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摘要:
半倾转构型旋翼飞行器作为一种新构型的垂直起降飞行器，由于其多舵面带来的操作冗余与倾转过渡轨迹相耦合问题，仍没有较好的解决方案。为此，基于最优控制理论，针对半倾转构型旋翼飞行器纵向操纵冗余问题，同步开展舵面分配与动态倾转过渡轨迹优化研究。针对半倾转构型特点建立纵向刚体飞行力学模型，采用操纵速率作为控制量，避免优化过程中出现跳跃不连续的操纵策略，分析纵向舵面分配问题，建立混合操纵方程。将飞行器过渡倾转过程的轨迹优化问题转化为非线性动态最优控制问题，选取合理的优化目标与约束条件，建立最优控制模型。选取不同的舵面分配方程与目标函数，多次开展正向和逆向倾转过渡过程的优化计算，并进行参数影响性分析，同步确定飞行器舵面分配及过渡飞行最优操纵策略与飞行轨迹。采用仿真分析验证了方法的有效性。相比于传统的先基于配平计算确定舵面分配，再通过优化计算确定飞行轨迹的策略制定方式，姿态的稳定性与操纵负荷得到显著的优化。
Abstract:The partial tilting aircraft, a novel kind of vertical take-off and landing aircraft, lacks a suitable way to address the operational redundancy brought on by its multiple rudders. Based on the optimal control theory, the problem of longitudinal manipulation of the partial tilting aircraft is carried out, and the distribution of rudder and the dynamic tilt rotation are optimized. The longitudinal rigid body flight mechanics model was established. The first derivative of the control quantity is used as the control quantity to avoid the jumping discontinuity in the optimization process. In this research, a hybrid control equation is established and the longitudinal control surface allocation problem is investigated. The trajectory optimization problem of the transition of the aircraft is transformed into a nonlinear dynamic optimal control problem. This study selects reasonable optimization objectives and constraints to establish an optimal control model. The equation and the target function of the rudder surface are selected. The control surface allocation and optimal maneuvering strategy for transitional flight of the aircraft are determined simultaneously with the flight trajectory. Compared with the traditional approach of first determining control surface allocation based on trim calculations and then determining the flight trajectory through optimization, this method significantly improves attitude stability and reduces control load. The effectiveness of the method has been validated through simulation analysis.
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图 1 半倾转构型旋翼飞行器飞行模式
Figure 1. Partial tilting configuration rotor aircraft flight modes
图 2 基于操纵面的正向动态倾转过渡最优解
Figure 2. Optimal solution for accelerating dynamic conversion based on control surfaces
图 3 基于操纵面的逆向动态倾转过渡最优解
Figure 3. Optimal solution for decelerating dynamic conversion based on control surfaces
图 5 基于舵面分配的正向动态倾转过渡最优解
Figure 5. Optimal solution for accelerating dynamic conversion based on control surface allocation
图 6 基于舵面分配的逆向动态倾转过渡最优解
Figure 6. Optimal solution for decelerating dynamic conversion based on control surface allocation
表 1 基于操纵面的正向过渡不同权重系数优化目标比值
Table 1. Optimizing objective ratios for different weight coefficients for accelerating dynamic conversion based on control surfaces
优化目标变量 优化目标比值 $ \displaystyle\int\theta _{(1 : 1)}^{2} : \displaystyle\int\theta _{(2 : 1)}^{2} : \displaystyle\int\theta _{(1 : 2)}^{2} $ 1∶0.78∶1.27 $ \displaystyle\int q_{(1 : 1)}^{2} : \displaystyle\int q_{(2 : 1)}^{2} : \displaystyle\int q_{(1 : 2)}^{2} $ 1∶0.85∶1.16 $ \displaystyle\sum\displaystyle\int\varDelta _{(1 : 1)}^{2} : \displaystyle\sum\displaystyle\int\varDelta _{(2 : 1)}^{2} : \displaystyle\sum\displaystyle\int{\varDelta }_{(1 : 2)}^{2} $ 1∶1.01∶0.99 $ \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(1 : 1)}^{2} : \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(2 : 1)}^{2} : \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(1 : 2)}^{2} $ 1∶1.09∶0.98 
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表 2 基于操纵面的逆向过渡不同权重系数优化目标比值
Table 2. Different weight coefficients for optimizing objective ratios for decelerating dynamic conversion based on control surfaces
优化目标变量 优化目标比值 $ \displaystyle\int\theta _{(1 : 1)}^{2} : \displaystyle\int\theta _{(2 : 1)}^{2} : \displaystyle\int\theta _{(1 : 2)}^{2} $ 1∶0.67∶1.44 $ \displaystyle\int q_{(1 : 1)}^{2} : \displaystyle\int q_{(2 : 1)}^{2} : \displaystyle\int q_{(1 : 2)}^{2} $ 1∶0.61∶1.91 $ \displaystyle\sum\displaystyle\int\varDelta _{(1 : 1)}^{2} : \displaystyle\sum\displaystyle\int\varDelta _{(2 : 1)}^{2} : \displaystyle\sum\displaystyle\int{\varDelta }_{(1 : 2)}^{2} $ 1∶1.12∶0.91 $ \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(1 : 1)}^{2} : \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(2 : 1)}^{2} : \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(1 : 2)}^{2} $ 1∶1.75∶0.64
