分析倾转旋翼无人机俯仰速率控制器在模型失配下的稳定性,给出可指导调参的可靠设计方法。
Linear Stability Analysis of an INDI Pitch-Rate Controller under Model Mismatch for a Tilt-Rotor VTOL UAV

- 基于闭环传递函数与劳斯判据,解析刻画控制器在模型失配下的稳定性边界。
- 发现控制效能失配(尤其分配符号错误)是最大失稳风险,远超执行器滞后和惯性偏差。
- 提出鲁棒与性能双目标调参策略,适用于保守或激进飞行场景。
增量非线性动态逆(INDI)因其对完整气动模型依赖度低且具备强抗干扰能力,被广泛应用于无人机飞行控制。然而,对于倾转旋翼垂直起降(VTOL)构型,其快速内环允许的模型失配范围尚未以参数显式方式得到解析表征。本文聚焦现有级联INDI控制器中的俯仰速率/升降舵子通道,研究其在模型失配下的线性稳定性。推导出包含控制器-估测器-执行器-被控对象全链路的五阶闭式传递函数,并通过参数化线性模型结合劳斯-赫尔维茨准则进行稳定性分析。两次典型三参数扫描生成可解释的稳定区域图。基于此,提出两种不确定性感知调参方法:一是以加权最差情况下的增益裕度与相位裕度之和最大化为目标的鲁棒设计;二是以最差闭环带宽最大化并满足裕度约束为目标的性能导向设计。结果表明,在额定增益下,执行器滞后和惯性失配影响较小,而控制效能失配,特别是分配矩阵符号错误,是最危险的失稳因素,据此给出保守与激进工况下的具体调参建议。
原文摘要 · Abstract (English)
Incremental Nonlinear Dynamic Inversion (INDI) is attractive for unmanned aerial vehicle (UAV) flight control because it reduces dependence on a full aerodynamic model while retaining strong disturbance-rejection capability. For a tilt-rotor vertical takeoff and landing (VTOL) architecture, however, the admissible model-mismatch range of the fast inner loop is still not characterized analytically in a parameter-explicit way. This paper isolates the pitch-rate/elevon subchannel of an existing cascaded INDI controller and studies its linear stability under model mismatch. A closed-form fifth-order transfer function is derived for the full controller-estimator-actuator-plant interconnection, and stability is characterized through the Routh-Hurwitz criterion over a parameterized linear model. Two representative three-parameter sweeps produce interpretable stability regions. Based on these feasibility maps, two uncertainty-aware tuning procedures are proposed: a robustness-oriented design that maximizes a weighted worst-case combination of gain margin and phase margin, and a performance-oriented design that maximizes worst-case closed-loop bandwidth subject to margin constraints. The results show that actuator lag and inertia mismatch are comparatively benign at nominal gain, whereas control-effectiveness mismatch, particularly a sign error in the allocation, is the most dangerous destabilizing factor, leading to concrete tuning recommendations for conservative and aggressive operating conditions.
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