Abstract This paper addresses a novel Constrained Magnetic Linear Quadratic Regulator (CM-LQR) scheme that generates a control torque vector on a plane approximately perpendicular to the local geomagnetic field. This control torque nearly precisely guarantees the production of an equivalent mechanical torque. The main ideas in the proposed method are (1) excluding the actuator dynamics from the system dynamics, and (2) incorporating the designed dynamics in the problem formulation using an algebraic mathematical constraint. In this way, a common time-variant system is transformed into a time-invariant system. The proposed CM-LQR generates the control torque via adjusting a time-variant control weighting matrix according to the geomagnetic field feedback. Unlike previous methods, our proposed control torque has a negligible parallel projection to the local geomagnetic field, and thus, it can be utilized fully by the magnetorquers. The hybrid Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) methods are applied to find an optimum state weighting matrix. Moreover, numerical simulation is performed to evaluate the performance and agility of the closed-loop control system. In addition, the obtained results are compared with a conventional magnetic LQR attitude controller to confirm that the presented scheme results in more agility and lower steady-state error in the attitude maneuver of the magnetically actuated satellites.

中文翻译：

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使用新型约束磁性线性二次调节器的卫星姿态控制

摘要 本文讨论了一种新颖的约束磁性线性二次调节器 (CM-LQR) 方案，该方案在近似垂直于局部地磁场的平面上生成控制扭矩矢量。该控制扭矩几乎精确地保证了等效机械扭矩的产生。所提出方法的主要思想是（1）从系统动力学中排除执行器动力学，以及（2）使用代数数学约束将设计的动力学纳入问题公式。这样，一个普通的时变系统就变成了一个时不变系统。所提出的 CM-LQR 通过根据地磁场反馈调整时变控制权重矩阵来产生控制转矩。不同于以往的方法，我们提出的控制转矩对当地地磁场的平行投影可以忽略不计，因此，它可以被磁力矩器充分利用。应用混合遗传算法 (GA) 和顺序二次规划 (SQP) 方法来寻找最佳状态加权矩阵。此外，进行数值模拟以评估闭环控制系统的性能和敏捷性。此外，将获得的结果与传统的磁 LQR 姿态控制器进行比较，以确认所提出的方案在磁致动卫星的姿态机动中具有更高的灵活性和更低的稳态误差。应用混合遗传算法 (GA) 和顺序二次规划 (SQP) 方法来寻找最佳状态加权矩阵。此外，进行数值模拟以评估闭环控制系统的性能和敏捷性。此外，将获得的结果与传统的磁 LQR 姿态控制器进行比较，以确认所提出的方案在磁致动卫星的姿态机动中具有更高的灵活性和更低的稳态误差。应用混合遗传算法 (GA) 和顺序二次规划 (SQP) 方法来寻找最佳状态加权矩阵。此外，进行数值模拟以评估闭环控制系统的性能和敏捷性。此外，将获得的结果与传统的磁 LQR 姿态控制器进行比较，以确认所提出的方案在磁致动卫星的姿态机动中具有更高的灵活性和更低的稳态误差。