decomposition

This paper focuses on the iterative identification problems for a class of Hammerstein nonlinear systems. By decomposing the system into two fictitious subsystems, a decomposition-based least squares iterative algorithm is presented for estimating the parameter vector in each subsystem. Moreover, a data filtering-based decomposition least squares iterative algorithm is proposed. The simulation results indicate that the data filtering-based least squares iterative algorithm can generate more accurate parameter estimates than the least squares iterative algorithm

Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited

On-line costate integration for nonlinear control

The optimal feedback control of nonlinear chemical processes, specially for regulation and set-point changing, is attacked in this paper. A novel procedure based on the Hamiltonian equations associated to a bilinear approximation of the dynamics and a quadratic cost is presented. The usual boundary-value situation for the coupled state-costate system is transformed into an initial-value problem through the solution of a generalized algebraic Riccati equation. This allows to integrate the Hamiltonian equations on-line, and to construct the feedback law by using the costate solution trajectory. Results are shown applied to a classical nonlinear chemical reactor model, and compared against standard MPC and previous versions of bilinear-quadratic strategies based on power series expansions.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Neuman, C.. Universidad Nacional del Litoral; Argentin

Research on RBF neural network model reference adaptive control system based on nonlinear U – model

The overall objective of this study is to design the nonlinear U-model-based radial basis function neural network model reference adaptive control system, through research into a class of complex time-varying nonlinear plants. First, the ideal nonlinear plant is adopted as the reference model and transformed into the U-model representation. In the process, the authors establish the corresponding relationship between the degrees of the reference nonlinear model and the controlled nonlinear plants, and carry out research into the corresponding coefficient relationship between the reference nonlinear model and the controlled nonlinear plants. Also, the impact of the adjusting amplitude and tracking speed of the model on the system control accuracy is analyzed. Then, according to the learning error index of the neural network, the paper designs the adaptive algorithm of the radial basis function neural network, and trains the network by the error variety. With the weight coefficients and network parameters automatically updated and the adaptive controller adjusted, the output of controlled nonlinear plants can track the ideal output completely. The simulation results show that the model reference adaptive control system based on RBF neural network has better control effect than the nonlinear U-model adaptive control system based on the gradient descent method

Research on parallel nonlinear control system of PD and RBF neural network based on U model

The modelling problem of nonlinear control system is studied, and a higher generality nonlinear U model is established. Based on the nonlinear U model, RBF neural network and PD parallel control algorithm are proposed. The difference between the control input value and the output value of the neural network is taken as the learning target by using the online learning ability of the neural network. The gradient descent method is used to adjust the PD output value, and ultimately track the ideal output. The Newton iterative algorithm is used to complete the transformation of the nonlinear model, and the nonlinear characteristic of the plant is reduced without loss of modelling precision, consequently, the control performance of the system is improved. The simulation results show that RBF neural network and PD parallel control system can control the nonlinear system. Moreover, the control system with Newton iteration can improve the control effect and anti-interference performance of the system

ROBUST GENERIC MODEL CONTROL FOR PARAMETER INTERVAL SYSTEMS

A multivariable control technique is proposed for a type of nonlinear system with parameter intervals. The control is based upon the feedback linearization scheme called Generic Model Control, and alters the control calculation by utilizing parameter intervals, employing an adaptive step, averaging control predictions, and applying an interval problem solution. The proposed approach is applied in controlling both a linear and a nonlinear arc welding system as well in other simulations of scalar and multivariable systems