多采样率系统的预见控制理论研究

发布时间：2018-05-22 07:39

本文选题：预见控制 + 离散提升技术　；参考：《北京科技大学》2017年博士论文

【摘要】：在预见控制理论和多采样率系统理论丰硕研究成果的基础上,本文进一步将预见控制理论与多采样率系统理论相结合,研究了几种不同类型的多采样率系统的最优预见控制问题.本文主要作了以下几方面的研究工作:(1)研究了具有输入多采样率特点的时变离散时间系统的最优预见控制问题.利用离散提升技术,把多采样率时变离散时间系统转化成一个形式上的单采样率系统.然后引入一阶前向差分算子并结合差分算子的性质构造扩大误差系统.利用时变系统最优控制的有关结果,得到原系统的最优预见控制输入,并通过矩阵分解,实现了 Riccati方程的降阶.(2)研究了一类输入多采样率不确定离散时滞系统的鲁棒预见控制问题.首先利用离散提升技术,分别将输入时滞和多采样率特点从形式上消除.再根据预见控制的基本方法,对不确定系统构造其对应的扩大误差系统,然后对其相应的标称系统设计带有预见作用的控制器.最后根据Lyapunov稳定性理论并结合矩阵范数的性质,得到其闭环系统的鲁棒稳定性判据.(3)研究了一类具有干扰预见的输出多采样率离散时间系统的最优预见控制问题.利用系统状态与稳态时的状态值之差代替以往差分算子的方法构造扩大误差系统,并引入积分器来消除静态误差,进而给出原系统预见控制器的设计方法.(4)研究了一类输出采样周期整数倍于输入采样周期的双率离散时间系统的最优输出调节器的设计问题.利用提升技术将原系统转化为单采样率增广系统.然后根据最优调节理论并通过矩阵的合同变换,修正了性能指标函数,进而得到原系统的最优输出调节器.并在此方法的基础上,研究了一般双率离散时间系统的最优预见控制问题,给出了一般双率离散时间系统的提升状态空间模型.结合预见控制理论,得到原系统带有预见补偿的控制器.上述所有的情况都对定理成立的条件给出了严格的数学证明,并且数值仿真结果验证了所提出的研究方法的有效性.
[Abstract]:On the basis of the abundant research results of the theory of foresight control and the theory of multi-sampling rate system, this paper further combines the theory of foresight control with the theory of multi-sampling rate system. The optimal foresight control problem for several different types of multi-sampling rate systems is studied. In this paper, we study the optimal foresight control problem for time-varying discrete time systems with input multi-sampling rate. The discrete lifting technique is used to transform the time-varying discrete time system with multiple sampling rates into a single sampling rate system. Then the first order forward difference operator is introduced and the extended error system is constructed by combining the properties of the difference operator. By using the results of optimal control for time-varying systems, the optimal predictive control input of the original system is obtained, and the matrix decomposition is used. The problem of robust predictive control for a class of uncertain discrete time-delay systems with multiple input sampling rates is studied. Firstly, the discrete lifting technique is used to eliminate the characteristics of input delay and multi-sampling rate respectively. Then according to the basic method of foresight control, the corresponding extended error system is constructed for uncertain system, and then the corresponding nominal system is designed with predictive controller. Finally, according to the Lyapunov stability theory and the properties of matrix norm, the robust stability criterion of the closed-loop system is obtained. The optimal predictive control problem for a class of discrete-time systems with multi-sampling rate output with disturbance foresight is studied. The extended error system is constructed by using the difference between the state value of the system and that of the steady state instead of the previous difference operator, and an integrator is introduced to eliminate the static error. Furthermore, the design method of predictive controller for the original system is given. (4) the design of optimal output regulator for a class of double-rate discrete time systems with an output sampling period integer times greater than the input sampling period is studied. The lifting technique is used to transform the original system into a single sampling rate augmented system. Then, according to the optimal adjustment theory and the matrix contract transformation, the performance index function is modified, and the optimal output regulator of the original system is obtained. On the basis of this method, the optimal foresight control problem for general double rate discrete time systems is studied, and the lifting state space model of general double rate discrete time systems is given. Combined with the theory of foresight control, the controller with predictive compensation in the original system is obtained. In all the above cases, strict mathematical proof is given for the conditions under which the theorem is established, and the numerical simulation results verify the validity of the proposed method.
【学位授予单位】：北京科技大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP13

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