• Title/Summary/Keyword: Approximate Feedback Linearization

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Nonlinear Time-Varying Control Based on Differential Geometry

  • Lee, Jong-Yong;Jung, Kye-dong;Cho, Seongsoo;Strzelecki, Michat
    • International Journal of Internet, Broadcasting and Communication
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    • v.6 no.2
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    • pp.1-9
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    • 2014
  • This paper presents a study on nonlinear time varying systems based on differential geometry. A brief introduction about controllability and involutivity will be presented. As an example, the exact feedback linearization and the approximate feedback linearization are used in order to show some application examples.

Approximate Linearization of Nonlinear Systems (비선형 시스템의 근사 선형화)

  • 남광희;이균경;탁민제
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.40 no.7
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    • pp.690-695
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    • 1991
  • The ability to linearize a nonlinear system by feedback and coordinate change reduces to finding an integrating factor for a one-form which is determined from the system dynamics. Utilizing Taylor series expansion of this one-form, we characterize approximate linearizabilitu. A constructive method is derived for approximate linearization up to order 2.

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Switching Control of Ball and Beam System using Partial State Feedback: Jacobian and Two-Step Linearization Methods (자코비안 및 2단 선형화 기법과 부분 상태궤환을 이용한 볼-빔 시스템의 스위칭 제어)

  • Lee, Kyung-Tae;Choi, Ho-Lim
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.66 no.5
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    • pp.819-832
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    • 2017
  • We propose a new switching control scheme for a ball and beam system by utilizing two linearization methods. First, the Jacobian linearization is applied and state observer is developed afterward. Then, motivated [6], the approximate input-output linearization is carried out, and after that, the Jacobian linearization is applied along with the design of state observer. Since the second approach requires two linearizations, it is called a two-step linearization method. The state observer is needed for the estimation of the velocities of ball and motor movement. Since the Jacobian linearization based controller tends to provide faster response at the initial time, and after that, the two-step linearization based controller tends to provide better response in terms of output overshoot and convergence to the origin, it is natural to give a switching control scheme to provide the best overall control response. The validity of our control scheme is shown in both simulation and experimental results.

The Control of Inverted Pendulum System Using Approximated Nonlinear Feedback Linearization (근사 비선형 궤환 선형화를 이용한 도립 진자 계통의 제어)

  • 이종용;이상효
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.18 no.3
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    • pp.372-384
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    • 1993
  • The inverted pendulum system has interesting and challenging problems related to robotics and rocket attitude control view of both control theory and applications. Generally approximately linearized plant models are employed to control the system. In this paper a recently developed control theory based on differentiable manifold theory is used to control the inverted pendulum system which is typically nonlinear. First, the nonlinear model is transformed into the approximate feedback linearized system by nonlinear state feedback. Secondly, the linear controller is designed using the pole-placement method for the approximate feedback linearized plant model, the output of which are finally inverse-transformed to yield the control input to the actual system of the inverted pendulum. The proposed method is evaluated by the computer simulation to compare with the 3rd order linearization model.

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Neural Network based Variable Structure Control for a Class of Nonlinear Systems (비선형 시스템 계통에서 신경망에 근거한 가변구조 제어)

  • Kim, Hyeon-Ho;Lee, Cheon-Hui
    • The KIPS Transactions:PartA
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    • v.8A no.1
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    • pp.56-62
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    • 2001
  • This paper presents a neural network based variable structure control scheme for nonlinear systems. In this scheme, a set of local variable structure control laws are designed on the basis of the linear models about preselected representative points which cover the range of the system operation of interest. From the combination of the set of local variable structure control laws, neural networks infer the approximate control input in between the operating points. The neural network based variable structure control alleviates the effects of model uncertainties, which cannot be compensated by the control techniques using feedback linearization. It also relaxes the discontinuity in the system’s behavior that appears when the control schemes based on the family of the linear models are applied to nonlinear systems. Simulation results of a ball and beam system, to which feedback linearization cannot be applied, demonstrate the feasibility of the proposed method.

