针对在轨磁悬浮飞轮高稳定度控制的难题，本项目探索基于复变量频率特性的在轨磁悬浮飞轮章动和进动稳定性的定量分析与控制方法。首先通过变量重构，将双输入双输出实变量系统转化为单输入单输出复变量系统，揭示变量重构前后系统极点的分布规律，研究复变量系统极点分布与章动、进动间的映射关系，提出区分在轨磁悬浮飞轮章动和进动的数学表征方法；其次推导章动和进动临界稳定的充要条件，提出复变量频率特性概念，建立在轨磁悬浮飞轮章动和进动的标称和鲁棒稳定判据，明晰姿态机动角速度和轨道角速度等天地差异因素对章动和进动相对稳定性的影响规律；最后提出自适应力矩补偿和模态鲁棒解耦相结合的控制方法，利用提出的稳定判据对控制器参数进行定量和优化设计。基于以上研究，突破现有理论无法从解析角度定量分析在轨磁悬浮飞轮章动和进动稳定性的瓶颈，消除因控制参数设计不当导致章动或进动失稳的隐患，为在轨磁悬浮飞轮的安全稳定运行奠定必要的基础。

Aimed at the high-stability control issues of the on-orbit magnetically suspended flywheels (MSFWs), the quantitative stability analysis and control of their nutation and precession modes has been studied based on complex-variable frequency charactersitics method. Firstly, the two-input two-output real-variable system is converted into the single-input single-output system with complex variable by variable reconstruction. The stability equivalence of the two systems before and after variable reconstruction has been proven, and the inherent relationships between the distribution of the closed-loop poles of the complex-variable system as well as the nutation and precession stability are revealed, yielding the mathematical token method of differentiating the nutation and precession modes for on-orbit MSFWs. Secondly, the necessary and sufficient conditions of the critical stability for nutation and precession are studied, and the concept of complex-variable frequency characteristics is proposed. Based on these, the nominal and robust stabiliy criteria of nutation and precession modes for on-orbit MSFWs are built, revealing analytically the effecting law of the attitude manevor speed,orbit angular rate and other space-ground differnece factors on the relative stability of the nutaton and precession modes. Finally, to realize the high-stability control for on-orbit MSFWs, the compound control method based on adaptive torque compensation of the magnetic force and robust modal decoupling strategy is pressented. According to the presented stability criteria, the controller parameters have been further designed quantificationally and optimized. This breaks through the dilemma in which the existing theories can't analyze the stability margins analytically, and avoids the latent instability of nutation or precession caused by improper controller coefficients, establishing the necessary foundation for the safe and stable applications of orbit-MSFWs.