混合多速率控制系统的LFT建模与基于μ的鲁棒性能分析
LFT modelling and $μ$-based robust performance analysis of hybrid multi-rate control systems
AI总结：
本文针对含参数不确定性的混合多速率控制系统，提出基于LFT建模和μ分析的鲁棒稳定性与H∞性能分析方法，并通过姿态控制示例验证其有效性。
摘要：
本文重点研究在参数不确定性存在的情况下，混合连续/离散时间线性多速率控制系统的鲁棒稳定性和H∞性能分析。这些不确定性以有理方式影响连续时间被控对象，随后将其建模为线性分式变换（LFT）。基于零阶保持（ZOH）LFT离散化过程，在付出有界可量化近似的代价下，进而利用保持LFT结构的下采样操作，推导出单速率离散时间闭环LFT模型。值得注意的是，对于任意阶跃输入以及不确定参数的任意容许取值，该模型的输出在最慢控制回路的每个采样时刻均覆盖了原始混合多速率闭环系统的输出。这样一个同时捕获离散化误差的LFT模型，随后可用于通过基于μ的方法评估鲁棒稳定性和保证的H∞性能。所提出的方法在一个受多速率姿态控制系统验证启发的现实且易于复现的示例上进行了说明。
英文摘要：
This paper focuses on robust stability and $H_\infty$ performance analyses of hybrid continuous/discrete time linear multi-rate control systems in the presence of parametric uncertainties. These affect the continuous-time plant in a rational way which is then modeled as a Linear Fractional Transformation (LFT). Based on a zero-order-hold (ZOH) LFT discretization process at the cost of bounded quantifiable approximations, and then using LFT-preserving down-sampling operations, a single-rate discrete-time closed-loop LFT model is derived. Interestingly, for any step inputs, and any admissible values of the uncertain parameters, the outputs of this model cover those of the initial hybrid multi-rate closed-loop system at every sampling time of the slowest control loop. Such an LFT model, which also captures the discretization errors, can then be used to evaluate both robust stability and guaranteed $H_\infty$ performance with a $μ$-based approach. The proposed methodology is illustrated on a realistic and easily reproducible example inspired by the validation of multi-rate attitude control systems.
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