多输入/多输出系统动态矩阵控制鲁棒稳定性

研究了基于脉冲响应模型的动态矩阵预测控制(DMC)算法,针对多输入、多输出(MIMO)系统脉冲响应模型的特点,利用脉冲响应系数误差矩阵范数平方和定义预测模型的模型误差,以线性矩阵不等式(LMI)的形式提出了DMC闭环鲁棒稳定充要条件,将DMC算法闭环稳定问题转换为一类线性矩阵不等式的可解问题.并且研究了模型误差与闭环系统稳定性之间的关系,给出了保证系统稳定条件下模型误差界的求取方法,通过求解一个线性矩阵不等式约束的凸优化问题得到保证闭环系统稳定的误差界.最后,利用算例对本文方法的有效性进行了验证.

Robust stability for DMC of multi-input/multi-output systems

The dynamic matrix control (DMC) algorithm based on finite impulse response model was studied.The model errors of multi-input/multi-output systems were described in terms of sum of norm-squares of impulse response coefficient errors matrix.The necessary and sufficient conditions for robust stability of DMC algorithm were provided in the form of linear matrix inequality (LMI).The problem of robust stability for DMC was transformed into the problem of solvability of a class of LMIs.And the relations of the model errors with the stability were also studied.The bound of model errors can be derived by solving a class of convex optimization problems with linear matrix inequality constraint with.The illustrative examples proved the validity of these results.