比例积分型广义预测控制系统的稳定性分析

Stability analysis of systems with proportional-integral generalized predictive control

广义预测控制(GPC)系统的闭环稳定性一直是控制理论分析的难点．本文通过对预测控制系统闭环特征多项式的研究,证明了一步预测比例积分型GPC系统的闭环稳定性;同时,利用根轨迹法分析了控制参数与闭环极点的关系,明确了比例积分型GPC中参数的物理意义．通过一个数值仿真例子,从频域分析的角度说明了比例积分型GPC较普通GPC的优越性．

The stability analysis of the generalized predictive control （GPC） systems is studied. Based on the analysis of the characteristic polynomial of the closed-loop GPC systems, the stability of the closed-loop systems with one step ahead proportional-integral GPCs is proved. By using the root-locus method, the relationship between the poles of the closed-loop and the design parameters is explored, and the practical meanings of the design parameters in the proportional-integral GPCs are clarified. A simulation example is presented, by which the superiority of the proportional-integral GPC over the conventional GPC is explained from the point of view of frequency domain.