分数阶系统频域辨识算法

Frequency domain identification of fractional order systems

分数阶微积分提供了一个很好的工具来描述一些复杂的实际系统，比整数阶模型更简洁准确．针对分数阶系统建模问题，阐述了一种同元次分数阶系统频域辨识的极大似然算法．为此首先简要地介绍了同元次分数阶系统的传递函数表达形式，然后在此基础上推导了分数阶系统频域极大似然算法，利用拉格朗日法证明了似然函数和代价函数的等价性，从而将辨识问题归结为一等价的优化问题，并进一步对采用Gauss-Newton优化计算方法进行了讨论．最后通过仿真实例验证了其有效性．

Fractional order calculus provides an excellent tool to describe some complicated real systems more adequately than integer order models. For the identification of fractional order systems, a maximum likelihood algorithm based on the transfer function in frequency domain is proposed in this paper. First, the fractional order transfer function is briefly introduced. Second, the algorithm is deduced in detail and the equivalence between likelihood function and cost function is verified via Lagrange method, and the identification problem is converted to an equivalent optimization problem. Third, Gauss-Newton method is applied to solve the optimization problem. Finally, this algorithm is validated via an illustrative example.