Nonlinear Feedback Controller

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Panagiotis D. Christofides - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE: Design and Application to a Sputtering Process
    Industrial & Engineering Chemistry Research, 2006
    Co-Authors: Yiming Lou, Panagiotis D. Christofides
    Abstract:

    In this work, we develop a method for Nonlinear Feedback control of the roughness of a one-dimensional surface whose evolution is described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourthorder Nonlinear stochastic partial differential equation. We initially formulate the stochastic KSE into a system of infinite Nonlinear stochastic ordinary differential equations by using Galerkin’s method. A finite-dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A Nonlinear Feedback Controller is then designed based on the finite-dimensional approximation to control the surface roughness. An analysis of the closed-loop Nonlinear infinite-dimensional system is performed to characterize the closed-loop performance enforced by the Nonlinear Feedback Controller in the closed-loop infinite-dimensional system. The effectiveness of the proposed Nonlinear Controller and the advantages of the Nonlinear Controller over a linear Controller resulting from the linearization of the Nonlinear Controller around the zero solution are demonstrated through numerical simulations. Finally, a successful application of a stochastic KSE-based Nonlinear Feedback Controller to the kinetic Monte Carlo model of a sputtering process is also demonstrated.

  • CDC - Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE
    Proceedings of the 45th IEEE Conference on Decision and Control, 2006
    Co-Authors: Yiming Lou, Panagiotis D. Christofides
    Abstract:

    In this work, we develop a method for Nonlinear Feedback control of the roughness of a one-dimensional surface whose evolution is described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourth-order Nonlinear stochastic partial differential equation. We initially formulate the stochastic KSE into a system of infinite Nonlinear stochastic ordinary differential equations by using modal decomposition. A finite-dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A Nonlinear Feedback Controller is then designed based on the finite-dimensional approximation to control the surface roughness. An analysis of the closed-loop Nonlinear infinite-dimensional system is performed to characterize the closed-loop performance enforced by the Nonlinear Feedback Controller in the closed-loop infinite-dimensional system. The effectiveness of the proposed Nonlinear Controller and the advantages of the Nonlinear Controller over a linear Controller resulting from the linearization of the Nonlinear Controller around the zero solution are demonstrated through numerical simulations.

  • Nonlinear control of incompressible fluid flows
    Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1
    Co-Authors: James Baker, Panagiotis D. Christofides
    Abstract:

    This paper proposes a methodology for the synthesis of Nonlinear finite-dimensional output Feedback Controllers for incompressible Newtonian fluid flows described by the two-dimensional Navier-Stokes equations. The method is used to synthesize a Nonlinear Feedback Controller for the two-dimensional channel flow that enhances the convergence to the parabolic velocity profile.

Nagesh Prabhu - One of the best experts on this subject based on the ideXlab platform.

  • Analysis and Performance evaluation of Type 1 Fuzzy Reactive Current Controller with STATCOM
    Energy Procedia, 2017
    Co-Authors: Dinesh Shetty, Nagesh Prabhu
    Abstract:

    Abstract The STATIC Synchronous Compensator is a shunt connected Voltage source converter (VSC) uses self-commutating devices such as GTOs thereby utilized for reactive power control. The purpose of employing STATCOM at the midpoint of long transmission line is for the enhancement of power transfer capability and/or reactive power control at the load centre by voltage regulation. For reactive current control, the use of PI Controller and Nonlinear Feedback Controller is investigated. PI Controller found to be causing oscillatory instability in inductive mode of operation of STATCOM and can be overcome by the Nonlinear Feedback Controller wherein the transient response of the STATCOM depends on the Controller parameters selected. There is always need for parameter optimization in Nonlinear Feedback Controller. This paper presents a model free approach using fuzzy logic Controller for reactive current control of STATCOM. The performance of the designed Controller is evaluated by transient simulation. It is observed that the STATCOM with fuzzy logic Controller shows excellent transient response for the step change in the reactive current reference. While the eigenvalue analysis and Controller design are based on D-Q model, the transient simulation is based on D-Q of STATCOM (which considers switching action of VSC).

  • Ziegler Nichols method based Robust reactive current Controller for STATCOM
    Energy Procedia, 2017
    Co-Authors: Dinesh Shetty, Nagesh Prabhu
    Abstract:

    Abstract The STATIC Synchronous Compensator is a shunt connected Voltage Source Converter (VSC) using self-commutating devices such as GTOs utilized for reactive power control. The purpose of employing STATCOM at somewhere in the middle of long transmission line by regulating the voltage at the point of connection for the intensification of power transfer capability or reactive power control at the load centre. The reactive current control, makes use of PI Controller without and with Nonlinear Feedback Controller. The step response of the reactive current and Eigen value analysis is carried out using 3phase model and D-Q models of STATCOM. It is observed that, fast acting conventional PI Controller causes reactive current oscillations in inductive mode of operation of STATCOM which leads to instability.. The problem of instability can be overcome by using Nonlinear Feedback Controller and by Controller parameter optimization for good transient response. The present work is mainly focused on elimination of the requirement of Nonlinear Feedback Controller while ensuring good transient response. This paper presents a approach of tuning the parameters of PI Controller using Ziegler Nichols method for reactive current control of STATCOM. The assessment of effectiveness of the designed Controller is carried out by transient simulation. It is observed that the proposed Controller exhibits good transient response while ensuring robust performance under varying operating conditions.

