• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.3
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• pp.315-321
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• 1988

The input-output relation for nonlinear systems can e explicitly represented by the volterra functional series and it is characterized by the Volterra kernels. A block diagram reduction method is proposed to determine the Volterra kernels for nonlinear differential equations and is compared with the direct substitution techniques. The former method can significantly reduce the computational complexity. A degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.137-140
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• 1999

A lot of researcher have proposed a method of kernel identifying nonlinear system by use of Wiener kernels[6-7] or Volterra kernel[5] and so on. In this research, the authors proposed a method of identifying Volterra kernels for nonlinear system by use of pseudorandom M-sequence in which a crosscorrelation function between input and output of a nonlinear system is taken[4]. we can be applied to an MISO nonlinear system or a system which depends on its input amplitude[2]. But, there exist many systems in which it is difficult to determine a Volterra kernel having the same time coordinate on the crosscorrelation function. In those cases, we have to estimate Volterra kernel by using its neighboring points[4]. In this paper, we propose a new method for not estimating but obtaining Volterra kernel having the same time coordinate using calculation between the neighboring points. Some numerical simulations show that this method is effective for obtaining higher order Volterra kernel of nonlinear control systems.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.597-600
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• 1997

In this paper, the authors propose a new method for linearizing a nonlinear dynamical system by use of polynomial compensation. In this method, an M-sequence is applied to the nonlinear system and the crosscorrelation function between the input and the output gives us every crosssections of Volterra kernels of the nonlinear system up to 3rd order. We construct a polynomial compensation function from comparison between lst order Volterra kernel and high order kernels. The polynomial compensation function is, in this case, of third order whose coefficients are variable depending on the amplitude of the input signal. Once we can get compensation function of nonlinear system, we can construct a linearization scheme of the nonlinear system. That is. the effect of second and third order Volterra kernels are subtracted from the output, thus we obtain a sort of linearized output. The authors applied this method to a saturation-type nonlinear system by simulation, and the results show good agreement with the theoretical considerations.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1443-1448
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• 2003

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impounded by linear models due to the lack of a similarly accepted nonlinear modelling or data based technique. The authors have recently developed a new method for obtaining Volterra kernels of up to third order by use of pseudorandom M-sequence. By use of this method, nonparametric NMPC is derived in discrete-time using multi-dimensional convolution between plant data and Volterra kernel measurements. This approach is applied to an industrial polymerisation process 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.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.26.3-26
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• 2001

Van de Vusse reactor is known as a highly nonlinear chemical process and has been considered by a number of researchers as a benchmark problem for nonlinear chemical process. Various identification methods for nonlinear system are also verified by applying these methods to Van de Vusse reactor. From the point of view of identification, only the Volterra kernel of second order has been obtained until now. In this paper, the authors show that Volterra kernels of nonlinear Van de Vusse reactor of up to 3rd order are obtained by use of M-sequence correlation method. A pseudo-random M-sequence is applied to Van de Vusse reactor as an input and its output is measured. Taking the cross correlation function between the input and the output, we obtain up to 3rd order Volterra kernels, which is ...

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.527-530
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• 1994

A method for obtaining Volterra kernels of a nonlinear system by use of pseudorandom M-sequences and correlation technique, proposed by the authors in 1993, is further analysed and some applications for identifying nonlinear system having feedback loop are shown.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.470-470
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• 2000

This paper describes a new method of identifcation of backlash nonlinear systems by use of M-sequence correlation method. In this method, we can obtain not only Volterra kernels of up to 3rd order of the nonlinear system, but also the width of the backlash element from observing the crosscorrelation between the input and the output. Here strictly speaking, a multi-valued nonlinear system such as backlash element can not be expressed by Volterra kernel representation mathematically. But in practice, we encounter many cases where it is difficult to treat them mathematically but they can be controlled from experience. So we here dare to suppose that backlash nonlinear system can be approximated by Volterra kernel representation. Simulations are carried out on a nonlinear system consisting of linear part plus backlash element. And Volterra kernels are measured. The output calculated from the observed Volterra kernels is in good agreement wi th the actual output. And we show that we can obtain the width of backlash element, which is one of the most important parameters, by observing the maximum value of crosscorrelation function between the input M-sequence and the output.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.280-284
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• 1998

Many classes of nonlinear systems can be represented by Volterra kernel expansion. Therefore, identification of Volterra kernels of nonlinear system is an important task for obtaining the nonlinear characteristics of the nonlinear system. Although one of the authors has recently proposed a new method for obtaining the Volterra kernels of a nonlinear system by use of M-sequence and correlation technique, our mettled of nonlinear system identification is limited to Wiener-type nonlinear system and we can not apply this method to the identification of Hammerstein-type nonlinear system. This paper describes a new mettled for obtaining Volterra kernels of Hammerstein nonlinear system by adding a linear element in front of tile Hammerstein system. First we calculate the linear element of Hammerstein system by use of conventional correlation method. Secondly, we put a linear element in front of Hammerstein system. Then the total system becomes Wiener-type nonlinear system. Therefore we can use our method on Volterra kernel identification by use of M-sequence. Thus we get the coefficients of the approximation polynomial of nonlinear element of Hammerstein system. From the results of simulation, a good agreement with theoretical considerations is obtained, showing a wide applicability of our method.

• Korean Journal of Optics and Photonics
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• v.23 no.6
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• pp.246-250
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• 2012

We derive analytical expressions for the output spectral density and the noise power $P_{\beta}$ in noise loading analysis using Volterra kernels to characterize fiber nonlinearities. The bandwidth of the input noise source has little effect on $P_{\beta}$, but the power of the input noise source and the dispersion parameter value of the fiber have a significant effect on $P_{\beta}$. The Volterra method predicts ${\Delta}P_{\beta}[dB]$ = 30 dB/decade, which agrees very accurately over a wide range of fiber parameters compared with the numerical results by the split-step Fourier method. Therefore the Volterra method could be useful to predict the performance of a dense WDM system when we plan to upgrade fiber or increase signal power.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.26.2-26
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• 2001

It is known that Volterra kernel model can represent a wide variety of nonlinear chemical processes. But almost all Volterra kernel models which appeared in the literature are up to second order, because it was difficult to measure higher order Volterra kernels. Kashiwagi has recently shown a method for measuring Volterra kernels up to third order using pseudorandom M-sequence signals. In this paper, the authors verified the applicability of this method for chemical processes using polymerization reactor simulation. Also, the authors have recently proposed a practical Identification method for chemical processes, which is based on the combination of off-line nonlinear identification and on-line linear identification. This method is also applied to the identification of polymerization reactor, and we obtained ...