Intelligent Digital Redesign for Uncertain Nonlinear Systems Using Power Series

성화창(Hwa Chang Sung),박진배(Jin Bae Park),고성현(Sung Hyun Go),주영훈(Young Hoon Joo) 한국지능시스템학회 2005 한국지능시스템학회논문지 Vol.15 No.7

분 논문은 복합 상태 공간에서의 퍼지 기반 제어기를 이용한 지능형 디지털 재설계의 전 역적 접근 방안에 대해 재안하고자 한다. 이산화를 통한 제어기 설계에 있어서 불확실성이 포함된 실시간 비선형 시스템에 대해 보다 효율적이고 안정적인 접근을 위해 TS 퍼지 모델이 사용되었다. 그리고 전 역적 접근을 위핸 방안으로서 문제를 볼록 최적화 관점으로 변환 후, 에라가 가질 수 있는 놈의 영역을 최소화 하여 상태 접합을 이루고자 하였다. 또한 power series를 사용함으로써 불확실성이 포함된 비선형 시스템을 보다 더 정확하게 분석하였다. 샘플링 기간이 충분히 작다면, 불확실 비선형 시스템의 실시간 시스템으로의 전환이 충분한 이유를 가지게 된다. 전 역적 접근을 통한 디지털로 제어된 시스템은 선형 행렬 부등식 형태로 바꾸어 시스템의 안정성을 보장하고자 하였다. 마지막으로 TS 퍼지 모델로 분석된 혼돈 Lorenz system에 적용함으로써 제안된 방법의 안정성과 효율성을 보장받게 된다. This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the en-or of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the power series, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an example to guarantee the stability and effectiveness of the proposed method.

불확실성을 고려한 비선형 제어 시스템의 선형화에 따른 H_∞ 강건성 제어

이상효 광운대학교 신기술연구소 1997 신기술연구소논문집 Vol.26 No.-

This paper is focussed on the problem of robustly stabilizing a linearizable nonlinear time-varying system. The considered system is a class of state feedback linearizable nonlinear systems. First, the nonlinear time-varying system is transformed into the pseudo-linear system composed with the time-invariant linear part and the nonlinear time-varying uncertainty part. Second, the solution to a quadratic stabilization problem in the pseudo linear system is given via Lyapunov methods. Then this solution is used to construct a stabilizing linear control law. Therefore a feedback linearizable nonlinear system with uncertainty is proved robust.

Locating and identifying model-free structural nonlinearities and systems using incomplete measured structural responses

Liu, Lijun,Lei, Ying,He, Mingyu Techno-Press 2015 Smart Structures and Systems, An International Jou Vol.15 No.2

Structural nonlinearity is a common phenomenon encountered in engineering structures under severe dynamic loading. It is necessary to localize and identify structural nonlinearities using structural dynamic measurements for damage detection and performance evaluation of structures. However, identification of nonlinear structural systems is a difficult task, especially when proper mathematical models for structural nonlinear behaviors are not available. In prior studies on nonparametric identification of nonlinear structures, the locations of structural nonlinearities are usually assumed known and all structural responses are measured. In this paper, an identification algorithm is proposed for locating and identifying model-free structural nonlinearities and systems using incomplete measurements of structural responses. First, equivalent linear structural systems are established and identified by the extended Kalman filter (EKF). The locations of structural nonlinearities are identified. Then, the model-free structural nonlinear restoring forces are approximated by power series polynomial models. The unscented Kalman filter (UKF) is utilized to identify structural nonlinear restoring forces and structural systems. Both numerical simulation examples and experimental test of a multi-story shear building with a MR damper are used to validate the proposed algorithm.

Locating and identifying model-free structural nonlinearities and systems using incomplete measured structural responses

Lijun Liu,Ying Lei,Mingyu He 국제구조공학회 2015 Smart Structures and Systems, An International Jou Vol.15 No.2

Structural nonlinearity is a common phenomenon encountered in engineering structures under severe dynamic loading. It is necessary to localize and identify structural nonlinearities using structural dynamic measurements for damage detection and performance evaluation of structures. However, identification of nonlinear structural systems is a difficult task, especially when proper mathematical models for structural nonlinear behaviors are not available. In prior studies on nonparametric identification of nonlinear structures, the locations of structural nonlinearities are usually assumed known and all structural responses are measured. In this paper, an identification algorithm is proposed for locating and identifying model-free structural nonlinearities and systems using incomplete measurements of structural responses. First, equivalent linear structural systems are established and identified by the extended Kalman filter (EKF). The locations of structural nonlinearities are identified. Then, the model-free structural nonlinear restoring forces are approximated by power series polynomial models. The unscented Kalman filter (UKF) is utilized to identify structural nonlinear restoring forces and structural systems. Both numerical simulation examples and experimental test of a multi-story shear building with a MR damper are used to validate the proposed algorithm.

