控制工程基础习题解答.

控制工程基础部分习题答案第二章习题解2-10：试求题图2-10所示无源电路网络的传递函数。111111)(212020212021CsRRCsRsUsUsGsIRsICssUsIRsICssIRsUtiRdttiCtutiRdttiCtiRtuaiii解：111111)(20020RCsLssUsUsGsICssUsIRsICssLsIsUdttiCtutRidttiCtidtdLtubiii解：第二章习题解sUsUsURRsIsIsLRsCRsIsLRsIsIsIsIsIsIsIRssILsIsCsUssILsIRsUsUtitititititiRtidtdLdttiCtutidtdLtiRtutuciii002171222271117652172625202111076521726252021110,1111)(又：解：21212121222121221212)(LLRRsLLRRsCLLRRLRRsLLRsG第二章习题解2-11：试求题图2-11所示有源电路网络的传递函数。CsRRRsUsUsGsICssUdttiCtusIRsURsUtiRtuRtuaicccci2120002010201111)(解：1111)(4212402020201401CsRRRCsRRsUsUsGsICsRsUdttiCtiRtusIRsURsUtiRtuRtubiii解：第二章习题解sUCsRsUtiRtutisIRsURsUsUsICssURsURsUtiRtutudttiCtuRtuRtutiticAcAcAAcAAiAcAAic202122021120211211)(的方向和解：关键是确定2122120CsRRRsUsUsGi第二章习题解11:)(1)(1)()()(1)(1)()()(2411252415122215452420454244550121454244550121sCRsCRsCRCRCRCRsCCRRRRRRsUsUsGsIsIsIsIsCsIRsUsIRsUsUsIsCsIRsUsIRsUtititidttiCtiRtutiRtutudttiCtiRtutiRtudiAAAiAAAi联立上述方程可求得解：第二章习题解2-12：试求题图2-12所示机械系统的传递函数。第二章习题解21212122321002200101121020010111)(JJDksJJJJksJDssJJksTssGssJsDsssksskssJsTtJtDttkttktJtTaiii解：第二章习题解11)(1222112122221211132112214212100220201202101012110202012110101211skDkDkDskJkJkkDDkJskkDJDJskkJJsTssGssJssDsskssJssDssksTssksTtJtDttktJtDttktTttktTbiii解：第二章习题解2-13：证明题图2-13中（a）与（b）表示的系统是相似系统。111111:)(1)(1)()(1)()(11)(1)()()(2122112212122112212122112122110212101102202211212101102202211sCRCRCRsCCRRsCRCRsCCRRsCRsCRsCRsCRsCRsUsUsGsIsIsIsIsCsUsUsIRsUsUsIsCsIRsUsIsCsIRsIRsUtititidttiCtututiRtutudttiCtiRtudttiCtiRtiRtuaiAAiiii联立上述方程可求得解：第二章习题解kRDCUXskDkDkDskkDDskDkDskkDDsDksDksDksDksDksDksDksDksDksGsXksXsXktxktxtxksDkkDksDksDkkDkbii111)(1222112212122112212111221111222211112201020102222221111111由拉氏变换，得：的等效刚度为：、的等效刚度为：、解：第二章习题解tFtykytyDtyMdttFdtdtkydtdtyDdtdtyMdtdtydtdkytydtdtkytkydtdtFtkytyDtyMtyMtkytyDtFiiii020003000020020303000030003033，整理的：两边乘两边求导，得：解：2-14：试用增量方程表示线性化后的系统微分方程关系式。第二章习题解2-15：如题图2-15所示系统，试求（1）以Xi(s)为输入，分别以X0(s)，Y(s)，B(s)，E(s)为输出的传递函数；（2）以N(s)为输入，分别以X0(s)，Y(s)，B(s)，E(s)为输出的传递函数。G1G2HXiX0+-++ENYBHGGGGsXsXi212101)()(HGGGGsXHsXsXsYii211101)()(1)()(HGGHGGsXHsXsXsBii212101)()()()(HGGsXsBsXsEii2111)()(1)()(第二章习题解G1G2HX0++ENYBHGGGHGGGsNsX212212011)()(HGGHGGsNHGsXsNsY2121101)()()()(HGGHGsNHsXsNsB21201)()()()(HGGGsXHsXsNsEi21201)()()()(-1第二章习题解2-17：试求函数f(t)的拉氏变换用二次罗必塔法则）对或：解：02200(1211lim)(1)()()(000tsesesstsFsssFtdtdtfststt2-18：试画出题图2-18系统的方块图，并求出其传递函数。sXkssXDsXsMsFsXsXsDsXsXksFsXsMsFsFtxktxDtxMtftxtxDtxtxktftxMtftftxtfaaaaaaiaaaaaaiaa010102102022201010102022、解：设中间变量第二章习题解+-1/M2s2k2+D2s+-Fi(s)X0(s)1/(M1s2+D1s+k1)FaXa(s)112221221121222211212222221121222201)()(ksDsMsMsDkksDsMsMsDkksDsMsDksMsDkksDsMsMsDksFsXsGiFaX0(s)第二章习题解2-19：某机械系统如题图2-19所示，试求：)()()()()()(2211sFsYsGsFsYsGii，sYkssYDsYsMsFsYsYsDsFsYkssYDsYsMsFsFtyktyDtyMtftytyDtftyktyDtyMtftftfaaaiaaaia22222222131111121222222213111111解：设中间变量+-D3s+-Fi(s)1M1s2+D1s+k1FaY1(s)1M2s2+D2s+k2Y2(s)，第二章习题解2121222131121222231121322223112122223221)()(kksDsDsMsMsDksDsMksDsMsDksDsMsDksDsMsDksDsMksDsMsDsFsYsGi2121222131121222223222112132222311213112122222112111111)()(11)()(kksDsDsMsMsDksDsMksDsMksDsDsMksDsMsDksDsMsDksDsMsDksDsMksDsMsFsYksDsMsFsYsGii2-20：如题图2-20所示系统，试求F1(s)，F2(s)，F3(s)，。第二章习题解stststessFtttttftesstessFtttttttttttttttttttttttttttttttfssFtttf0002230030220222000000000000000202022211)()(1)(sin)(sincon)()(consin)(sinconsinsinsinconconconsinconconsinsinconconsinconconsinsinconsinsin)(1sin)()()(1sin)(解：2-24：试求题图2-24所示机械系统的传递函数。kDsMsbasFsXsGskXsDsXsXMssFsbFsaFtk