Masayoshi Tomizuka - One of the best experts on this subject based on the ideXlab platform.

  • a Nonlinear Feedback Controller for aerial self righting by a tailed robot
    International Conference on Robotics and Automation, 2013
    Co-Authors: Evan Changsiu, Thomas Libby, Matthew Brown, Robert J Full, Masayoshi Tomizuka
    Abstract:

    In this work, we propose a control scheme for attitude control of a falling, two link active tailed robot with only two degrees of freedom of actuation. We derive a simplified expression for the robot's angular momentum and invert this expression to solve for the shape velocities that drive the body's angular momentum to a desired value. By choosing a body angular velocity vector parallel to the axis of error rotation, the Controller steers the robot towards its desired orientation. The proposed scheme is accomplished through Feedback laws as opposed to feedforward trajectory generation, is fairly robust to model uncertainties, and is simple enough to implement on a miniature microController. We verify our approach by implementing the Controller on a small (175 g) robot platform, enabling rapid maneuvers approaching the spectacular capability of animals.

  • ICRA - A Nonlinear Feedback Controller for aerial self-righting by a tailed robot
    2013 IEEE International Conference on Robotics and Automation, 2013
    Co-Authors: Evan Chang-siu, Thomas Libby, Robert J Full, Matthew S. Brown, Masayoshi Tomizuka
    Abstract:

    In this work, we propose a control scheme for attitude control of a falling, two link active tailed robot with only two degrees of freedom of actuation. We derive a simplified expression for the robot's angular momentum and invert this expression to solve for the shape velocities that drive the body's angular momentum to a desired value. By choosing a body angular velocity vector parallel to the axis of error rotation, the Controller steers the robot towards its desired orientation. The proposed scheme is accomplished through Feedback laws as opposed to feedforward trajectory generation, is fairly robust to model uncertainties, and is simple enough to implement on a miniature microController. We verify our approach by implementing the Controller on a small (175 g) robot platform, enabling rapid maneuvers approaching the spectacular capability of animals.

Tahereh Binazadeh - One of the best experts on this subject based on the ideXlab platform.

Yiming Lou - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE: Design and Application to a Sputtering Process
    Industrial & Engineering Chemistry Research, 2006
    Co-Authors: Yiming Lou, Panagiotis D. Christofides
    Abstract:

    In this work, we develop a method for Nonlinear Feedback control of the roughness of a one-dimensional surface whose evolution is described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourthorder Nonlinear stochastic partial differential equation. We initially formulate the stochastic KSE into a system of infinite Nonlinear stochastic ordinary differential equations by using Galerkin’s method. A finite-dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A Nonlinear Feedback Controller is then designed based on the finite-dimensional approximation to control the surface roughness. An analysis of the closed-loop Nonlinear infinite-dimensional system is performed to characterize the closed-loop performance enforced by the Nonlinear Feedback Controller in the closed-loop infinite-dimensional system. The effectiveness of the proposed Nonlinear Controller and the advantages of the Nonlinear Controller over a linear Controller resulting from the linearization of the Nonlinear Controller around the zero solution are demonstrated through numerical simulations. Finally, a successful application of a stochastic KSE-based Nonlinear Feedback Controller to the kinetic Monte Carlo model of a sputtering process is also demonstrated.

  • CDC - Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE
    Proceedings of the 45th IEEE Conference on Decision and Control, 2006
    Co-Authors: Yiming Lou, Panagiotis D. Christofides
    Abstract:

    In this work, we develop a method for Nonlinear Feedback control of the roughness of a one-dimensional surface whose evolution is described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourth-order Nonlinear stochastic partial differential equation. We initially formulate the stochastic KSE into a system of infinite Nonlinear stochastic ordinary differential equations by using modal decomposition. A finite-dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A Nonlinear Feedback Controller is then designed based on the finite-dimensional approximation to control the surface roughness. An analysis of the closed-loop Nonlinear infinite-dimensional system is performed to characterize the closed-loop performance enforced by the Nonlinear Feedback Controller in the closed-loop infinite-dimensional system. The effectiveness of the proposed Nonlinear Controller and the advantages of the Nonlinear Controller over a linear Controller resulting from the linearization of the Nonlinear Controller around the zero solution are demonstrated through numerical simulations.