Parameter optimization method of thrust vector/pneumatic rudder composite control law for aircraft based on singular value method
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摘要:
推力矢量/气动舵布局的先进飞机存在显著的控制耦合问题，传统的单回路控制参数设计方法在该场景下无法兼顾多控制回路的性能。因此提出一种基于回差矩阵奇异值的控制律参数优化方法，利用时域控制性能指标确定控制参数优化区间，在此基础上用奇异值方法衡量多输入多输出(MIMO)系统的稳定裕度，并建立相应的最优目标函数，从而对控制器参数寻优。采用数值仿真验证了该方法的可行性，结果显示所设计的控制参数优化算法相较于传统单回路控制参数设计方法具有更好的时域控制性能与更大的系统稳定裕度。
Abstract:Control coupling is a major problem for advanced aircraft with thrust vector/aerodynamic rudder layouts, as the performance of numerous control loops cannot be balanced using conventional single loop control parameter design techniques. Therefore, a control law parameter optimization method based on the singular value of the feedback matrix is proposed. The optimization interval of the control parameters is first established using the time domain control performance index. The stability margin of the multiple-in multiple-out (MIMO) system is then measured using the singular value method, and the corresponding optimal objective function is established to optimize the controller parameters. The feasibility of this method was verified through numerical simulation, and the results showed that the designed control parameter optimization algorithm has better time-domain control performance and a larger system stability margin compared to traditional single loop control parameter design methods.
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图 4 不同回路控制器参数仿真包线
Figure 4. Simulation envelope of different loop controller parameters
图 5 不同组控制参数时的最小奇异值
Figure 5. Minimum singular value for different sets of control parameters
图 7 俯仰角速度环阶跃响应曲线及控制性能
Figure 7. Step response curve and control performance of pitch angular velocity loop
图 10 单输入控制设计仿真和多回路控制设计仿真速度对比结果
Figure 10. Comparison of speed results between single input control design simulation and multi loop control design simulation
图 11 单输入控制设计仿真和多回路控制设计仿真俯仰角速度对比结果
Figure 11. Comparison results of pitch angular velocity between single input control design simulation and multi loop control design simulation
图 14 加入干扰后俯仰角速度环对比曲线
Figure 14. Comparison curve of pitch angular velocity loop after adding interference
表 1 不同传递函数的分子系数
Table 1. Molecular coefficients of different transfer functions
传递函数 K4 K3 K2 K1 K0 GVδth 6.045 9.012 28.49 −0.033 0.019 Gωzδth −0.016 −0.017 0.013 −3.4×10−5 −4.95×10−20 GVδe 9.942 13.37 −52.61 22.85 0.024 Gωzδe −5.280 −2.329 −0.077 −5.196×10−5 9.712×10−18 GVδtz 0.083 −0.115 34.26 −9.072 −7.493×10−4 Gωzδtz 1.827 0.902 0.035 1.959×10−7 −1.257×10−20 
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表 2 回路控制性能指标内容及要求
Table 2. Content and requirements of loop control performance indicators
指标要求 阶跃信号 调节时间/s 超调量/% 状态误差/% 速度回路 100 m/s 5 10 1 姿态回路 0.1 rad/s 5 10 5
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表 3 控制参数优化区间与步长
Table 3. Optimization interval and step size of control parameters
优化区间
及步长速度回路 姿态回路 Kp Ki K I 下限 2×106 2×105 2×106 1×102 上限 8×106 3×105 8×106 8×102 步长 106 104 106 102
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表 4 最优控制器参数下的多输入多输出系统裕度
Table 4. MIMO system margin under optimal controller parameters
幅值裕度/dB 相角裕度/（°） 6.2342 63.3222
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表 5 不同分配比例情况下的指标结果
Table 5. Indicator results under different allocation ratios
比例情况 奇异值优化结果 幅值裕度/dB 相角裕度/（°） 5∶5 1.0498 6.2342 63.3222 4∶6 1.0540 6.2520 63.6064 3∶7 1.0585 6.2708 63.9063 2∶8 1.0624 6.2875 64.1744 1∶9 1.0668 6.3060 64.4715
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表 6 两种控制参数设计方法稳定裕度对比结果
Table 6. Comparison results of stability margin between two control parameter design methods
控制参数设计方法 奇异值 幅值裕度/dB 相角裕度/（°） 单输入 0.8272 5.2355 48.8593 基于奇异值的多回路 1.0498 6.2342 63.3222 注：奇异值、幅值裕度、相角裕度的提升幅度分别为26.9%，19.1%，29.6%。
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