多输入输出反馈系统虚轴的零点对跟踪问题的约束

反馈系统的设计会受到闭环系统特性的制约. 本文给出了反馈控制系统接近虚轴或虚轴上的稳定零点对跟踪误差的时间域积分约束. 这一时间域积分约束是任何一个线性时不变系统为保证其闭环系统的稳定性, 其跟踪误差必须满足的. 接近虚轴或虚轴上的稳定零的存在表明跟踪误差与调节时间之间存在某种折中. 对固定的调节时间, 本文给出了在虚轴上存在零点情形下, 其跟踪误差的无穷范数下界的一个有效估计. 此估计表明, 零点的绝对值越小, 其无穷范数的下界越大. 这些约束由一个例子加以解释.

Limitation on the tracking problem due to jω-axis zeros in MIMO feedback control systems

The process of feedback design is necessarily performed in the presence of hard constraints upon properties of the closed-loop system. This paper gives the time domain integral constraints of the feedback control systems tracking error that arise from the presence of stable zeros on or near the jω-axis, which shows that for a linear time invariant system, in order to guarantee the stability of the closed-loop system, the time domain integral constraints must be satisfied by the tracking error. The presence of stable zeros near or on the jω-axis shows that there is trade offs between the tracking error and the settling time. For fixed settling time, this paper gives an effective lower bound on the infinite norm of the tracking error, which shows that when the absolute value of the stable zero on the jω-axis becomes small, the lower bound becomes large. The constraints are illustrated by an example.