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表 3 正向过渡舵面操纵分配系数
Table 3. Control distribution coefficients of rudder for accelerating dynamic conversion
$ {\omega }_{1} : {\omega }_{2} $ $ \dfrac{\partial {\theta }_{{\rm{coll}}}}{\partial \delta } : \dfrac{\partial \varOmega }{\partial \delta } : \dfrac{\partial {\theta }_{\rm{tail}}}{\partial \delta } $ 2∶1 $ \theta _{{\rm{coll}}}^{\max } : 1.94 {\varOmega }^{\max } : 0.41 \theta _{\mathrm{tail}}^{\max } $ 1∶1 $ \theta _{{\rm{coll}}}^{\max } : 1.54 {\varOmega }^{\max } : 0.37 \theta _{\mathrm{tail}}^{\max } $ 1∶2 $ \theta _{{\rm{coll}}}^{\max } : 1.31 {\varOmega }^{\max } : 0.33 \theta _{\mathrm{tail}}^{\max } $
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表 4 基于舵面分配的正向过渡不同权重系数优化目标比值
Table 4. Optimizing objective ratios for different weight coefficients for accelerating dynamic conversion based on control surface allocation
优化目标变量 优化目标比值 $ \displaystyle\int\theta _{(1 : 1)}^{2} : \displaystyle\int\theta _{(2 : 1)}^{2} : \displaystyle\int\theta _{(1 : 2)}^{2} $ 1∶0.69∶1.24 $ \displaystyle\int q_{(1 : 1)}^{2} : \displaystyle\int q_{(2 : 1)}^{2} : \displaystyle\int q_{(1 : 2)}^{2} $ 1∶0.61∶1.37 $ \displaystyle\sum\displaystyle\int\varDelta _{(1 : 1)}^{2} : \displaystyle\sum\displaystyle\int\varDelta _{(2 : 1)}^{2} : \displaystyle\sum\displaystyle\int{\varDelta }_{(1 : 2)}^{2} $ 1∶1.32∶0.87 $ \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(1 : 1)}^{2} : \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(2 : 1)}^{2} : \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(1 : 2)}^{2} $ 1∶1.57∶0.83
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表 5 逆向过渡舵面操纵分配系数
Table 5. Control distribution coefficients of rudder for decelerating dynamic conversion
$ {\omega }_{1} : {\omega }_{2} $ $ \dfrac{\partial {\theta }_{{\rm{coll}}}}{\partial \delta } : \dfrac{\partial \varOmega }{\partial \delta } : \dfrac{\partial {\theta }_{\rm{tail}}}{\partial \delta } $ 2∶1 $ \theta _{{\rm{coll}}}^{\max } : 0.42 {\varOmega }^{\max } : 1.55 \theta _{\mathrm{tail}}^{\max } $ 1∶1 $ \theta _{{\rm{coll}}}^{\max } : 0.45 {\varOmega }^{\max } : 1.11 \theta _{\mathrm{tail}}^{\max } $ 1∶2 $ \theta _{{\rm{coll}}}^{\max } : 0.45 {\varOmega }^{\max } : 0.98 \theta _{\mathrm{tail}}^{\max } $
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表 6 基于舵面分配的逆向过渡不同权重系数优化目标比值
Table 6. Optimizing objective ratios for different weight coefficients for decelerating dynamic conversion based on control surface allocation
优化目标变量 优化目标比值 $ \displaystyle\int\theta _{(1 : 1)}^{2} : \displaystyle\int\theta _{(2 : 1)}^{2} : \displaystyle\int\theta _{(1 : 2)}^{2} $ 1∶1.01∶0.93 $ \displaystyle\int q_{(1 : 1)}^{2} : \displaystyle\int q_{(2 : 1)}^{2} : \displaystyle\int q_{(1 : 2)}^{2} $ 1∶1.17∶0.82 $ \displaystyle\sum\displaystyle\int\varDelta _{(1 : 1)}^{2} : \displaystyle\sum\displaystyle\int\varDelta _{(2 : 1)}^{2} : \displaystyle\sum\displaystyle\int{\varDelta }_{(1 : 2)}^{2} $ 1∶0.98∶1.01 $ \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(1 : 1)}^{2} : \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(2 : 1)}^{2} : \displaystyle\sum\displaystyle\int\dot{\varDelta }_{(1 : 2)}^{2} $ 1∶0.97∶1.05
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表 7 舵面操纵分配系数
Table 7. Control distribution coefficients of rudder
$ {\omega }_{1} : {\omega }_{2} $ $ \dfrac{\partial {\theta }_{{\rm{coll}}}}{\partial \delta } : \dfrac{\partial \varOmega }{\partial \delta } : \dfrac{\partial {\theta }_{\rm{tail}}}{\partial \delta } $ 2∶1 $ \theta _{{\rm{coll}}}^{\max } : 0.98 {\varOmega }^{\max } : 0.96 \theta _{\mathrm{tail}}^{\max } $ 1∶1 $ \theta _{{\rm{coll}}}^{\max } : 0.88 {\varOmega }^{\max } : 0.72 \theta _{\mathrm{tail}}^{\max } $ 1∶2 $ \theta _{{\rm{coll}}}^{\max } : 0.85 {\varOmega }^{\max } : 0.64 \theta _{\mathrm{tail}}^{\max } $
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