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第一章答案1-1 试求图1-27系统的模拟结构图，并建立其状态空间表达式。
图1-27系统方块结构图解：系统的模拟结构图如下：图1-30双输入--双输出系统模拟结构图系统的状态方程如下：u K K x K K x K K x X K x K x x x x J K x J x J K x J K x x J K x x x pp p p n p b1611166131534615141313322211+--=+-==++--===••••••令y s =)(θ，则1x y =所以，系统的状态空间表达式及输出方程表达式为[]⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡+⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡-----=⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡••••••654321165432111111112654321000001000000000000010010000000000010x x x x x x y uK K x x x x x x K K K K K K J K J J K J K J K x x x x x x p p pp npb1-2有电路如图1-28所示。
以电压)(t u 为输入量，求以电感中的电流和电容上的电压作为状态变量的状态方程，和以电阻2R 上的电压作为输出量的输出方程。
U图1-28 电路图解：由图，令32211,,x u x i x i c ===，输出量22x R y =有电路原理可知：•••+==+=++3213222231111x C x x x x R x L ux x L x R 既得22213322222131111111111x R y x C x C x x L x L R x u L x L x L R x =+-=+-=+--=•••写成矢量矩阵形式为：[]⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡+⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎣⎡----=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡32121321222111321000*********x x x R y u L x x x CCL L R L L R x x x 。
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《现代控制理论参考答案》第一章答案1-1 试求图1-27系统的模拟结构图，并建立其状态空间表达式。
11K s K K p +sK s K p 1+s J 11sK n 22s J K b -++-+-)(s θ)(s U 图1-27系统方块结构图解：系统的模拟结构图如下：)(s U )(s θ---+++图1-30双输入--双输出系统模拟结构图1K pK K 1pK K 1+++pK n K ⎰⎰⎰11J ⎰2J K b ⎰⎰-1x 2x 3x 4x 5x 6x系统的状态方程如下：u K K x K K x K K x X K x K x x x x J K x J x J K x J K x x J K x x x pp p p n pb1611166131534615141313322211+--=+-==++--===∙∙∙∙∙∙令y s =)(θ，则1x y =所以，系统的状态空间表达式及输出方程表达式为[]⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡+⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡-----=⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡∙∙∙∙∙∙654321165432111111112654321000001000000000000010010000000000010x x x x x x y uK K x x x x x x K K K K K K J K J J K J K J K x x x x x x p p pp npb1-2有电路如图1-28所示。
以电压)(t u 为输入量，求以电感中的电流和电容上的电压作为状态变量的状态方程，和以电阻2R 上的电压作为输出量的输出方程。
R1L1R2L2CU---------Uc---------i1i2图1-28 电路图解：由图，令32211,,x u x i x i c ===，输出量22x R y =有电路原理可知：∙∙∙+==+=++3213222231111x C x x x x R x L ux x L x R 既得22213322222131111111111x R y x C x C x x L x L R x u L x L x L R x =+-=+-=+--=∙∙∙写成矢量矩阵形式为：[]⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡+⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎣⎡----=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡32121321222111321000*********x x x R y u L x x x CCL L R L L R x x x 。
