一类MIMO系统连续状态空间模型的参数辨识频域方法

Identification of Continuous State-space Model Parameters for a Class of MIMO Systems: A Frequency Domain Approach

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.

In parameter identification of continuous-time statespace 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.