一类时滞系统的代数辨识法及其应用研究

发布时间：2018-06-24 21:33

本文选题：时滞系统 + Non-A代数法　；参考：《南京理工大学》2017年硕士论文

【摘要】：时滞现象在实际工程中普遍存在,如:智能交通、航空航天和网络控制等。时滞的存在会使系统特性变得复杂,辨识难度增加,控制效果下降,也会导致整个系统的不稳定。因而时滞系统的研究具有重要的理论研究意义和应用价值。一方面,由于技术的缺乏或经济成本的限制,部分系统参数和状态难以直接测量获得;同时,为了实现系统的闭环控制对参数辨识和状态估计的快速性提出了更高的要求。另一方面,有限时间估计可在极小的有限时间内精确地估计出系统状态。因此,本课题主要针对一类线性时滞系统的辨识问题,基于Non-A代数法研究系统有限时间收敛的参数辨识法和状态估计法,有别于一般的渐近收敛方法,从而实现时滞系统的在线辨识;并将Non-A代数法运用到无模型控制中,同时将状态估计法运用至时滞系统状态反馈控制器中。主要内容如下:针对一类线性时滞系统(时滞已知),采用Non-A代数法及算子运算理论等研究并提出了有限时间参数辨识方法,给出了具体的参数辨识数学表达式;并通过数值算例仿真验证了结果的正确性以及快速性,同时与其它参数辨识法进行研究比较。针对时滞已知、含未知参数的线性时滞系统,基于Non-A代数法和如上所研究的有限时间参数辨识法,研究推导了时滞系统有限时间状态估计方法,并通过数值算例仿真验证了基于Non-A代数法的状态估计的有效性。基于Non-A代数法的无模型控制应用研究中,在滑动窗口中我们将系统未建模部分分别近似为常数和多项式两种情况,相应地推导了未建模部分的具体数学估计表达式并应用到iPID控制中,且通过数值算例验证了方法的正确性。运用有限时间状态估计法至时滞系统状态反馈控制中,以单时滞系统为例,基于有限时间状态估计法设计时滞系统的状态反馈控制器,并通过数值算例仿真验证了基于代数状态估计法的时滞系统状态反馈控制器设计的有效性。
[Abstract]:The phenomenon of time delay is widely used in practical engineering, such as intelligent transportation, aerospace and network control. The existence of time delay will make the system characteristics become more complex, the difficulty of identification will increase, and the control effect will decline, which will lead to the instability of the whole system. Therefore, the study of time-delay systems has important theoretical significance and application value. On the one hand, due to the lack of technology or the limitation of economic cost, it is difficult to obtain some system parameters and states directly. At the same time, in order to realize the closed-loop control of the system, a higher requirement is put forward for the speed of parameter identification and state estimation. On the other hand, the finite time estimation can accurately estimate the state of the system in a minimal finite time. Therefore, this paper mainly focuses on the identification problem of a class of linear time-delay systems. Based on Non-A algebra method, the parameter identification method and the state estimation method for finite time convergence of the system are studied, which are different from the general asymptotic convergence methods. In order to realize the on-line identification of time-delay systems, Non-A algebra method is applied to model-free control, and the state estimation method is applied to the state feedback controller of time-delay systems. The main contents are as follows: for a class of linear time-delay systems (time-delay is known), a finite time parameter identification method is proposed by means of Non-A algebraic method and operator operation theory, and the mathematical expression of parameter identification is given. The correctness and rapidity of the results are verified by numerical examples and compared with other parameter identification methods. For linear time-delay systems with known delays and unknown parameters, a finite time state estimation method for time-delay systems is derived based on Non-A algebraic method and finite time parameter identification method, as discussed above. The effectiveness of state estimation based on Non-A algebra method is verified by numerical simulation. In the application of model-free control based on Non-A algebraic method, in the sliding window we approximate the unmodeled part of the system to two cases: constant and polynomial. The mathematical estimation expressions of the unmodeled part are derived and applied to the iPID control, and the correctness of the method is verified by a numerical example. In this paper, a state feedback controller for time-delay systems is designed based on finite time state estimation method, which is based on the finite time state estimation method, and takes a single time-delay system as an example. The effectiveness of the state feedback controller design based on algebraic state estimation method for time-delay systems is verified by numerical simulation.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13

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