Detection of nonlinear structural behavior using time-frequency and multivariate analysis

J. Prawin,A. Rama Mohan Rao 국제구조공학회 2018 Smart Structures and Systems, An International Jou Vol.22 No.6

Most of the practical engineering structures exhibit nonlinearity due to nonlinear dynamic characteristics of structural joints, nonlinear boundary conditions and nonlinear material properties. Hence, it is highly desirable to detect and characterize the nonlinearity present in the system in order to assess the true behaviour of the structural system. Further, these identified nonlinear features can be effectively used for damage diagnosis during structural health monitoring. In this paper, we focus on the detection of the nonlinearity present in the system by confining our discussion to only a few selective time-frequency analysis and multivariate analysis based techniques. Both damage induced nonlinearity and inherent structural nonlinearity in healthy systems are considered. The strengths and weakness of various techniques for nonlinear detection are investigated through numerically simulated two different classes of nonlinear problems. These numerical results are complemented with the experimental data to demonstrate its suitability to the practical problems.

구분적선형시스템을 이용한 해양 구조물의 거동분석

마호성 한국전산구조공학회 1997 전산구조공학 Vol.10 No.4

A piecewise-linear system is utilized to model the offshore mooring system. The approximated piecewise-linear restoring force is obtained to be compared with the analytically derived restoring force of a mooring system. Two systems are compared to verify the applicability of the piecewise-linear system to evaluate responses of the mooring system. Using the piecewise-linear system, the response behaviors of mooring systems are examined under various excitations. Nonlinearity of the system and effects of both system and excitation parameters are intensively examined. System responses are identified mainly by observing Poincare maps. The mooring system is found to have various types of responses such as regular harmonic, subharmonic and complex nonlinear behaviors, including chaos by utilizing a piecewise-linear system. Various values of parameters are applied to determine the effects of parameters upon system responses. Response domains are determined by establishing parametric maps. 해양계선시스템(offshore mooring system)의 거동을 구분적선형시스템(piecewise-linear system)을 이용하여 분석하였다. 계선시스템의 복원력을 유도하고 거기에 상응하는 근사치 구분적선형시스템의 복원력을 구하여 두 시스템의 복원력을 비교하였다. 다양한 파력 하에서의 계선시스템의 응답거동을 분석하였다. 시스템의 비선형정도 및 매개변수의 영향에 대하여 집중적으로 연구하였다. 시스템의 응답거동의 특성은 포인케어맵(Poincare map)을 통하여 확인하였다. 구분적선형시스템을 이용하여 분석한 결과, 계선시스템은 일반 조화, 열조화 및 복잡한 비선형거동인 chaos를 포함한 다양한 응답거동을 갖음을 알아냈다. 여러 값의 매개변수를 적용하여 시스템의 응답거동에 미치는 영향을 알아냈으며, 매개변수지도를 통하여 응답거동의 영역을 확인하였다.

Intelligent Digital Redesign of Uncertain Nonlinear Systems : Global approach

성화창(Hwachang Sung),주영훈(Younghoon Joo),박진배(Jinbae Park),김도완(Dowan Kim) 한국지능시스템학회 2005 한국지능시스템학회 학술발표 논문집 Vol.15 No.2

This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also by using the power series, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, we prove the effectiveness and stabilization of the proposed intelligent digital redesign method by applying the chaotic Lorentz system.

