• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권3호
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• pp.225-242
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• 2016

The phase-type representation is strongly connected with the positive realization in positive system. We attempt to transform phase-type representation into sparse mono-cyclic positive representation with as low order as possible. Because equivalent positive representations of a given phase-type distribution are non-unique, it is important to find a simple sparse positive representation with lower order that leads to more effective use in applications. A Hypo-Feedback-Coxian Block (HFCB) representation is a good candidate for a simple sparse representation. Our objective is to find an HFCB representation with possibly lower order, including all the eigenvalues of the original generator. We introduce an efficient nonlinear optimization method for computing an HFCB representation from a given phase-type representation. We discuss numerical problems encountered when finding efficiently a stable solution of the nonlinear constrained optimization problem. Numerical simulations are performed to show the effectiveness of the proposed algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.76.1-76
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• 2002

This paper addresses a method for nonlinear controller construction for a general nonlinear system with the separation of controller construction and manipulated values generation. The nonlinear system model is firstly expressed with the coefficients of state-depended representation. The nonlinear control is designed without any approximation based on the model with state-depended representation. At the stage of controller implementation for the nonlinear system, the manipulated values are calculated accurately by use of an algorithm of the numerical analysis. The numerical error for calculating the manipulated value can be reduced to zero by selecting the sampling interval being a small val...

• Journal of Mechanical Science and Technology
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• 제18권7호
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• pp.1107-1120
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• 2004

This study proposes a new scheme for the sampled-data representation of nonlinear systems with time-delayed multi-input. The proposed scheme is based on the Taylor-series expansion and zero-order hold assumption. The mathematical structure of a new discretization scheme is explored. On the basis of this structure, the sampled-data representation of nonlinear systems including time-delay is derived. The new scheme is applied to nonlinear systems with two inputs and then the delayed multi-input general equation is derived. The resulting time-discretization provides a finite-dimensional representation of nonlinear control systems with time-delay enabling existing controller design techniques to be applied to them. In order to evaluate the tracking performance of the proposed scheme, an algorithm is tested for some of the examples including maneuvering of an automobile and a 2-DOF mechanical system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.327-332
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• 2003

A new discretization method for nonlinear system with time-delay is proposed. It is based on the well-known Taylor series expansion and the zero-order hold (ZOH) assumption. We know that a discretization of linear system can be obtained with the ZOH assumption and within the sampling interval. A similar line of thinking is available in nonlinear case. The mathematical structure of the new discretization method is explored and under the structure, the sampled-data representation of nonlinear system including time-delay is computed. Provided that the discrete form of the single input nonlinear system with time-delay is derived, this result is easily extended to nonlinear system with multi-input time-delay. For simplicity two inputs are considered in this study. It is enough to generalize that of multiple inputs. Finally, the time-discretization of non-affine nonlinear system with time-delay is investigated for apply all nonlinear system

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 심포지엄 논문집 정보 및 제어부문
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• pp.125-127
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• 2005

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sample-data representation of a nonlinear system with constant state tine-delay. The mathematical expressions of the discretization scheme are presented and the effect of the time-discretization method on key properties of nonlinear control system with state tine-delay, such as equilibrium properties and asymptotic ability, is examined. The proposed scheme provides a finite-dimensional representation for nonlinear systems with state time-delay enabling existing controller design techniques to be applied to then. The performance of the proposed discretization procedure is evaluated using a nonlinear system. For this nonlinear system, various sampling rates and time-delay values are considered.

• 한국산학기술학회논문지
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• 제16권5호
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• pp.3000-3005
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• 2015

신뢰할 수 있는 공정 감시와 진단은 생산 공정의 안전과 최종제품의 품질을 보장이라는 관점에서 중요하다. 공정진단의 목적은 특정한 공정 이상의 원인을 밝혀내는 것이다. 본 연구에서는 분류기법에 기반한 공정진단 체계를 제시한다. 여기서는 공정데이터를 비선형 데이터 표현기법을 통해 변환함으로써 데이터의 크기를 줄이며 효율적인 데이터 표현이 가능하다. 추가적인 단계로서 공정 데이터의 전처리 과정을 통해 진단에 무관한 공정 패턴을 제거하고 진단 성능을 높이고자 한다. 진단 성능을 평가하기 위해 회분식 공정에 대한 사례연구를 수행한 결과 기존 선형 진단 방법론 및 전처리 과정이 없는 방법론에 비해 향상된 진단 결과를 얻을 수 있었다.

• International Journal of Control, Automation, and Systems
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• 제4권3호
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• pp.293-301
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• 2006

A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the well-known Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a time-delayed input is derived. This method is applied to obtain a sampled-data representation of a non-affine nonlinear system, with a constant input time delay. In particular, the effect of the time discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 'Hybrid' discretization schemes that result from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method parameters to meet CPU time and accuracy requirements are examined as well. The performance of the proposed method is evaluated using a nonlinear system with a time-delayed non-affine input.

• Journal of Mechanical Science and Technology
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• 제18권8호
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• pp.1297-1305
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• 2004

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sampled-data representation of a non-affine nonlinear system with constant input time-delay. The mathematical expressions of the discretization scheme are presented and the ability of the algorithm is tested for some of the examples. The proposed scheme provides a finite-dimensional representation for nonlinear systems with time-delay enabling existing controller design techniques to be applied to them. For all the case studies, various sampling rates and time-delay values are considered.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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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.

• 한국통신학회논문지
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• 제13권4호
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• pp.309-321
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• 1988

본 논문에서는 단면(cross section)이 원(circle)인 곡면물체를 처리하는 방법인 G.C표현에 있어서 필요한 축방정식과 반경함수를 구하는 방법을 제안한다. 우선 입력으로 들어온 깊이 데이터에서 clustering을 통해 선형축을 가지고 있는 부분과 비선형축을 가지는 부분을 분리하였으며 각 표면마스크조각(surface mask patch)들의 법선 벡터를 통하여 축상의 점들을 추출하였다. 또한 추출된 축상의 점들이 비선형인 경우 Hermite 곡선으로 축방정식을 표현하였으며 본 논문의 유용성을 실험에 의하여 입증하였다.