基于多椭圆集序列的鲁棒模型预测优化控制

摘要

The offline algorithm and online algorithm are two parts of the robust model prediction algorithm based on linear matrix inequality,and the ellipsoid set sequence constructed offline is the basis of online algorithm.In order to get the suitable control law and make the system response fast and steady,the paper presented a new algorithm.In the case of offline,according to each one dimensional subspace of the state variables,we got multiple corresponding ellipsoid set sequences.In the case of online,in each of the sampling period,according to the value of the current state variables,we selected an appropriate ellipsoid set sequence in multiple ellipsoid set sequences.The position of the state variables can be determined between two ellipsoid sets within the selecting ellipsoid sets sequence.The state variables can be accurate located to obtain the system control variable by optimization way.In this paper,the design of the offline algorithm was given,and the online optimization theory was proved rigorously.Simulation results indicate that the algorithm is more effective than traditional algorithm.%在工业过程的模型预测控制中,离线算法和在线算法是基于线性矩阵不等式的鲁棒模型预测算法的两个部分,离线得到的椭圆集序列是在线算法的基础.为了得到合适的控制规律,使系统的响应快速稳定,离线时根据状态变量的每个一维子空间得到相应的多个椭圆集序列.在线时,每个采样周期根据当前测量的状态变量值,在多个椭圆集序列中选择一个合适椭圆集序列,确定状态变量位于其中的两个椭圆集之间,并用优化的方式精确定位状态变量的位置,并得到系统控制量,使在线优化得到了证明.通过和传统算法的仿真比较,验证了所提出算法对系统的响应更迅速.