Identification of Continuous State-space Model Parameters for a Class of MIMO Systems:A Frequency Domain Approach
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摘要: 在连续时间状态空间模型的参数辨识中,针对系统状态微分项获取困难这一问题,对输入、状态及输出序列应用离散傅里叶变换,得到复数域线性回归方程,并给出了不同形式的最小二乘解估计式.以飞行器多输入多输出(Multiple-input multiple-output, MIMO)状态空间模型为例,设计正交多正弦信号对系统进行多通道同时激励,在一次激励的情况下就可以辨识出所有模型参数,从而提高辨识实验效率.仿真实验证明了方法的有效性和结果的准确性.Abstract: In parameter identification of continuous-time state-space model, one of the difficulties is obtaining the derivative values of system states. To resolve this problem, we propose a discrete Fourier transform of the system inputs, states, and outputs sequences. As a result, a complex domain linear regression equation is derived. Then, different forms of the solution for the least-squares regression equation are presented. For the case study of a multiple-input multiple-output(MIMO) state-space model of an aircraft, orthogonal multi-sine signals are designed to excite all system input channels, thus, all model parameters can be identified simultaneously so as to enhance the efficiency of identification. Simulations show the effectiveness of the proposed method and accuracy of the results.
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图 2 正交多正弦信号的时间历程(采样点数= 1000)
Fig. 2 Plots of orthogonal multi-sine signals (Samples =1000)
图 3 F-16飞机纵向通道输入及响应时间历程
Fig. 3 Plots of input and response of F-16 aircraft longitudinal channel
图 5 单输入系统参数辨识结果的误差及其置信区间
Fig. 5 Error and confidence interval of identification results for a single-input system
图 9 MIMO 系统参数辨识结果的误差及置信区间
Fig. 9 Error and con¯dence interval of identi¯cation results for a MIMO system
表 1 不同频域最小二乘算法的结果比较
Table 1 Comparison of results with different frequency domain least-square algorithms
LS algorithm ${\hat{A}_{{\text{lon}}}}$ $\hat{B}_{{\rm{lon}}}$ LS_Re -0.0161 -3.8292 -1.0548 -32.0137 10.1047 -0.0003 -0.7514 0.9272 -0.0020 -0.1613 -0.0004 -4.1575 -1.3190 -0.1572 -14.1069 0.0009 -0.0693 1.0046 0.0579 0.0139 LS_Im -0.0175 -3.7048 -1.0633 -32.1205 10.0944 -0.0002 -0.7543 0.9274 0.0005 -0.1609 0.0026 -4.3783 -1.3070 0.0307 -14.0746 0.0019 -0.1118 1.0048 0.0929 0.0298 LS_EAM -0.0165 -3.7773 -1.0591 -32.0588 10.1050 -0.0002 -0.7523 0.9273 -0.0012 -0.1613 0.0002 -4.2252 -1.3142 -0.0985 -14.1047 0.0010 -0.0655 1.0036 0.0544 0.0161 
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