分数阶系统的动态矩阵控制算法研究

发布时间：2018-02-11 15:19

本文关键词： 分数阶微积分分数阶系统动态矩阵控制 PID控制分布式动态矩阵控制　出处：《杭州电子科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：分数阶微积分,是将微积分的阶次从常规的整数域推广至实数域甚至是复数范围所得。现实中的动态系统大多为分数阶的,整数阶微分方程描述的模型往往只能体现控制系统的部分动态特性,而分数阶微积分的任意阶次数及其特有的记忆特性,使得分数阶微分方程恰能更精确的表征系统的内在特性。因而研究分数阶系统的控制问题具有极其重要的理论意义和工程价值。动态矩阵控制(DMC)作为预测控制中的代表性算法,具有对于模型要求低、鲁棒性强、处理时延简单易行等优点,在强耦合、大时滞及无法建立精确数学模型的过程中十分适用。然而该方法同时也存在在线计算量大、采样周期不宜过小等局限,从而使得其在模型阶次、环境扰动及非线性等方面存在不确定性较大的控制系统中往往难以达到预期的控制效果。因此本文对传统的动态矩阵控制方法进行改进,并将其运用于分数阶系统的控制中。本文的主要工作可以分为三个部分:第一部分为:对两种改进的动态矩阵控制方法进行介绍,并通过稳定汽油蒸汽压力控制的仿真实例与传统的动态矩阵控制进行对比。仿真结果表明基于PID控制结构改进的DMC方法在整体性能上的优势。第二部分为:将PID型动态矩阵控制方法运用于一类单入单出分数阶线性系统中,并通过加热炉温度控制的仿真实例中验证了该方法的控制性能。第三部分:考虑一类多变量分数阶系统,通过在分布式控制结构中引入PID型动态矩阵控制方法,得到一种改进的分布式动态矩阵控制方法,并将其用于一类多变量分数阶系统的控制中,最后通过MATLAB仿真研究验证了所提方法的可行性和有效性。
[Abstract]:Fractional calculus is obtained by extending the order of calculus from normal integer domain to real number domain or even complex number domain. The model described by integer-order differential equations can only reflect the partial dynamic characteristics of the control system, while the fractional calculus has arbitrary order and its special memory characteristics. It makes the fractional differential equation more accurate to represent the inherent characteristics of the system. Therefore, the study of the control problem of fractional order system has very important theoretical significance and engineering value. Dynamic matrix control (DMC) is used as the representative algorithm in predictive control. It has the advantages of low requirement for the model, strong robustness, simple and easy to deal with delay, etc. It is very suitable in the process of strong coupling, large time delay and the inability to establish accurate mathematical model. However, this method also has a large amount of on-line computation. The sampling period should not be too small, so that it is in the order of the model. It is difficult to achieve the desired control effect in control systems with high uncertainty in environmental disturbance and nonlinearity. Therefore, the traditional dynamic matrix control method is improved in this paper. The main work of this paper can be divided into three parts: the first part introduces two improved dynamic matrix control methods. The simulation results show that the improved DMC method based on PID control structure has advantages in overall performance. The second part is divided into two parts: PID. Dynamic matrix control method is applied to a class of single-in-single-output fractional linear systems. The control performance of this method is verified by a simulation example of heating furnace temperature control. Part three: considering a class of multivariable fractional order system, the PID dynamic matrix control method is introduced into the distributed control structure. An improved distributed dynamic matrix control method is proposed and applied to the control of a class of multivariable fractional order systems. Finally, the feasibility and effectiveness of the proposed method are verified by MATLAB simulation.
【学位授予单位】：杭州电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP273

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