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摘要:
针对刚弹耦合运载火箭，设计了一种具备自适应能力的改进比例-微分(PD)控制器，旨在实现对制导指令的高品质跟踪。该控制器引入自适应增广控制(AAC)模块，提升了参数调整能力，使其能同时自适应地调整比例和微分系数。此外，还融入自适应滤波器模块，其传递函数的幅相特性以滞相为主、减幅为辅，根据弹性频率的辨识结果来自适应调整滤波效果，应用于速率反馈通道时，该滤波器能有效实现一阶弹性模态的相角稳定与高阶弹性模态的幅值稳定。数值仿真结果表明：设计的自适应改进PD控制器不仅结构简单，参数易选取，还具有显著的自适应能力和弹性振动抑制效果，适用于时变系统，特别在模型参数存在明显偏差的情况下仍可以维持系统稳定，展现了较好的工程应用价值。
Abstract:An improved proportional-derivative (PD) controller with adaptive capability is designed for the rigid-elastic coupled launch vehicle, aiming to achieve high-quality tracking of guidance instructions. The controller introduces an adaptive augmenting control (AAC) module, enhancing its parameter adjustment capabilities so that it can adaptively adjust both proportional and derivative coefficients simultaneously. Furthermore, an adaptive filter module is incorporated, with amplitude reduction complementing phase lag in the amplitude-phase characteristics of the transfer function. This filter adjusts its filtering effect adaptively based on the identification results of the elastic frequency. When applied to the pitch angle rate feedback channel, this filter effectively stabilizes the phase angle of the first-order elastic mode and the amplitude of the higher-order elastic mode. Numerical simulation results demonstrate that the designed adaptive improved PD controller not only has a simple structure and is easy to select parameters, but also exhibits excellent adaptive capabilities and significant elastic vibration suppression effects. Its remarkable engineering application value is demonstrated by its suitability for time-varying systems and its capacity to preserve system stability even in the presence of large model parameter variations.
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图 2 PD控制下开环传递函数Nyquist曲线
Figure 2. Nyquist plot of the open loop transfer function under PD control
图 3 滤波器参数$ \alpha $不同取值下的Bode图
Figure 3. Bode plot of filter parameter $ \alpha $ with different values
图 4 微分控制下开环传递函数Nyquist曲线
Figure 4. Nyquist plot of the open loop transfer function under derivative control
图 5 改进PD控制下开环传递函数Nyquist曲线
Figure 5. Nyquist plot of the open loop transfer function under improved PD control
图 9 一阶弹性频率的辨识仿真结果
Figure 9. Simulation results of first order elastic frequency identification
表 1 AAC参数取值
Table 1. AAC parameter values
误差
系数频谱阻尼器
系数回归
系数增益
基值增益最大
改变值误差融合
系数2000 10000 0.5 0.5 1.5 1.0 
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表 2 自适应滤波器参数取值
Table 2. Adaptive filter parameter values
IpDFT采样
时间间隔/sIpDFT采样
总时长/s迭代修正时间
间隔/s频率预测模型
截距初值频率预测模型
斜率初值频率预测模型
斜率最大值频率预测模型
斜率最小值频率预测模型
斜率修正值0.05 10 1 8.0 0.025 0.050 0 0.001
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表 3 拉偏参数取值
Table 3. Deflected parameter values
$ {b}_{2} $/% $ {b}_{3} $/% $ 2{\xi }_{1}{\omega }_{1} $/% $ \omega _{1}^{2} $/% $ {D}_{31} $/% $ R_{{\textit{z}}1}^{\text{gz}} $/% $ R_{{\textit{z}}1}^{\text{st}} $/% $ 2{\xi }_{2}{\omega }_{2} $/% $ \omega _{2}^{2} $/% $ {D}_{32} $/% $ R_{{\textit{z}}2}^{\text{gz}} $/% $ R_{{\textit{z}}2}^{\text{st}} $/% $ +50 $ $ -50 $ $ -30 $ $ -30 $ $ +50 $ $ -150 $ $ -150 $ $ -30 $ $ -30 $ $ +50 $ $ -200 $ $ -200 $
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表 4 外部扰动取值
Table 4. External disturbance values
扰动名称 扰动形式 扰动大小 施加时刻 控制量扰动 正态分布 0.1° 所有时刻 俯仰角
观测量扰动正态分布 0.1° 所有时刻 俯仰角速率
观测量扰动正态分布 0.1(°)/s 所有时刻 俯仰角
状态量扰动突变扰动 2° 飞行第75 s
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