输入变量关联约束对约束优化控制的影响特性分析

过程工业控制中除了存在常见的输入变量和输出变量幅值高低限约束, 由于工艺或者控制的需要也可能具有关于输入变量线性函数的关联约束. 不同约束条件之间的矛盾可能会造成约束条件无法全部满足, 失去了实施预测控制的基础. 从凸体顶点角度, 将具有输入关联约束的约束优化控制的可行性判定转化为凸多面集是否非空的问题. 为保证具有输入关联约束预测控制的有效实施, 本文将输入关联约束纳入到预测控制控制律的求解当中. 基于Newton控制框架, 考虑具有输入关联约束条件下, 得到基于区间控制思想的预测控制律的解析表达式, 从而分析输入关联约束条件对控制的影响. 通过典型系统模型的控制仿真实验, 验证以上方法的有效性.

Analysis of Constrained Optimal Control with Related Constraints of Input Variables

The constraints of input and output variables commonly exist in the chemical process control. These constraints are high-low limits of input variable, input variable variation and output variable. For the requirement of process or control, there may be a few related constraints of input variable. The inconsistency in different constraints cannot make all the constraints satisfied, which will lose the basis of implementation of model predictive control (MPC). From the view of polyhedral pole, the feasibility analysis of constrained optimal control is transformed into whether the convex polyhedron is empty or not. Based on the Newton control framework, for linear system with the related constraints of input variables, the analytical solution of control law of constrained predictive control based on zone control is deducted. The control law can be used to discuss the impact of related constraints on control. Simulation results of a typical system control problem show the effectiveness of the proposed methods.