基于QP转化的约束非方系统模型预测控制

针对带约束非方系统的控制问题,设计了一种基于标准二次规划(QP)转化方法的快速模型预测控制算法。首先利用非方传递函数矩阵对Diophantine方程进行求解,结合系统的单位阶跃响应矩阵重构系统的预测模型;然后,考虑系统的约束条件,包括输入输出变量、控制增量约束,通过引入松弛变量及等式转化,将模型预测控制MPC过程中的最小化目标函数问题转化为带有不等式约束的标准QP问题,实现最优控制律在迭代过程中的一步求解,从而解决传统控制方法中计算量大、不能够直接应用于在线控制的问题。将本文所提出的方法应用于经典的Kalman非方系统的控制。得到仿真结果表明,该预测控制方法在系统的抗噪声扰动、设定值跟踪等方面均有着较好的性能,同时能满足系统的约束条件,并得到满意的控制效果。

QP transformation based model predictive control for a non-square system with constraints

A model predictive control algorithm based on standard quadratic programming to solve the control problem for a non-square system with constraints has been studied. The transfer function of the non-square system is first used to solve the Diophantine equation and the model prediction is rebuilt by combination with the step response matrix of the system. Then, constraints of input variables, output variables and control increments are considered, and some slack variables are introduced to transform the minimization problem of MPC into a standard QP problem in order to obtain the optimal control law in one step during the iteration. The problems caused by computational complexity and infeasibility of traditional control methods can thus be solved. Simulation results for Kalman’s system control show that the proposed algorithm has good performance in noise disturbance rejection and set-point tracing under the condition of constraints.