基于运算矩阵的分数阶系统辨识及控制器参数整定

发布时间：2018-10-23 21:27

【摘要】：分数阶系统是整数阶系统的一般化,因为其阶数可以为任意实数,在描述动态系统上具有更大的灵活性。此外,分数阶控制器相比于整数阶控制器具有阶数可调的新优势。因此,分数阶系统分析及分数阶控制方法已成为研究热点。然而,分数阶微分是非局部算子,相比于整数阶微分其计算要复杂得多。为此,本文运用分数阶积分运算矩阵开展了分数阶系统分析、分数阶系统辨识等相关问题的研究。主要工作如下:考虑到分数阶微分的非局部性特征,运用Haar小波来逼近系统的输入、输出信号,给出一种基于Haar小波积分运算矩阵的分数阶系统分析方法,推导了分析过程,并通过系统准确解和其它算法结果的对比验证了所提方法的正确性。分数阶系统辨识相比整数阶系统辨识要复杂,主要是系统阶数辨识的问题,若把分数阶阶数当成参数直接辨识会导致一个非线性优化问题,为此,本文通过给定阶数将其转化为最小二乘优化问题,然后采用在一定范围内寻找最优阶数的办法来避免非线性优化问题。除此之外,受小波多分辨分析的启发,通过舍弃输入输出的高频系数来降低运算矩阵维数,最终,给出了一种能够加快分数阶系统辨识的方法。通过对已知系统的辨识验证了方法的可行性和正确性,并将所提方法应用到多质量弹性扭转系统辨识上,通过整数阶模型辨识和分数阶模型辨识的比较,结果表明分数阶模型的均方误差更小。根据辨识的多质量弹性扭转系统模型,设计了PIλD)μ控制器对系统进行控制,仿真结果表明,分数阶IλDμ较整数阶PID控制器具有更好地控制效果,分数阶PIλD μ控制效果在实际平台上得到了验证。
[Abstract]:Fractional order system is the generalization of integer order system, because its order can be arbitrary real number, so it has more flexibility in describing dynamic system. In addition, fractional order controller has a new advantage over integer order controller. Therefore, fractional order system analysis and fractional order control methods have become a hot topic. However, fractional differential is more complicated than integer differential. Therefore, in this paper, fractional order system analysis and fractional order system identification are studied by using fractional integral operation matrix. The main work is as follows: considering the nonlocal characteristic of fractional differential, using Haar wavelet to approximate the input and output signals of the system, a method of fractional order system analysis based on Haar wavelet integral matrix is presented, and the analysis process is deduced. The correctness of the proposed method is verified by comparing the system exact solution with the results of other algorithms. Fractional order system identification is more complicated than integer order system identification, which is mainly the problem of system order identification. If fractional order system is directly identified as a parameter, it will lead to a nonlinear optimization problem. In this paper, the given order is transformed into the least square optimization problem, and then the method of finding the optimal order in a certain range is used to avoid the nonlinear optimization problem. In addition, inspired by the wavelet multi-resolution analysis, the dimension of the operation matrix is reduced by abandoning the high-frequency coefficients of the input and output. Finally, a method to speed up the fractional system identification is presented. The feasibility and correctness of the proposed method are verified by the identification of known systems, and the proposed method is applied to the identification of multi-mass elastic torsion systems. The comparison between integer order model identification and fractional order model identification is given. The results show that the mean square error of fractional order model is smaller. According to the identified multi-mass elastic torsion system model, the PI 位 D) 渭 controller is designed to control the system. The simulation results show that the fractional order I 位 D 渭 has better control effect than the integer order PID controller. The fractional-order PI 位 D 渭 control effect is verified on a practical platform.
【学位授予单位】：南京信息工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：N945.14;O231

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