Boundary Constrained Control of Flexible String Systems Subject to Disturbances
01 Jan 2020-IEEE Transactions on Circuits and Systems Ii-express Briefs (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 67, Iss: 1, pp 112-116
TL;DR: The hyperbolic barrier Lyapunov function and auxiliary systems are adopted to develop boundary constrained control with a disturbance observer for restraining vibrations, eliminating input and state constraints, and tackling external disturbances.
Abstract: This brief concentrates on controller design for flexible string systems subjected to external disturbances, input constraints, and state constraints. The hyperbolic barrier Lyapunov function and auxiliary systems are adopted to develop boundary constrained control with a disturbance observer for restraining vibrations, eliminating input and state constraints, and tackling external disturbances. The suggested control can ensure the input and state constraints and achieve asymptotic stability in the controlled system. With appropriate design parameters, the simulation results obtained verify the control performance.
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TL;DR: Two new boundary anti-disturbance control strategies are presented to eliminate vibration, track disturbance, and determine angle position for the flexible manipulator system possessing external disturbances.
Abstract: This paper examines the boundary disturbance observer-based control for a vibrating single-link flexible manipulator system possessing external disturbances. Two new boundary anti-disturbance control strategies are presented to eliminate vibration, track disturbance, and determine angle position for the flexible manipulator system. Achieving rigorous analysis with no model reduction, the derived control can ensure the angle positioning and bounded stability in the controlled system. By appropriately designing parameters, the resulting simulation results can demonstrate the control performance.
144 citations
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TL;DR: In this article, an adaptive fault tolerant control strategy is developed to suppress the vibrations of the flexible panel in the course of the attitude stabilization, and a Lyapunov-based stability analysis is conducted to determine whether the system energies, angular velocities and transverse deflections, remain bounded and asymptotically decay to zero in the case of infinite number of actuator failures.
Abstract: In this paper, we address simultaneous control of a flexible spacecraft’s attitude and vibrations in a three-dimensional space under input disturbances and unknown actuator failures. Using Hamilton’s principle, the system dynamics is modeled as an infinite dimensional system captured using partial differential equations. Moreover, a novel adaptive fault tolerant control strategy is developed to suppress the vibrations of the flexible panel in the course of the attitude stabilization. To determine whether the system energies, angular velocities and transverse deflections, remain bounded and asymptotically decay to zero in the case wherein the number of actuator failures is infinite, a Lyapunov-based stability analysis is conducted. Finally, extensive numerical simulations are performed to demonstrate the performance of the proposed adaptive control strategy.
103 citations
TL;DR: By visualizing input errors and extrinsic disturbances as an unknown “disturbance-like” term, a new robust adaptive vibration control technology and online updating laws can be constructed for riser systems to guarantee the oscillation reduction and compensation of uncertainties and dead zone.
Abstract: This article provides a framework of dead zone compensation and robust adaptive vibration control for uncertain spatial flexible riser systems. First, nonsymmetric dead zone nonlinearity is represented in the form of the desired control input with the addition of an extra nonlinear input error. Second, by visualizing those input errors and extrinsic disturbances as an unknown “disturbance-like” term, a new robust adaptive vibration control technology and online updating laws can be constructed for riser systems to guarantee the oscillation reduction and compensation of uncertainties and dead zone. Third, the constructed control ensures and achieves bounded Lyapunov stability in the controlled system. Ultimately, control performances are demonstrated with appropriate design parameters.
102 citations
Cites background from "Boundary Constrained Control of Fle..."
...Therefore, devising effective control strategies to dampen vibrations has become an attractive issue [14], [15]....
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TL;DR: An adaptive neural-network boundary control scheme for a flexible manipulator subject to input constraints, model uncertainties, and external disturbances is developed and the control performance of the developed control technique is examined by a numerical example.
Abstract: This article develops an adaptive neural-network (NN) boundary control scheme for a flexible manipulator subject to input constraints, model uncertainties, and external disturbances. First, a radial basis function NN method is utilized to tackle the unknown input saturations, dead zones, and model uncertainties. Then, based on the backstepping approach, two adaptive NN boundary controllers with update laws are employed to stabilize the like-position loop subsystem and like-posture loop subsystem, respectively. With the introduced control laws, the uniform ultimate boundedness of the deflection and angle tracking errors for the flexible manipulator are guaranteed. Finally, the control performance of the developed control technique is examined by a numerical example.
80 citations
References
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Book•
11 Feb 1992
TL;DR: In this article, the authors considered the generation and representation of a generator of C0-Semigroups of Bounded Linear Operators and derived the following properties: 1.1 Generation and Representation.
