The use of the linear form of dynamical equations of the satellite attitude control system for its analysis and synthesis

Moldabekov, Meirbek; Sukhenko, Anna; Shapovalova, Darya; Yelubayev, Suleimen

doi:10.15632/jtam-pl/129071

Cited by 2 publications

(9 citation statements)

References 7 publications

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“…Proof. Necessity: If the nonlinear system in Equation ( 7) is asymptotically stable, then due to the equivalence of this system and the system in Equation (18), where the latter is also asymptotically stable for every matrix B(t). This is uniquely determined by a solution for the system in Equation ( 7) which satisfies Cauchy's theorem regarding the existence and uniqueness of its solution.…”

Section: Necessary and Sufficient Conditions For Asymptotic Stability...mentioning

confidence: 99%

“…All that remains is to satisfy the condition of asymptotic stability of a linear system with constant parameters (Equation ( 20)). The last condition is fulfilled since the matrix of the linear system (Equation ( 20)) is the ultimate matrix of the system in Equation (18); that is, we have…”

Section: Necessary and Sufficient Conditions For Asymptotic Stability...mentioning

confidence: 99%

“…The article by the authors of [18] outlines a method for synthesizing the control law parameters in accordance with the stability conditions and requirements for the quality indicators of transients in the satellite control system. The method is based on specifying the desired location of the roots of the characteristic equation (Equation ( 22)) of the system of equations in Equation (20).…”

Section: Synthesis Of the Control Law Parametersmentioning

confidence: 99%

“…Under the conditions in Equation ( 28), the coefficients for the characteristic equation of the system in Equation ( 20) will take the following form: Then, the sufficient conditions for asymptotic stability [18] of the system in Equation ( 20) will be as follows:…”

Section: Synthesis Of the Control Law Parametersmentioning

confidence: 99%

“…The authors of [18] analyzed the nonlinear equations of SACS dynamics with reaction wheels. The equations were obtained for a special choice of variables for the state vector of the SACS.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics Analysis of a Nonlinear Satellite Attitude Control System Using an Exact Linear Model

Moldabekov,

Sukhenko,

Orazaly

et al. 2023

Mathematics

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This study aims to analyze the nonlinear dynamics of a satellite attitude control system equipped with reaction wheels and a PD controller. Based on the angular momentum conservation theorem for a closed mechanical system, the nonlinear equations of the attitude control system dynamics are presented as a linear system of differential equations with time-varying parameters. The asymptotic properties of the angular momentum of a mechanical system including a satellite and reaction wheels as rigid bodies are investigated. A relation has been established between the dynamic parameters of the attitude control system and the initial value of the angular momentum of the satellite. The issue of asymptotic stability for differential equations with time-varying parameters is simplified to the asymptotic stability problem for the ultimate homogeneous system of linear differential equations with constant elements. The dependencies of the dynamic parameters of the attitude control system on the constant parameters of this ultimate system of linear differential equations, as well as the initial values of the satellite’s angular momentum, enable us to apply proven and effective engineering methods. These methods are used not only for analyzing the stability of the control system but also for synthesizing the parameters of the control law based on the quality requirements of transient processes such as the stability margin, responsiveness, oscillation, transient time, and overshoot. In this case, the calculation of the control law parameters will be grounded in exact equations, not on approximate equations of the control system dynamics obtained by linearization.

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Section: Necessary and Sufficient Conditions For Asymptotic Stability...mentioning

confidence: 99%

Section: Necessary and Sufficient Conditions For Asymptotic Stability...mentioning

confidence: 99%

Section: Synthesis Of the Control Law Parametersmentioning

confidence: 99%

Section: Synthesis Of the Control Law Parametersmentioning

confidence: 99%

“…The authors of [18] analyzed the nonlinear equations of SACS dynamics with reaction wheels. The equations were obtained for a special choice of variables for the state vector of the SACS.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Dynamics Analysis of a Nonlinear Satellite Attitude Control System Using an Exact Linear Model

Moldabekov,

Sukhenko,

Orazaly

et al. 2023

Mathematics

Self Cite

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Optimal Synthesis of a Satellite Attitude Control System under Constraints on Control Torques and Velocities of Reaction Wheels

Moldabekov,

Aden,

Orazaly

et al. 2024

Mathematics

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The problem of optimal synthesis of a nonlinear system’s control law parameters of satellite attitude control under constraints is considered. The maximum stability degree of a system is considered as an optimality criterion. The reaction wheels’ control moments and angular velocities achievable within the drives’ physical characteristics are considered as constraints. A linear model of the system converted from the original nonlinear model was used to solve the problem. The decomposition method, based on the transition from real time to relative time, is used to separate the tasks of optimality criterion maximization and constraints consideration. A method of synthesizing the optimal form of system transient process according to the maximum stability degree criterion is developed. An analytical method for determining the optimal values of control law parameters is proposed, based on the structural features of the linear differential equations system. A method that takes into account constraints on control moments and angular velocities of reaction wheels, based on transition scale from relative time to real time and its calculation algorithm, ensuring that conditions of all constraints are met, is developed. An example of solving the problem of optimal system synthesis is considered. The results demonstrate the effectiveness and simplicity of the proposed methods and algorithm for targeted selection of a system’s technical characteristics, taking into account constraints on reaction wheels’ maximum angular velocities and control moments values.

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The use of the linear form of dynamical equations of the satellite attitude control system for its analysis and synthesis

Cited by 2 publications

References 7 publications

Dynamics Analysis of a Nonlinear Satellite Attitude Control System Using an Exact Linear Model

Dynamics Analysis of a Nonlinear Satellite Attitude Control System Using an Exact Linear Model

Optimal Synthesis of a Satellite Attitude Control System under Constraints on Control Torques and Velocities of Reaction Wheels

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