Stiffening control of a class of nonlinear affine systems

Karray, Fakhri; Grewal, Anant; Glaum, M.; Modi, V. J.

doi:10.1109/7.575886

Cited by 76 publications

(34 citation statements)

References 6 publications

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“…Thus, deformations of solar panels should be discretized with finite element method (FEM) [4] or modal approach using mode shapes [5][6][7][8]. The FEM model is not convenient for designing control system, because its degree of freedom is usually too large [9].…”

mentioning

confidence: 99%

“…It should be pointed out that the modes used in Refs. [5][6][7][8]11,12] are modes for a particular flexible body, such as beam functions [8] or other admissible basis functions satisfying the geometric boundary conditions of flexible structures [5,7], not for the whole system. In other words, those modes of particular appendages are used to assume the global modes of the system and thus called 'assumed modes.'…”

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confidence: 99%

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Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh–Ritz method

2016

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With extending the Rayleigh-Ritz procedure to study the hub-plate system, the characteristics of global analytical modes are addressed for a typical rigid-flexible coupling dynamic system, i.e., a threeaxis attitude stabilized spacecraft installed with a pair of solar arrays. The displacement field of the solar arrays is expressed as a series of admissible functions which is a set of characteristic orthogonal polynomials generated directly by employing Gram-Schmidt process. The rigid body motion of spacecraft is represented by the product of constant and generalized coordinate. Then, through Rayleigh-Ritz procedure, the eigenvalue equation of the three-axis attitude stabilized spacecraft installed with a pair of solar arrays is derived. Solving this eigenvalue equation, the frequencies and analytical expressions of global modes for the flexible spacecraft are obtained. To validate the present analysis, comparisons between the results of the present method and ANSYS software are performed and very good agreement is achieved. The convergence studies demonstrate the high accuracy, excellent convergence and high efficiency of the present approach. Finally, the method is applied to study the characteristics of global modes of the flexible spacecraft.

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confidence: 99%

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confidence: 99%

Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh–Ritz method

2016

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“…Based on the Lyapunov stability, nonlinear PID-like control design method for the rigid body attitude stabilization was also presented in Reference [2]. The design of robust and nonlinear attitude control systems has been attempted in References [3][4][5]. In face of the increasingly complex and highly uncertain nature of spacecraft dynamical systems, the insensitivity and robustness of variable structure control (VSC) to certain types of disturbances and uncertainties make it attractive for spacecraft control problems [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Neural network‐based adaptive attitude tracking control for flexible spacecraft with unknown high‐frequency gain

2009

Adaptive Control & Signal

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Adaptive control design using neural networks (a) is investigated for attitude tracking and vibration stabilization of a flexible spacecraft, which is operated at highly nonlinear dynamic regimes. The spacecraft considered consists of a rigid body and two flexible appendages, and it is assumed that the system parameters are unknown and the truncated model of the spacecraft has finite but arbitrary dimension as well, for the purpose of design. Based on this nonlinear model, the derivation of an adaptive control law using neural networks (NNs) is treated, when the dynamics of unstructured and state-dependent nonlinear function are completely unknown. A radial basis function network that is used here for synthesizing the controller and adaptive mechanisms is derived for adjusting the parameters of the network and estimating the unknown parameters. In this derivation, the Nussbaum gain technique is also employed to relax the sign assumption for the high-frequency gain for the neural adaptive control. Moreover, systematic design procedure is developed for the synthesis of adaptive NN tracking control with L 2 -gain performance. The resulting closed-loop system is proven to be globally stable by Lyapunov's theory and the effect of the external disturbances and elastic vibrations on the tracking error can be attenuated to the prescribed level by appropriately choosing the design parameters. Numerical simulations are performed to show that attitude tracking control and vibration suppression are accomplished in spite of the presence of disturbance torque/parameter uncertainty.

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“…VISs mostly have contained torque-generating instruments as control devices and have been dealt with by control methods that can take nonlinearity into account. [1][2][3][4] Alternatively, a concept of using the variable inertia to control VISs has been proposed. For example, an adaptive gyroscopic damper (AGD) system has been presented 5) and studied as one of the adaptive structure systems.…”

Section: Introductionmentioning

confidence: 99%

“…There are primarily two FLTs: the local coordinates transformation 4) and the noninteracting control.…”

Section: Introductionmentioning

confidence: 99%

Feedback Linearization Technique in Variable Inertia Systems.

Ozawa

Furuya

2002

Trans. Japan Soc. Aero. S Sci.

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A formula of variable inertia systems, which contain controllable inertia, is introduced, and a feedback linearization technique for the variable inertia systems is proposed. This linearization technique allows us to control the variable inertia systems through linear control methods without linear control inputs. The formula of variable inertia systems consists of two subsystems related to rotation and variable inertia. The rotational subsystem contains an ordinary differential equation, and the subsystem of variable inertia is independent from the alternative subsystem. Because of these system properties, the proposed technique is composed of a noninteracting condition to linear control inputs for the rotational subsystem, and a servo controller for the subsystem of variable inertia to satisfy the noninteracting condition. The resulting closed-loop system becomes linear. To validate the feedback linearization technique, a vibration suppression controller for a 2-DOF variable inertia system without dampers is derived, and numerical simulations of the controlled system are carried out. The simulation results confirm that the system is sufficiently controlled through the feedback linearization technique without linear control inputs.

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Stiffening control of a class of nonlinear affine systems

Cited by 76 publications

References 6 publications

Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh–Ritz method

Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh–Ritz method

Neural network‐based adaptive attitude tracking control for flexible spacecraft with unknown high‐frequency gain

Feedback Linearization Technique in Variable Inertia Systems.

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