Hammerstein Box-Jenkins System Identification of the Cascaded Tanks Benchmark System

Ibrahim A Aljamaan,David T Westwick,Mujahed M Al-Dhaifallah,Tirivanhu Chinyoka

doi:10.1155/2021/6613425

Abstract

A common process control application is the cascaded two-tank system, where the level is controlled in the second tank. A nonlinear system identification approach is presented in this work to predict the model structure parameters that minimize the difference between the estimated and measured data, using benchmark datasets. The general suggested structure consists of a static nonlinearity in cascade with a linear dynamic filter in addition to colored noise element. A one-step ahead prediction error-based technique is proposed to estimate the model. The model is identified using a separable least squares optimization, where only the parameters that appear nonlinearly in the output of the predictor are solved using a modified Levenberg–Marquardt iterative optimization approach, while the rest are fitted using simple least squares after each iteration. Finally, MATLAB simulation examples using benchmark data are included.

Highlights

System identification attracted the attention of many researchers and practitioners because of the difficulty in modeling many systems using physical modeling approaches
A prediction error minimization (PEM) nonlinear system identification parametric approach, similar to the one proposed in [10], is applied to approximate the two-tank cascaded model, where the benchmark data provided by Schoukens et al [26] were used. e main contribution is to use such general nonlinear model structure, Hammerstein Box-Jenkins model, and separable least squares (SLS) identification approach to predict the parameters of cascaded tanks system. e suggested model structure to fit this application is Hammerstein Box-Jenkins model, where a static nonlinearity is in series with a linear dynamic filter whose output is summed with an autoregressive moving average (ARMA) noise model
MATLAB simulation examples using two datasets of 1024 points each, identification and validation data, were provided by Vlaar et al [15]. ese datasets were collected from the cascade tanks system shown in Figure 2. e input u (t) is a multisine signal, which is the voltage applied to pump the water from the reservoir to the upper tank with frequency range between 0 and 0.0144 Hz and sampling time Ts equal to 4 seconds. e water level of the lower tank is the output of the system, y (t), with signal to noise ratio, SNR, approximately equal to 40 dB

Summary

Introductions

System identification attracted the attention of many researchers and practitioners because of the difficulty in modeling many systems using physical modeling approaches. Unlike the nonlinear state-space method proposed by Relan et al [1], Birpoutsoukis et al [14] developed a nonparametric Volterra series-based approach. In this latter method, cancelling the undesired transient part played an important role in minimizing the error. A prediction error minimization (PEM) nonlinear system identification parametric approach, similar to the one proposed in [10], is applied to approximate the two-tank cascaded model, where the benchmark data provided by Schoukens et al [26] were used. E main contribution is to use such general nonlinear model structure, Hammerstein Box-Jenkins model, and separable least squares (SLS) identification approach to predict the parameters of cascaded tanks system.

Problem Definition

Preliminary

Experimental Results

Method

Conclusions