状态空间表达下控制系统的稳态误差

The Steady-state Error to Control Systems in State-space Expression

经典控制理论对系统稳态误差的讨论从传递函数入手,重点是对系统开环传递函数的研究,当系统的输入是任意函数时,引入动态误差系数方法来研究稳态误差,但是当输入具有高阶导数时,动态误差系数将很难得到。现代控制理论中的状态空间表达下求系统的稳态误差很好地解决了这个问题,利用矩阵之间的运算来表示动态误差系数,并且可以得到任意输入下的稳态误差值,在线性定常系统下的推导结果还可以适用于线性时变系统,具有一定的普遍性。

The discussion of system steady-state error in classical control theory starts from transfer function and focuses on the study of the system open-loop transfer function. When the system input is an arbitrary function, it introduces the dynamic error coefficient method to study steady-state error, but when the input has high-order derivative, the dynamic error coefficients is very difficult to obtain. This problem is solved perfectly when tl^e system steady-state error is researched in state-space expression of modern control theory. The dynamic error coefficient can be obtained through operation of the interrelated matrixes and the steady-state error can also be obtained to any input, The result which is deduced in linear time-invariant system can he implied in linear time-variant system, so it has some universality.