구분적선형시스템을 이용한 해양 구조물의 거동분석

마호성 한국전산구조공학회 1997 한국전산구조공학회논문집 Vol.10 No.4

해양계선시스템(offshore mooring system)의 거동을 구분적선형시스템(piecewise-linear system)을 이용하여 분석하였다. 계선시스템의 복원력을 유도하고 거기에 상응하는 근사치 구분적선형시스템의 복원력을 구하여 두 시스템의 복원력을 비교하였다. 다양한 파력 하에서의 계선시스템의 응답거동을 분석하였다. 시스템의 비선형정도 및 매개변수의 영향에 대하여 집중적으로 연구하였다. 시스템의 응답거동의 특성은 포인케어맵(Poincare map)을 통하여 확인하였다. 구분적선형시스템을 이용하여 분석한 결과, 계선시스템은 일반 조화, 열조화 및 복잡한 비선형거동인 chaos를 포함한 다양한 응답거동을 갖음을 알아냈다. 여러 값의 매개변수를 적용하여 시스템의 응답거동에 미치는 영향을 알아냈으며, 매개변수지도를 통하여 응답거동의 영역을 확인하였다. A piecewise-linear system is utilized to model the offshore mooring system. The approximated piecewise-linear restoring force is obtained to be compared with the analytically derived restoring force of a mooring system. Two systems are compared to verify the applicability of the piecewise-linear system to evaluate responses of the mooring system. Using the piecewise-linear system, the response behaviors of mooring systems are examined under various excitations. Nonlinearity of the system and effects of both system and excitation parameters are intensively examined. System responses are identified mainly by observing Poincare maps. The mooring system is found to have various types of responses such as regular harmonic, subharmonic and complex nonlinear behaviors, including chaos by utilizing a piecewise-linear system. Various values of parameters are applied to determine the effects of parameters upon system responses. Response domains are determined by establishing parametric maps.

Detection and parametric identification of structural nonlinear restoring forces from partial measurements of structural responses

Lei, Ying,Hua, Wei,Luo, Sujuan,He, Mingyu Techno-Press 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.54 No.2

Compared with the identification of linear structures, it is more challenging to conduct identification of nonlinear structure systems, especially when the locations of structural nonlinearities are not clear in structural systems. Moreover, it is highly desirable to develop methods of parametric identification using partial measurements of structural responses for practical application. To cope with these issues, an identification method is proposed in this paper for the detection and parametric identification of structural nonlinear restoring forces using only partial measurements of structural responses. First, an equivalent linear structural system is proposed for a nonlinear structure and the locations of structural nonlinearities are detected. Then, the parameters of structural nonlinear restoring forces at the locations of identified structural nonlinearities together with the linear part structural parameters are identified by the extended Kalman filter. The proposed method simplifies the identification of nonlinear structures. Numerical examples of the identification of two nonlinear multi-story shear frames and a planar nonlinear truss with different nonlinear models and locations are used to validate the proposed method.

비선형 최적화 기법 기반 실내외 GPS/VIO 시스템

최영동(Yeong-Dong Choi),김규원(Kyu-Won Kim),정태기(Tae-Ki Jung),서성훈(Seong-Hun Seo),지규인(Gyu-In Jee) 제어로봇시스템학회 2019 제어·로봇·시스템학회 논문지 Vol.25 No.12

Indoor-Outdoor navigation systems are essential for unmanned vehicles. If navigation results are provided indoors and outdoors, the moving range of the unmanned vehicle is widened. For example, an unmanned vehicle can travel not only on the road but also inside buildings with an indoor-outdoor navigation system. This broadens the range of services that an unmanned vehicle can provide. Outdoor navigation system typically uses the Global Positioning System (GPS). GPS outputs are based on the geodetic coordinate system. In contrast, the indoor environment is a GPS signal shadow area. It is possible to create indoor navigation systems mainly using LiDAR, Camera, IMU, etc. However, unlike GPS, these sensors use the relative coordinate system. This coordinate system has a disadvantage in that even for the same trajectory, the coordinate values are different depending on the starting pose. As above, the indoor and outdoor coordinate systems are inconsistent with each other. To overcome this, a system that can navigate not only outdoors but also indoors based on an absolute coordinate system is needed. We implemented a GPS with visual inertial Odometry (GPS/VIO) system that integrates the indoor and outdoor coordinate systems into an absolute coordinate system. This system also solves the problem of the accumulation of position errors of VIO over time. The GPS/VIO system is implemented using the nonlinear optimization method. An experiment was conducted indoors and outdoors. The trajectory was drawn in Google Earth to verify that the navigation results were generated correctly in the absolute coordinate system.