《自動(dòng)控制原理》其次章和第六章部分課后習(xí)題解答

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d2xodxodxi?(f?f)?f2.1(a)m(不考慮物塊的重力)121dt2dtdt(b)f(K1?K2)dxodxi?K1K2xo?K1fdtdtdxodx?(K1?K2)xo?fi?K1xi(c)fdtdt2.2

C1f2R1u1K2AxiR2u0f1x0BC2K1x(a)(b)

U(s)(a)o?Ui(s)R2?1C2sR11C1s1R2??C2sR?11C1sR1R2C1C2s2?(R1C1?R2C2)s?1?R1R2C1C2s2?(R1C1?R2C2?R1C2)s?1(b)A點(diǎn)：f2(dxidxodxdx?)?K2(xi?xo)?f1(o?)（1）dtdtdtdtdxdxB點(diǎn)：f1(o?)?K1x（2）

dtdt由（1）和（2）得

f2(dxidxo?)?K2(xi?xo)?K1x（3）dtdt由（3）解出x，并代入（2）得：

f1f2d2xof1f1f2dxof1f2d2xif1f2dxi?(??)?x??(?)?xio22K1K2dtK1K2K2dtK1K2dtK1K2dt經(jīng)比較可以看出，電網(wǎng)絡(luò)（a）和機(jī)械系統(tǒng)(b)兩者參數(shù)的相像關(guān)系為

K1~2.3?Q?11,K1~,C1C1f1~R1,f2~R2

K?P2P012s2?4s?2?1?]??(t)?e?t?2e?2t2.4G(s)?2g(t)?L[1?s?1s?2s?3s?22.5

?h1??h2??q1(1)R1C1d?h1??qi??q1(2)dt

?h2??q2(3)R2d?h2??q1??q2dt(4)C2G(s)?2.6

H2(s)R2?2Qi(s)R1C1R2C2s?(R1C1?R2C2?R2C1)s?1G(s)?2C(s)10?H(s)?

4s?1E(s)3s?5C(s)10G(s)100(4s?1)??2R(s)1?G(s)H(s)12s?23s?25E(s)1010(12s2?23s?5)??2R(s)1?G(s)H(s)12s?23s?252.7

1Uo(s)R0C0R1C1s2?(R0C0?R1C1)s?1C1s????1Ui(s)R0C1sR0C0s1R0?C0sR1?2.8（1）K0?E?m?30330???180?180??V/rad11?K1??3,K2??2

（2）假設(shè)電動(dòng)機(jī)時(shí)間常數(shù)為Tm，忽略電樞電感的影響，可得直流電動(dòng)機(jī)的傳遞函數(shù)為

Km?(s)?1?，Km為電動(dòng)機(jī)的傳遞系統(tǒng)，單位為(rad?s)/V。

Ua(s)Tms?1又設(shè)測(cè)速發(fā)電機(jī)的傳遞系數(shù)為Kt（V/(rad?s?1)）

系統(tǒng)的傳遞函數(shù)為：

?o??i1

Tm1?K2K3KmKt2s?s?1K0K1K2K3KmK0K1K2K3Km2.9

2.10

第六章

6.2取

?c?20rads,??0.2，Gc(s)?1??TS1?0.5S?

1?TS1?2.5S6.3

S?120Gc1(s)?G(s)?10S?1S(0.1S?1)

（3）比較兩種校正方案的優(yōu)缺點(diǎn)

穩(wěn)態(tài)性能一樣，動(dòng)態(tài)性能比較如下：?1%??2%???550??2???63.40?1radrad?????c1?2s??c2?20ss1s2Gc2(s)?0.1S?10.01S?1t?t

動(dòng)態(tài)性能超前網(wǎng)絡(luò)Gc2)校正系統(tǒng)好于滯后網(wǎng)絡(luò)Gc1(s)校正系統(tǒng)(s

G抗高頻干擾滯后網(wǎng)絡(luò)G校正系統(tǒng)優(yōu)于超前網(wǎng)絡(luò)cs)校正系統(tǒng)(s)2(c1

6.5

Gc(j?)G(j?)?0400(j??0)?j??02(0?1)(10j??0)0?1,?c1?6.3rads?1?180??(?c)?180?2?90?arctan0.01?6.3?arctan10?6.3?arctan1?6.30??3.40?89.10?810＝－11.50?0Gc(j?)G(j?)?400(0.1j??0)?j??2(0?1)(0?1)?1,?c2?40rads?2?1800??(?c)?1800?2?900?arctan0.01?40?arctan0.01?40?arctan0.1?40??21.80?21.80?760?32.40Gc(j?)G(j?)?

400(0.5j??0)(0.5j??0)?j??2(0?1)(10j??0)(0?1)?1,?c3?10rads?arctan?3?1800??(?c)?1800?2?900?arctan0.01?1010?10?arctan0.025?10?2arctan0.5?10??5.70?89.40?140?157.30?48.20（1）C圖網(wǎng)絡(luò)種最好

（2）12Hz正弦噪聲削減10倍，C種網(wǎng)絡(luò)滿足。12Hz對(duì)