基于分段常数调节增益的无奇点MRAC及其在飞控系统中的应用
Piecewise constant tuning gain based singularity-free MRAC with application to aircraft control systems
AI总结：
本文提出一种带分段常数调节增益的无奇点输出反馈MRAC方法，将估计误差方程转为线性回归形式以直接估计未知参数，无需高频增益先验知识，可保证闭环稳定与渐近跟踪，经飞控仿真验证有效。
摘要：
本文提出了一种创新的无奇点输出反馈模型参考自适应控制（MRAC）方法，适用于各类具有一般相对阶的连续时间线性时不变（LTI）系统。现有方案如Nussbaum方法和基于多模型的方法通过持续切换和重复参数估计来处理未知高频增益，而所提方法无需高频增益的先验知识，也无需额外设计条件，即可规避这些问题。该方法的核心创新在于，通过本文提出的带分段常数调节增益的改进MRAC律，将估计误差方程转化为线性回归形式。这与现有MRAC系统存在显著差异——现有系统的估计误差方程通常为双线性回归形式。线性回归形式可实现所有未知参数的直接估计，从而简化了自适应控制过程。所提方法可保持闭环稳定性并确保渐近输出跟踪，克服了Nussbaum方法和基于多模型的方法等现有方案的部分局限性。通过飞控系统场景下的详细仿真结果，验证了所开发MRAC方法的实际有效性。
英文摘要：
This paper introduces an innovative singularity-free output feedback model reference adaptive control (MRAC) method applicable to a wide range of continuous-time linear time-invariant (LTI) systems with general relative degrees. Unlike existing solutions such as Nussbaum and multiple-model-based methods, which manage unknown high-frequency gains through persistent switching and repeated parameter estimation, the proposed method circumvents these issues without prior knowledge of the high-frequency gain or additional design conditions. The key innovation of this method lies in transforming the estimation error equation into a linear regression form via a modified MRAC law with a piecewise constant tuning gain developed in this work. This represents a significant departure from existing MRAC systems, where the estimation error equation is typically in a bilinear regression form. The linear regression form facilitates the direct estimation of all unknown parameters, thereby simplifying the adaptive control process. The proposed method preserves closed-loop stability and ensures asymptotic output tracking, overcoming some of the limitations associated with existing methods like Nussbaum and multiple-model based methods. The practical efficacy of the developed MRAC method is demonstrated through detailed simulation results within an aircraft control system scenario.
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