• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.271-274
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• 1998

This paper describes a new method for separation of the Volterra kernels which are identified by use of M-sequence. One of the authors has proposed a method for identification of Volterra kernels of nonlinear systems using M-sequence and correlation technique. When M-sequence are applied to a nonlinear systems, the cross-correlation function between the input and the output of the nonlinear systems includes cross-sections of high-order Volterra kernels. However, if various order Volterra kernels exixt on the obtained cross-correlation function, it is difficult to separate the Volterra kernels. In this paper, the authors show that the magnitude of Volterra kernels is maginified by the amplitude of M-sequence according to the order of Volterra kernels. By use of this property, each order Volterra kernels is obtained by solving linear equations. Simulations are carried out for some nonlinear systems. The results show that Volterra kernels can be separated in each order successfully by the proposed method.

• Transactions on Control, Automation and Systems Engineering
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• 제4권2호
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• pp.109-113
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• 2002

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 crosscorrelation function between the input and the output, we obtain up to 3rd order Volterra kernels, which is the highest order Volterra kernel obtained until now for Van de Vusse reactor. Computer simulations show that when Van de Vusse chemical process is identified by use of up to 3rd order Volterra kernels, a good agreement is observed between the calculated output and the actual output.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.476-479
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• 1995

A real time and adaptive method for obtaining Volterra kernels of a nonlinear system by use of pseudorandom M-sequences and correlation technique is proposed. The Volterra kernels are calculated real time and the obtained Volterra kernels becomes more accurate as time goes on. The simulation results show the effectiveness of this method for identifying time-varying nonlinear system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1999년도 제14차 학술회의논문집
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• pp.141-144
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• 1999

The authors have recently developed a new method for identification of Volterra kernels of nonlinear systems by use of pseudorandom M-sequence and correlation technique. And it is shown that nonlinear systems which can be expressed by Volterra series expansion are well identified by use of this method. However, there exist many nonlinear systems which can not be expressed by Volterra series mathematically. A nonlinear system having backlash type nonliear element is one of those systems, since backlash type nonlinear element has multi-valued function between its input and output. Since Volterra kernel expression of nonlinear system is one of the most useful representations of non-linear dynamical systems, it is of interest how the method of Volterra kernel identification can be ar plied to such backlash type nonlinear system. The authors have investigated the effect of application of Volterra kernel identification to those non-linear systems which, accurately speaking, is difficult to express by use of Volterra kernel expression. A pseudorandom M-sequence is applied to a nonlinear backlash-type system, and the crosscorrelation function is measured and Volterra kernels are obtained. The comparison of actual output and the estimated output by use of measured Volterra kernels show that we can still use Volterra kernel representation for those backlash-type nonlinear systems.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.451-454
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• 1998

This paper proposes a new method of Model Predictive Control (MPC) of nonlinear process by us-ing the measured Volterra kernels as the nonlinear model. A nonlinear dynamical process is usually de-scribed as Volterra kernel representation, In the authors' method, a pseudo-random M-sequence is ar plied to the nonlinear process, and its output is measured. Taking the crosscorrelation between the input and output, we obtain the Volterra kernels up to 3rd order which represent the nonlinear characteristics of the process. By using the measured Volterra kernels, we can construct the nonlinear model for MPC. In applying Model Predictive Control to a nonlinear process, the most important thing is, in general, what kind of nonlinear model should be used. The authors used the measured Volterra kernels of up to 3rd order as the process model. The authors have carried out computer simulations and compared the simulation results for the linear model, the nonlinear model up to 2nd Volterra kernel, and the nonlinear model up to 3rd order Vol-terra kernel. The results of computer simulation show that the use of Valterra kernels of up to 3rd order is most effective for Model Predictive Control of nonlinear dynamical processes.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(II)
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• pp.1181-1184
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• 1987

The input-output relation for nonlinear systems can be 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 and is compared with the direct substitution technique. The former method can significantly reduce the computational complexity.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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• pp.161-164
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• 1996

The authors have recently proposed a new method for identifying Volterra kernels of nonlinear control systems by use of M-sequence and correlation technique. A specially chosen M-sequence is added to the nonlinear system to be identified, and the crosscorrelation function between the input and output is calculated. Then every crosssection of Volterra kernels up to 3rd order appears at a specified delay time point in the crosscorrelation. This method is applied to a saturation-type nonlinear feedback control system of mechanical-electrical servo system having torque saturation nonlinearity. Simulation experiments show that we can obtain Volterra kernels of saturation-type nonlinear system, and a good agreement is observed between the observed output and the calculated one from the measured Volterra kernels.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1999년도 제14차 학술회의논문집
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• pp.145-148
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• 1999

It is known that Volterra kernel models can represent a wide variety of nonlinear chemical processes. Also, it is necessary for Volterra model identification to excite the process to be identified with a signal having wide range of frequency spectrum and high enough amplitude of input signals. Kashiwagi[4 ∼ 7] has recently shown a method for measuring Volterra kernels up to third order using pseudorandom M-sequence signals. However, in practice, since it is not always possible to apply such input sequences to the actual chemical plants. Even when we can apply such a pseudorandom signal to the process, it takes much time to obtain higher order Volterra kernels. Considering these problems, the authors propose here a new method for practical identification of Volterra kernels by use of approximate open differential equation (ODE) model and simple plant test. Simulation results are shown for verifying the usefulness of our method of identification of nonlinear chemical processes.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 16-17 Oct. 1987
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• pp.145-149
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• 1987

The input-output relation for nonlinear systems can be explicitly represented by the Voltera functional series and it is characterized by the Volterra Kernels. A block diagram reduction method is introduced to determine the Volterra Kernels for the nonlinear systems represented by nonlinear differential equations. Degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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• pp.149-152
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• 1996

In this paper, the authors propose a new method for linearizing a nonlinear dynamical system by use of Volterra kernel of the nonlinear system. The authors have recently obtained a new method for measuring Volterra kernels of nonlinear control systems by use of a pseudo-random M-sequence and correlation technique. 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 crosssection of Volterra kernels up to 3rd order. Once we can get Volterra kernels of nonlinear system, we can construct a linearization method of the nonlinear system. Simulation results show good agreement between the observed results and the theoretical considerations.