• Title, Summary, Keyword: Nonlinear systems

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Observers for nonautonomous discrete-time nonlinear systems

  • Nam, Kwanghee;Lee, Wonchang
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1828-1832
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    • 1991
  • We study the observer design problem for nonautonomous discrete-time nonlinear systems. We investigate the structure of nonautonomous discrete-time systems which are state equivalent to the nonlinear observer form and characterize their class. Necessary and sufficient conditions for the existence of an input independent (local) diffeomorphism axe derived which transforms multi-input, multi-output nonlinear systems into the nonlinear observer form.

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Application of Volterra functional series to the analysis of nonlinear systems (비선형 시스템 해석을 위한 볼테라 시리지의 응용)

  • 성단근
    • 제어로봇시스템학회:학술대회논문집
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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.

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Chaos in PID Controlled Nonlinear Systems

  • Ablay, Gunyaz
    • Journal of Electrical Engineering and Technology
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    • v.10 no.4
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    • pp.1843-1850
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    • 2015
  • Controlling nonlinear systems with linear feedback control methods can lead to chaotic behaviors. Order increase in system dynamics due to integral control and control parameter variations in PID controlled nonlinear systems are studied for possible chaos regions in the closed-loop system dynamics. The Lur’e form of the feedback systems are analyzed with Routh’s stability criterion and describing function analysis for chaos prediction. Several novel chaotic systems are generated from second-order nonlinear systems including the simplest continuous-time chaotic system. Analytical and numerical results are provided to verify the existence of the chaotic dynamics.

Observer Design for Multi-Output Unobservable Nonlinear Systems (관측가능하지 않은 다중출력 비선형 시스템의 관측기 설계기법)

  • 조남훈
    • Journal of Institute of Control, Robotics and Systems
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    • v.10 no.7
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    • pp.575-582
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    • 2004
  • The observer design problem is studied for a class of multi-output nonlinear systems that are not necessarily observable. Generalized nonlinear observer canonical form is introduced for multi-output nonlinear systems to design nonlinear observers. Sufficient conditions are given for a nonlinear system to be transformed by state-space change of coordinates into generalized nonlinear observer canonical form. Based on this canonical from, a sufficient condition is also given for the existence of nonlinear observers. An illustrative example is presented to show the design procedure of the proposed method.

Identification of Volterra Kernels of Nonlinear System Having Backlash Type Nonlinearity

  • Rong, Li;Kashiwagi, H.;Harada, H.
    • 제어로봇시스템학회:학술대회논문집
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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.

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Observer for Nonlinear Systems Using Approximate Observer Form (근사 관측기 형태를 이용한 비선형 시스템의 관측기)

  • 이성렬;신현석;박민용
    • 제어로봇시스템학회:학술대회논문집
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    • pp.207-207
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    • 2000
  • This paper presents an observer for nonlinear systems using approximate observer form. It is shown that if a nonlinear system is approximately error linearizable, then there exists a local nonlinear observer whose estimation error converges exponentially to zero. Since the proposed method relaxes strong geometric conditions of previous works, it improves the existing results for a nonlinear observer design. Finally, some examples are given to show the effectiveness of this scheme.

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Decentralized Adaptive Control for Nonlinear Systems with Time-Delayed Interconnections: Intelligent Approach (시간 지연 상호 연계를 가진 비선형 시스템의 분산 적응 제어: 지능적인 접근법)

  • Yoo, Sung-Jin;Park, Jin-Bae
    • Journal of Institute of Control, Robotics and Systems
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    • v.15 no.4
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    • pp.413-419
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    • 2009
  • A decentralized adaptive control method is proposed for large-scale systems with unknown time-delayed nonlinear interconnections unmatched in control inputs. It is assumed that the time-delayed interaction terms are bounded by unknown nonlinear bounding functions. The nonlinear bounding functions and uncertain nonlinear functions of large-scale systems are compensated by the function approximation technique using neural networks. The dynamic surface control method is extended to design the proposed memoryless local controller for each subsystem of uncertain nonlinear large-scale time delay systems. Therefore, although the interconnected systems consist of a large number of subsystems, the proposed controller can be designed simply. We prove that all the signals in the total closed-loop system are semiglobally uniformly bounded and the control errors converge to an adjustable neighborhood of the origin. Finally, an example is given to demonstrate the effectiveness and applicability of the proposed scheme.

Output regulation of nonlinear sampled-data systems (비선형 샘플치 시스템의 출력조절)

  • 정선태
    • 제어로봇시스템학회:학술대회논문집
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    • pp.391-394
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    • 1996
  • The effects of time-sampling on nonlinear output regulation problem is investigated. Output regulatedness is preserved under time sampling as in linear systems, however output regulatability is not robust with respect to time-sampling, and thus one needs to seek an approximate nonlinear sampled-data output regulator.

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A simple method for treating nonlinear control systems through state feedback

  • Han, Kyeng-Cheng
    • 제어로봇시스템학회:학술대회논문집
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    • pp.931-933
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    • 1989
  • If the nonlinear term in a nonlinear control system equation can be deleted by state feedback control, the original system becomes a linear system. For this linear control system, many well known methods may be used to handle it, and then reverse it back to nonlinear form. Many problems of nonlinear control systems can be solved in this way. In this paper, this method will be used to transfer the identification problem of nonlinear systems into a linear control problem. The nonlinear observer is established by constructing linear observer. Then the state control of nonlinear systems is realized. Finally, the technique of the PID controller obtained by using bang-bang tracker as a differentiator provides a stronger robust controller. Even though the method in this paper may not theoretically perfect, many numerical simulations show that it is applicable.

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Time Domain Identification of nonlinear Structural Dynamic Systems Using Unscented Kalman Filter (Unscented Kalman Filter를 이용한 비선형 동적 구조계의 시간영역 규명기법)

  • 윤정방
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • pp.180-189
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    • 2001
  • In this study, recently developed unscented Kalman filter (UKF) technique is studied for identification of nonlinear structural dynamic systems as an alternative to the extended Kalman filter (EKF). The EKF, which was originally developed as a state estimator for nonlinear systems, has been frequently employed for parameter identification by introducing the state vector augmented with the unknown parameters to be identified. However, the EKF has several drawbacks such as biased estimations and erroneous estimations especially for highly nonlinear dynamic systems due to its crude linearization scheme. To overcome the weak points of the EKF, the UKF was recently developed as a state estimator. Numerical simulation studies have been carried out on nonlinear SDOF system and nonlinear MDOF system. The results from a series of numerical simulations indicate that the UKF is superior to the EKF in the system identification of nonlinear dynamic systems especially highly nonlinear systems.

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