Generalized Frequency Domain State-Space Models for Analyzing Flexible Rotating Spacecraft

Turner, James D.; Elgohary, Tarek A.

doi:10.1007/s40295-013-0028-7

Cited by 4 publications

(6 citation statements)

References 4 publications

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“…The function f that represents the elements of the solution is derived from the matrix exponential solution of the flexible appendage sub-problem, [6,27], and is given by…”

Section: The Generalized State Space Modelmentioning

confidence: 99%

“…Generally, both the aerospace and the control communities have been content with the numerical approximations following finite elements or assumed modes techniques for the past decade. Building on previous developments, this work presents a new approach for the dynamics and control of distributed parameters models by deriving the analytic transfer functions to obtain the system truncation-error-free frequency response, [6,8,26,27]. The existence of the exact transfer functions is then utilized in frequency domain control for gains selection of a Lyapunov stable controller designed to drive the system from its initial state to a target state while suppressing the vibrations of the flexible appendages.…”

Section: Introductionmentioning

confidence: 99%

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Analytic Transfer Functions for the Dynamics & Control of Flexible Rotating Spacecraft Performing Large Angle Maneuvers

2015

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A symmetric flexible rotating spacecraft can be modeled as a distributed parameter system of a rigid hub attached to two flexible appendages with tip masses. First, Hamilton's extended principle is utilized to establish a general treatment for deriving the dynamics of multi-body dynamical systems to establish a hybrid system of integro-partial differential equations that model the evolution of the system in space and time. A Generalized State Space (GSS) system of equations is constructed in the frequency domain to obtain analytic transfer functions for the rotating spacecraft. This model does not include spatial discretization. The frequency response of the generally modeled spacecraft and a special case with no tip masses are presented. Numerical results for the system frequency response obtained from the analytic transfer functions are presented and compared against the classical assumed modes numerical method with two choices of admissible functions. The truncation-errorfree analytic results are used to validate the numerical approximations and to agree well with the classical widely used finite dimensional numerical solutions. Fundamentally, we show that the rigorous transfer function, without introduction of spatial T.A. Elgohary is a AAS Member. J of Astronaut Sci discretization, can be directly used in control law design with a guarantee of Lyapunov stable closed loop dynamics. The frequency response of the system is used in a classical control problem where the Lyapunov stable controller is derived and tested for gain selection. The correlation between the controller design in the frequency domain utilizing the analytic transfer functions and the system response is analyzed and verified. The derived analytic transfer functions provide a powerful tool to test various control schemes in the frequency domain and a validation platform for existing numerical methods for distributed parameters models. The same platform has been used to obtain the frequency response of more complex beam models following Timoshenko beam theory and the control problem for such models can be pursued in future works.

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“…The function f that represents the elements of the solution is derived from the matrix exponential solution of the flexible appendage sub-problem, [6,27], and is given by…”

Section: The Generalized State Space Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytic Transfer Functions for the Dynamics & Control of Flexible Rotating Spacecraft Performing Large Angle Maneuvers

2015

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“…(22) are presented in previous works. 14,15 The expressions obtained can then be expressed in the general form,…”

Section: The Generalized State Space Modelmentioning

confidence: 99%

“…6,8,9,10,11,12 Analytical transfer functions for both models, no tip mas and tip mass, have been previously developed. 13,14,15 The transfer functions are used to analyze the system frequency response and numerical results are compared and verified against the assumed modes solution.…”

Section: Introductionmentioning

confidence: 99%

“…11,12 A comprehensive literature survey, 22 covers the modeling and control of flexible appendage in the controls community. In this work the existence of the exact transfer functions 13,14,15 for both models is utilized in developing frequency domain control schemes for the spacecraft. The frequency response developed is used to obtain the gains required to implement a the controller that would drive the system from its initial state to a target state.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics and Controls of a Generalized Frequency Domain Model Flexible Rotating Spacecraft

Elgohary

Turner

Junkins

2014

SpaceOps 2014 Conference

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Modeling a flexible rotating spacecraft as a distributed parameters system of a rigid hub attached to a flexible appendage is very common. When considering large angle maneuvers the same model applies to flexible robotic manipulators by adding a tip mass at the end of the flexible appendage to account for the payload. Following Euler-Bernoulli beam theory the dynamics for both no tip mass and tip mass models are derived. A Generalized State Space (GSS) system is constructed in the frequency domain to completely solve for the input-output transfer functions of the models. The analytical solution of the GSS is obtained and compared against the classical assumed modes method. The frequency response of the system is then used in a classical control problem where a Lyapunov stable controller is derived and tested for gain selection. The assumed modes method is used to obtain the time response of the system to verify the gain selections and draw connections between the frequency and the time domains. The GSS approach provides a powerful tool to test various control schemes in the frequency domain and a validation platform for existing numerical methods utilized to solve distributed parameters models.

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Onboard estimation of unknown dynamics of flexible spacecraft

Woodward,

Bevilacqua

2024

Acta Astronautica

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Generalized Frequency Domain State-Space Models for Analyzing Flexible Rotating Spacecraft

Cited by 4 publications

References 4 publications

Analytic Transfer Functions for the Dynamics & Control of Flexible Rotating Spacecraft Performing Large Angle Maneuvers

Analytic Transfer Functions for the Dynamics & Control of Flexible Rotating Spacecraft Performing Large Angle Maneuvers

Dynamics and Controls of a Generalized Frequency Domain Model Flexible Rotating Spacecraft

Onboard estimation of unknown dynamics of flexible spacecraft

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