• Title/Summary/Keyword: Lyapunov Function

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Modeling and designing intelligent adaptive sliding mode controller for an Eight-Rotor MAV

  • Chen, Xiang-Jian;Li, Di
    • International Journal of Aeronautical and Space Sciences
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    • v.14 no.2
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    • pp.172-182
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    • 2013
  • This paper focuses on the modeling and intelligent control of the new Eight-Rotor MAV, which is used to solve the problem of the low coefficient proportion between lift and gravity for the Quadrotor MAV. The Eight-Rotor MAV is a nonlinear plant, so that it is difficult to obtain stable control, due to uncertainties. The purpose of this paper is to propose a robust, stable attitude control strategy for the Eight-Rotor MAV, to accommodate system uncertainties, variations, and external disturbances. First, an interval type-II fuzzy neural network is employed to approximate the nonlinearity function and uncertainty functions in the dynamic model of the Eight-Rotor MAV. Then, the parameters of the interval type-II fuzzy neural network and gain of sliding mode control can be tuned on-line by adaptive laws based on the Lyapunov synthesis approach, and the Lyapunov stability theorem has been used to testify the asymptotic stability of the closed-loop system. The validity of the proposed control method has been verified in the Eight-Rotor MAV through real-time experiments. The experimental results show that the performance of the interval type-II fuzzy neural network based adaptive sliding mode controller could guarantee the Eight-Rotor MAV control system good performances under uncertainties, variations, and external disturbances. This controller is significantly improved, compared with the conventional adaptive sliding mode controller, and the type-I fuzzy neural network based sliding mode controller.

Stochastic Analysis of Base-Isolated Pool Structure Considering Fluid-Structure Interaction Effects (유체-구조물 상호작용을 고려한 면진구조물의 추계학적 응답해석)

  • Koh, Hyun Moo;Kim, Jae Kwan;Park, Kwan Soon;Ha, Dong Ho
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.3
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    • pp.463-472
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    • 1994
  • A method of stochastic response analysis of base-isolated fluid-filled pool structures subject to random ground excitations is studied. Fluid-structure interaction effects between the flexible walls and contained fluid are taken into account in the form of added mass matrix derived by FEM modeling of the contained fluid motion. The stationary ground excitation is represented by Modified Clough-Penzien spectral model and the nonstationary one is obtained by imposing an envelope function on the stationary one. The stationary and nonstationary response statistics of the two different isolation systems are obtained by solving the governing Lyapunov covariance matrix differential equations.

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Non-linear Adaptive Attitude Controller Design of Quadrotor UAV (쿼드로터 무인기 비선형 적응 자세제어기 설계)

  • Choi, In-Ho;Park, Mu-Hyuk;Kim, Hyun-Gi
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.13 no.6
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    • pp.2421-2427
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    • 2012
  • This paper is discussed the design on non-linear adaptive attitude controller for quadrotor UAV. Quadrotor UAV featured to have four rotor, required the special controller to compensate for the model parameter uncertainties as the unstable nonlinear system. In this research, we designed the adaptive controller to compensate for the payload changes even though it is changed with industrial applications. Especially, based on the mathematical model of UAV, non-linear adaptive controller is suggested and the stability is verified using the Lyapunov function and finally proved its performance and effectiveness of update laws with various payload by simulation.

Output Feedback Robust $H^infty$ Control for Uncertain Fuzzy Dynamic Systems (불확실성을 갖는 퍼지 시스템의 출력궤환 견실 $H^infty$ 제어)

  • Lee, Kap-Lai;Kim, Jong-Hae;Park, Hong-Bae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.37 no.6
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    • pp.15-24
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    • 2000
  • This paper presents an output feedback robust H$\infty$ control problem for a class of uncertain nonlinear systems, which can be represented by an fuzzy dynamic model. The nonlinear system is represented by Takagi-Sugeno fuzzy model, and the control design is carried out on the basis of the fuzzy model. Using a single quadratic Lyapunov function, the globally exponential stability and disturance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust H$\infty$ controllers are given in terms of linear matrix inequalities(LMIs). Constructive algorithm for design of robust H$\infty$ controller is also developed. The resulting controller is nonlinear and automatically tuned based on fuzzy operation.

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Delay-dependent Fuzzy H Controller Design for Delayed Fuzzy Dynamic Systems (시간지연 퍼지 시스템의 지연 종속 퍼지 H제어기 설계)

  • Lee, Kap-Rai
    • Journal of the Korean Institute of Intelligent Systems
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    • v.14 no.5
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    • pp.571-576
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    • 2004
  • This paper presents a delay dependent fuzzy $H_{\infty}$ controller design method for delayed fuzzy dynamic systems. Using delay-dependent Lyapunov function, the global exponential stability and $H_{\infty}$ performance problem arc discussed. A sufficient conditions for the existence of fuzzy controller is presented in terms of linear matrix inequalities(LMIs). A simulation example is given to illustrate the design procedures and performances of the proposed methods.