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Flight Control of Tilt-Rotor Airplane In Rotary-Wing Mode Using Adaptive Control Based on Output-Feedback (출력기반 적응제어기법을 이용한 틸트로터 항공기의 회전익 모드 설계연구)

  • Ha, Cheol-Keun;Im, Jae-Hyoung
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.3
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    • pp.228-235
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    • 2010
  • This paper deals with an autonomous flight controller design problem for a tilt-rotor aircraft in rotary-wing mode. The inner-loop algorithm is designed using the output-based approximate feedback linearization. The model error originated from the feedback linearization is cancelled within allowable tolerance by using single-hidden-layer neural network. According to Lyapunov direct stability theory, the adaptive update law is derived to run the neural network on-line, which is based on the linear observer dynamics. Moreover, the outer-loop algorithm is designed to track the trajectory generated from way-point guidance. Especially, heading and flight-path angle line-of-sight guidance are applied to the outer-loop to improve accuracy of the landing tracking performance. The 6-DOF nonlinear simulation shows that the overall performance of the flight control algorithm is satisfactory even though the collective input response shows instantaneous actuator saturation for a short time due to the lack of the neural network and the saturation protection logic in that loop.

Anticontrol of Chaos for a Continuous-time TS Fuzzy System via Time-delay Feedback

  • Zhong Li;Park, Jin-Bea;Joo, Young-Hoon
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.108.1-108
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    • 2001
  • A time-delay feedback control approach is proposed for making a given stable continuous-time Takagi-Sugeno (TS) fuzzy system chaotic, which is based on the fuzzy feedback linearization and a suitable approximate relationship between a time-delay differential equation and a discrete map. The time-delay feedback controller, chosen among several candidates, is a simple sinusoidal function of the delay states of the system, which has small amplitude. This approach is mathematically proven for rigorous generation of chaos from stable continuous-time TS fuzzy systems, where the generated chaos is in the sense of Li and Yorke. Numerical examples are included to visualize the theoretical analysis and the controller design.

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Tracking Controller Design Using Delayed Output Feedback For Systems With Stiff Nonlinearities (심한 비선형성을 갖는 시스템의 시간지연 출력궤환을 이용한 추종제어기의 설계)

  • 나승유
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.16 no.4
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    • pp.342-349
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    • 1991
  • In this paper, a method is presented for designing a tracking and disturbance rejecting controller for a nonlinear control system in which approximate linearization is not applicable due to a s stiff nonlinearity. Only the measurable variables are used for the controller synthesis. The system is augmented by a compensator at the output side for the tracking and disturbance rejection. An output delayed feedback controller is designed for the augmented system without nonlinearity. Then the feedback parameters are adjusted by describing function method to overcome the limit cycle due to the nonlinearity.

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Implementation of Stable Adaptive Neural Networks for Feedback Linearization (피이드백 선형화를 위한 안정한 적응 신경회로망 구현)

  • Kim, Dong-Hun;Yang, Hai-Won
    • Proceedings of the KIEE Conference
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    • 1996.11a
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    • pp.58-61
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    • 1996
  • For a class of single-input single-output continuous-time nonlinear systems, a multilayer neural network-based controller that feedback-linearizes the system is presented. Control action is used to achieve tracking performance for a state-feedback linearizable but unknown nonlinear system. The multilayer neural network(NN) is used to approximate nonlinear continuous function to any desired degree of accuracy. The weight-update rule of multilayer neural network is derived to satisfy Lyapunov stability. It is shown that all the signals in the closed-loop system are uniformly bounded. Initialization of the network weights is straightforward.

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Application of Nonlinear Feedback Control to an Articulated Manipulator (수직다관절 매니퓰레이터에 대한 비선형 되먹임제어의 응용)

  • Y.S. Baek;C.I. Yang;H.S. Aum
    • Journal of the Korean Society for Precision Engineering
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    • v.12 no.9
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    • pp.104-114
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    • 1995
  • Mathematical models of industrial robots or manipulators are composed of highly nonlinear equations with nonlinear couplings between the variables of motions. These nonlin- earities were not considered important in the first stage that the working speed of the manipulator was not so fast, but the effect of nonlinear forces has become serious, as the working speed has been increased. So more improvement of performance cannot be expected by the control of manipulator using approximate linearization. As an approach for solving these problems, there is a method that eliminates nonlinear theory, which makes possible cecoupling of coupling terms and arbitrary arranging of poles is briefly introduced in this study. When the theory is applied to design the control law, its feasibility is examined whether the reasonable control results are obtained by simulating position, velocity, torque and tracing trajectory. The relations between the coefficients of the linearized differential equations and the maximum error and torque for the prescribed trajectory are also examined. Finally, the method for selecting the values for getting the most rapid and precise response within maximum torque of each drive is suggested in the choice of coefficients of characteristic equations which are obtained as a result of the control.

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