高效显式模型预测控制在两容水箱中的应用

Application of Efficient Explicit Model Predictive Control in Two Tank System

摘要:

针对一类具有分段仿射形式的混杂系统模型的控制方法问题,提出了一种高效显式模型预测控制算法；该算法通过将最优控制问题转化为多参数规划问题,离线求得具有分段仿射形式的显式控制器；在线过程,应用一种新的搜索算法,它能够快速准确地对系统状态点进行定位,确定其所属的控制器分区,再根据该分区所对应的子控制率,进行简单的线性运算,即可得到系统的输入；该控制方法避免了反复的在线优化计算,大大减少了计算量,并且,在线计算的速度更快,控制的实时性更好；将该算法应用到具有典型混杂特性的两容水箱系统中,仿真结果表明:水箱的液位从初始液位能够快速平稳的达到期望的液位,且与其它的控制算法相比较,该算法更加高效。

Abstract:

An efficient explicit model predictive control algorithm is proposed for a class of hybrid systems based on piecewise affine (PWA) model. The algorithm solves the optimization problem off line by transforming it into an equivalent multi-parameter programming problem and therefore obtains an explicit controller with piecewise affine form. For on-line process,a new search method is used to determine the position of the system state in the partitions of the controller and gets the optimal input according to the control law corresponding to the partition via evaluating a simple linear function. The algorithm greatly reduces the computation complexity. Moreover,it leads to higher computation speed and better real-time performance. Finally,an application case study on two tank system is given to illustrate this method and the simulation results show that it is more efficient comparing with other algorithms.