预测控制约束边界效应与解决方法研究

约束预测控制（Constrained model predictive control，CMPC）中，因约束的存在，优化过程中最优控制作用可能会在可行域的边界取值，也就是说会 有一个或多个变量饱和，即约束边界效应. 而过程控制中操纵变量饱和是我们不希望出现的. 对此，首先基于稳态模型，对期望值位于可行域内时最优解必在期望值处达到给出证明；同时证明了期望值在可行域外时最优解可转化为期望值到可行域的投影. 其次，针对变量在动态及稳态过程中饱和的情况提出了改善控制性能的措施——调整目标函数；终端约束的加入，为预测控制系统稳定性提供了保障. 通过对包含约束的连续搅拌釜式反应器（Continuous stirred tank reactor，CSTR）系统进行仿真实验，验证了所提方法的正确性，并说明了对目标函数进行适当调整，可有效改善系统的控制性能.

Constraint Boundary Effect in Model Predictive Control and Corresponding Solution

In constrained predictive control, the optimal control sequence may reach the boundary of the feasible domain during optimization due to the existence of constraints, in other words, one or more variables will be saturated, which is the constraint boundary effect. However, it is undesirable that the manipulated variables get saturated in process control. Therefore, firstly based on a steady-state model, it is proved that the optimal solution will reach the desired value when it is in the feasible domain; it is shown that the optimal solution can be viewed as the projection of the desired value onto the feasible region when the desired value is outside of the feasible region. Secondly, to avoid the saturation of variables when the system is in a transient or steady state, the parameters of the objective function are altered and the control performance is improved. The terminal constraint is imposed to guarantee the stability. Finally, the simulation of a constrained continuous stirred tank reactor (CSTR) model verifies the correctness of the proposed method and the effectiveness of adjustment of objective function.