Question

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From equation (4) and equalities of u(k+1)=u(k+1), ---, u(k+n)=u(k+n), we obtain equation (6) indicative of the feedback control rule in the extended system shown in FIG. 2. In equation (6), symbols A, B, and x indicate matrixes. ##STR1##

From equations (4) and (5), we obtain the following n+1 equations. ##EQU2##

From the n+1 equations given above, we obtain equation (7). ##EQU3##

Assuming that there is a matrix H(hn - - - h0) which satisfies equation (8) given below, the feedback control rule represented by equation (6) may be modified as shown in equation (9). ##EQU4##

The feedback control rule represented by the equation (9) does not include the state variable x of the controlled object 1. Thus, the feedback control rule can be executed by the control unit shown in FIG. 3. In FIG. 3, symbol u(k+n) indicates a cyclic target input sampled at a sampling point k+n. Symbol u(k) indicates an input to the controlled object 1 (FIG. 2) at a sampling point k+n, and symbol -y(k) indicates the additive inverse of an output of the controlled object 1. Symbols h0-hn and ml-mn respectively indicate the gains of the gain elements shown by blocks, and Wi(k+n) each indicate an output of the i-th (i=1, 2, - - - , n) adder element illustrated.

In view of FIG. 3, the following n equations are fulfilled. ##EQU5##

By combining, equation (10-1) through equation (10-n), we obtain equation (11). ##EQU6##

By substituting k+n-1, - - - , k+3, k+2, and k+1 for the variable k+n indicative of a sampling point and contained in equation (10-2) to equation (10-n), we obtain equation (14-2) to equation (14-n). Meanwhile, equation (10-1) is shown again. ##EQU7##

The feedback control rule for embodying the discrete-type repetitive control method of this embodiment is represented by the foregoing equations (10-1), (12), (13), and (14-2) to (14-n). A series compensator corresponding to this feedback control rule is shown in FIG. 4. In the case of embodying the repetitive control of the embodiment by the use of the series compensator, the deviation yr(k)-y(k) between the cyclic target input yr(k) (FIG. 1) and the output y(k) of the controlled object (FIG. 2) is applied, in place of the input -y(k) shown in FIG. 4, to the series compensator.

Answer 1

从方程式(4)和等式铀(钾1+1)=美国(十一)--吴(氮钾)=铀(氮钾) 我们得到方程(6)表明在延长统治的反馈控制系统图所示. 2. 在方程(6),一个符号、乙、第十显示矩阵. ##月##str1方程(4)和(5),得到下列方程一氮. ##月##equ2方程的N+1以上,得到方程(7). ##equ3##假设有一位矩阵H(HN蛋白---哈勃常数),满足方程(8)如下, 反馈控制规则由方程式(6)可修改公式(9)所示. ####equ4反馈控制规则由方程式(9)不包括第十受控状态变 对象1. 因此,反馈控制规则可以执行的控制单元列无花果. 3. 在无花果. 3、象征美(氮钾)循环指标显示输入采样时采样点钾国宝 象征美国(十一)显示一个投入受控对象1(图二)在取样点氮钾、 符号和Y型(十一)显示一个逆添加剂产量受控对象1. 符号的H0-HN蛋白和毫升锰分别标明增益要素收益表现座 而无线(氮钾)的产量分别显示我次(=1,2,---,n)的加法单元说明. 由于无花果. 3、氮下列方程到位. ####equ5结合,通过方程(10-1)方程(10-N)基金,得到方程(11). ##equ6##代氮钾-1---、钾3、钾二、 一、钾的氮钾不为人知的可变采样点和所载方程式(10-2)方程(10氮) 我们得到方程(14-2)方程(14-N)基金. 另外,方程(10-1)列. ####equ7反馈控制规律,体现了党的离散式重复控制这种方法是由前述化身 方程(10-1),(12),(13)、(14-2)(14-N)基金. 与此相应的一系列补偿反馈控制规则表无花果. 4. 在发生重复控制的化身体现了一系列使用补偿、 偏差岁(十一)Y型(十一)输入岁之间循环指标(十一)(图1)和输出肽Y(k)的受控对象(图 2)适用,代替投入肽Y(十一)列无花果. 4、对串联补偿.