自控习题及其答案

定理直接求传递函数。Р 1Р ?R2)//LsР Uc(s)R2LCR2s2(a) ???Ur(s)R?(?R)//Ls?R(R1?R2)LCs?(R1R2C?L)s?R1Р 122Р CsCsР (Р U(s)Р ?1?(b) cР Ur(s)Р R1//Р 1C1sР R1R2C1C2s2?(R1C1?R2C2)s?1R1R2C1C2s2?(R1C1?R2C2?R1C2)s?1Р 11(R1//)?R2?Р C1sC2sР ?Р 1Р //(R2?Ls)Р Uc(s)R2?Ls??(c) Ur(s)R?//(R?Ls)R1LCs?(R1R2C?L)s?R1?R2Р 12Р CsР 1CsР (R?Р 1Р )//RCsР (d)Р Uc(s)RР ???Р 111Ur(s)(R?1)//R?1(R?)//R?R?Р C1sC2sC1sC2sC1sР 5Р 第二部分古典控制理论基础习题详解一概述Р ?R2C1C2s2?2RC1s?Р 1Р RC1C2s?(2RC1?RC2)s?122Р 2-2-3 工业上常用孔板和差压变送器测量流体的流量。通过孔板的流量Q与孔近作微小变化,试将流量方程线性化。Р 【解】:取静态工作点(P0,Q0),将函数在静态工作点附近展开成泰勒级数,并近似取前两项Р Q?Q0?Q?P?P(P?P0)?Q0?012kP0(P?P0)?Q?Q0?k2P0(P?P0)Р 设1k?(R为流动阻力),并简化增量方程为 R2P0Р Q?1PР RР 【解】:对微分方程组进行零初始条件下的Laplace变换得:Р X1(s)?R(s)?C(s)Р T1sX2(s)?k1X1(s)?X2(s)Р X3(s)?X2(s)?k3C(s)Р T2sC(s)?C(s)?k2X3(s)Р 绘制方框图Р 题2-2-4图Р 6Р 第二部分古典控制理论基础习题详解一概述Р 传递函数为