Abstract: 1 Generation and Representation.- 1.1 Uniformly Continuous Semigroups of Bounded Linear Operators.- 1.2 Strongly Continuous Semigroups of Bounded Linear Operators.- 1.3 The Hille-Yosida Theorem.- 1.4 The Lumer Phillips Theorem.- 1.5 The Characterization of the Infinitesimal Generators of C0 Semigroups.- 1.6 Groups of Bounded Operators.- 1.7 The Inversion of the Laplace Transform.- 1.8 Two Exponential Formulas.- 1.9 Pseudo Resolvents.- 1.10 The Dual Semigroup.- 2 Spectral Properties and Regularity.- 2.1 Weak Equals Strong.- 2.2 Spectral Mapping Theorems.- 2.3 Semigroups of Compact Operators.- 2.4 Differentiability.- 2.5 Analytic Semigroups.- 2.6 Fractional Powers of Closed Operators.- 3 Perturbations and Approximations.- 3.1 Perturbations by Bounded Linear Operators.- 3.2 Perturbations of Infinitesimal Generators of Analytic Semigroups.- 3.3 Perturbations of Infinitesimal Generators of Contraction Semigroups.- 3.4 The Trotter Approximation Theorem.- 3.5 A General Representation Theorem.- 3.6 Approximation by Discrete Semigroups.- 4 The Abstract Cauchy Problem.- 4.1 The Homogeneous Initial Value Problem.- 4.2 The Inhomogeneous Initial Value Problem.- 4.3 Regularity of Mild Solutions for Analytic Semigroups.- 4.4 Asymptotic Behavior of Solutions.- 4.5 Invariant and Admissible Subspaces.- 5 Evolution Equations.- 5.1 Evolution Systems.- 5.2 Stable Families of Generators.- 5.3 An Evolution System in the Hyperbolic Case.- 5.4 Regular Solutions in the Hyperbolic Case.- 5.5 The Inhomogeneous Equation in the Hyperbolic Case.- 5.6 An Evolution System for the Parabolic Initial Value Problem.- 5.7 The Inhomogeneous Equation in the Parabolic Case.- 5.8 Asymptotic Behavior of Solutions in the Parabolic Case.- 6 Some Nonlinear Evolution Equations.- 6.1 Lipschitz Perturbations of Linear Evolution Equations.- 6.2 Semilinear Equations with Compact Semigroups.- 6.3 Semilinear Equations with Analytic Semigroups.- 6.4 A Quasilinear Equation of Evolution.- 7 Applications to Partial Differential Equations-Linear Equations.- 7.1 Introduction.- 7.2 Parabolic Equations-L2 Theory.- 7.3 Parabolic Equations-Lp Theory.- 7.4 The Wave Equation.- 7.5 A Schrodinger Equation.- 7.6 A Parabolic Evolution Equation.- 8 Applications to Partial Differential Equations-Nonlinear Equations.- 8.1 A Nonlinear Schroinger Equation.- 8.2 A Nonlinear Heat Equation in R1.- 8.3 A Semilinear Evolution Equation in R3.- 8.4 A General Class of Semilinear Initial Value Problems.- 8.5 The Korteweg-de Vries Equation.- Bibliographical Notes and Remarks.
11,637 citations
TL;DR: The global exponential stability of the proposed disturbance observer (DO) is guaranteed by selecting design parameters, which depend on the maximum velocity and physical parameters of robotic manipulators.
Abstract: A new nonlinear disturbance observer (NDO) for robotic manipulators is derived in this paper. The global exponential stability of the proposed disturbance observer (DO) is guaranteed by selecting design parameters, which depend on the maximum velocity and physical parameters of robotic manipulators. This new observer overcomes the disadvantages of existing DOs, which are designed or analyzed by linear system techniques. It can be applied in robotic manipulators for various purposes such as friction compensation, independent joint control, sensorless torque control and fault diagnosis. The performance of the proposed observer is demonstrated by the friction estimation and compensation for a two-link robotic manipulator. Both simulation and experimental results show the NDO works well.
1,424 citations
"Boundary Constrained Control of Fle..." refers background in this paper
...This is a reasonable assumption since there is no prior information on ḋ [24]....
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01 Jan 2016
TL;DR: Semigroups of linear operators and applications to partial differential equations, a large number of people have search numerous times for their favorite novels like this, but end up in harmful downloads.
Abstract: Thank you very much for downloading semigroups of linear operators and applications to partial differential equations. As you may know, people have search numerous times for their favorite novels like this semigroups of linear operators and applications to partial differential equations, but end up in harmful downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they cope with some malicious bugs inside their desktop computer.
1,059 citations
"Boundary Constrained Control of Fle..." refers methods in this paper
...Hence, we use the Lumer-Phillips theorem to obtain that there is a generated C0 semigroup Q(t) contracted on Υ [25] with Q(t) as a bounded linear operator on Υ for t ≥ 0....
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TL;DR: Cooperative control laws are proposed and the integral-barrier Lyapunov functions are employed for stability analysis of the closed-loop system and Adaption laws are developed for handling parametric uncertainties.
496 citations
"Boundary Constrained Control of Fle..." refers background in this paper
...He and Ge [19] constructed an active cooperative boundary control to eliminate the oscillation and tension constraints in nonuniform crane systems under the influence of unknown disturbances....
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TL;DR: A unified framework of iterative learning control for typical flexible structures under spatiotemporally varying disturbances is proposed and Boundary iterativelearning control (BILC) laws are proposed to guarantee the learning convergence.
264 citations
"Boundary Constrained Control of Fle..." refers background or methods in this paper
...[17] devised an iterative learning control framework for an input-restricted flexible system....
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...The research in [15] and [17]–[20] employed hyperbolic tangent functions (HTF) or barrier Lyapunov functions (BLF) to provide effective solutions for flexible systems with input or output constraints....
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