Reduced-order Parameter-dependent Robust $H_{\infty}$ Filtering for Discrete Uncertain Singular Systems (이산 불확실 특이시스템의 변수종속 차수축소 강인 $H_{\infty}$ 필터링)

  • Kim, Jong-Hae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.48 no.5
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    • pp.59-65
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    • 2011
  • In this paper, we present a reduced-order parameter-dependent robust $H_{\infty}$ filter design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for parameter-dependent singular systems is derived from a parameter-dependent Lyapunov function. On the basis of the obtained BRL, low order robust $H_{\infty}$ filter design method is presented by polytopic approach, new reduced-order method, and LMI(linear matrix inequality) technique. Finally, a numerical example is presented to illustrated the feasibility of the proposed method.

A VSMFC Controller Design of Robot Manipulators Using Computed Torque Method (CTM을 위한 로보트 매니퓰레이터의 VSMFC 제어기 설계)

  • Park, Sei-Seung;Park, Chong-Kug
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.27 no.10
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    • pp.53-59
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    • 1990
  • In the control of robot manipulators, this paper presents a design of a new variable structure model following controller(VSMFC) using computed torque method (CTM). A sufficient condition for the existence of a sliding mode is derived by Lyapunov function. The reference model is a double integrators and the acceleration input consists of a proportional-derivative controller for the purpose of the stabilization of system and the desired performance. The proposed control scheme which consists of upper bounded and estimated value of each term of the manipulator of matrix inversion. Therefore the simulation results show that this controller is improved to the convergence of desired trajectories.

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Design of Multiple Sliding Surface Control System for a Quadrotor Equipped with a Manipulator (매니퓰레이터 장착 쿼드로터를 위한 다중 슬라이딩 평면 제어의 시스템 설계)

  • Hwang, Nam Eung;Park, Jin Bae;Choi, Yoon Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.22 no.7
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    • pp.502-507
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    • 2016
  • In this paper, we propose a tracking control method for a quadrotor equipped with a 2-DOF manipulator, which is based on the multiple sliding surface control (MSSC) method. To derive the model of a quadrotor equipped with a 2-DOF manipulator, we obtain the models of a quadrotor and a 2-DOF manipulator based on the Lagrange-Euler formulation separately - and include the inertia and the reactive torque generated by a manipulator when these obtained models are combined. To make a quadrotor equipped with a manipulator track the desired path, we design a double-loop controller. The desired position is converted into the desired angular position in the outer controller and the system's angle tracks the desired angular position through the inner controller based on the MSSC method. We prove that the position-tracking error asymptotically converges to zero based on the Lyapunov stability theory. Finally, we demonstrate the effectiveness of the proposed control system through a computer simulation.

ExperimPerformance Evaluation of Modified Sliding Mode Control Algorithm for Nonlinear Structures (비선형 구조물에 대한 수정 슬라이딩모드 제어알고리즘 성능 평가)

  • Lee, Sang-Hyun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.20 no.2
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    • pp.147-155
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    • 2007
  • In this study, the performance of the modified sliding mode control proposed in the previous study is evaluated for seismic response control of nonlinear hysteretic structures. Modified sliding mode control(MSMC) utilizes the target derivative of Lyapunov function in order to calculate control force, and its performance was evaluated only lot linear structures in the previous study. However, considering that most structures subject to strong earthquake show nonlinear hysteretic behivior, the results from the previous study have limitations in practical application. The results from numerical analyses of single degree of freedom systems and base isolated system, which were described using Bouc-Wen model, indicate that the proposed MSMC algorithm shows better control performance than the existing sliding mode controller.

Double Sliding Surfaces based on a Sliding Mode Control for a Tracking Control of Mobile Robots (이동 로봇의 추종 제어를 위한 이중 슬라이딩 표면에 기반한 슬라이딩 모드 제어)

  • Lee, Jun Ku;Choi, Yoon Ho;Park, Jin Bae
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.6
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    • pp.495-500
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    • 2013
  • This paper proposes a double sliding surfaces based on a sliding mode control for a tracking control of nonholonomic mobile robots in the Cartesian coordinates. In order to remove sliding surface constraints, we design the additional sliding surface for the heading angle with respect to the newly defined coordinates. Then, we define the switching law based on the posture error to combine the designed sliding surface with the previous one. By using the double sliding surfaces and the switching law, we obtain the control law for arbitrary trajectories. It is proved that the position tracking error and the heading direction error asymptotically converge to zero, respectively, with the Lyapunov stability theory. Finally, through computer simulations, we demonstrate the effectiveness of the proposed control system.