显式模型预测控制的可达分区点定位算法

REACHABLE PARTITIONS ALGORITHM FOR THE POINT LOCATION PROBLEM IN EXPLICIT MODEL PREDICTIVE CONTROL

显式模型预测控制(explicit model predictive control,EMPC)避免了传统的模型预测控制中最为繁琐的反复在线优化过程.显式模型预测控制系统分为离线计算获得每个分区上控制律和在线查找控制律这两个不同阶段.离线计算阶段通过多参数二次规划(multi-parametric quadratic program,mp-QP)对系统状态空间进行凸划分,并计算得到系统在每个状态分区上的分段仿射(piece-wise affine,PWA)控制律;在线计算阶段通过查表确定系统当前状态所在的分区(即进行点定位运算)从而直接得到相应的控制律.研究工作在于如何快速确定系统当前状态所在的分区,属于在线计算过程范畴.文章在离线计算所得的状态分区数据基础上,根据可达域的思想,设计可达分区点定位算法使在线计算时搜索范围大幅减少,从而显著降低在线计算所需时间,提高EMPC系统的实时性.通过两个仿真实验将可达分区算法与直接查找法相互对比,证明可达分区算法的优势.作为一个应用例子,将文章显式模型预测控制可达分区点定位算法用于直流无刷电机显式模型预测控制,表明所用方法的有效性.

The repeated oMine optimizatioa problem of the traditional model pre- dictive control （MPC） is avoided in the explicit model predictive control （EMPC） system. The explicit model predictive control system consists of 2 separated stages,i.e. the offtine calculation of control law over every state region, and the online lookup in the control law tables. By using the multi-parametric quadratic programming （mp- QP）, the state space partitions of the system are obtained and the piece-wise affine （PWA） control laws over the state partitions are calculated offiine. In the online stage, when the current system states are available, the corresponding state region in which the current states lie is found by using the point location technique, and the corresponding control law can be extracted directly. The research work of this paper aimed to establish the fast point location algorithm. Based on offline obtained state partitions and the idea of the reachable region, a new approach called reachable partitions algorithm is developed in this paper for online point location problem in EMPC. The proposed approach decreases the number of region to be searched on- line, speeds up online lookup in the control law tables and improves the real time performances of the EMPC. Two simulation examples show the advantages of the proposed approach compared with the direct table search method. The application of the developed approach in explicit model predictive control of Brushless DC Motor shows its effectiveness.