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教师: 王晓甜 [email protected]. 第二章 自动控制系统的数学模型. 系统的 数学 模型. 什么是数学模型? 数学模型 :描述系统内部各 物理量 之间因果关系 的 数学表达式 。 物理量 : 高度、速度、温度、压力、流量、电压、电流 。 数学表达式 : 代数方程、 微分方程 数学模型的特点 1) 相似性:不同性质的系统,具有相同的数学模型。抽象的变量和系统 2) 简化性和准确性:忽略次要因素,简化之,但不能太简单,结果合理 3) 动态模型:变量各阶导数之间关系的微分方程。 性能分析 - PowerPoint PPT Presentation
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1 1) 2) 3) 4) 1) 2) 3)
[email protected]=S3LogoContents1 2 3 4 MATLAB 542.1 [email protected]
(SISO)r(t): c(t):
n,m
52.1 [email protected] 1) ()
2)
62.1 [email protected]
1) 2) 3) 4) 5) 72.1 [email protected](SISO), :
,r(t)c(t)c(n)(t)c(t)tn;ai(i=1,2,,n)bj(j=0,1, ,m)
82.1 EG1. [email protected]
92.1 EG1. R-L-Cur(t)uc(t)[email protected]
1ur(t)uc(t)i(t) 23KVL
4iuc :
5
6
102.1 [email protected], m,;f(t),y(t)
2 ,
ky(t) ,
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2.1 EG3 3,ui(t)uo(t), [email protected] 2-4
122.1 [email protected], , , k, ; ( ), ; ,,,
132.2 2.2.1 [email protected]. tf(t)e-st(s=+j), 0,+t, F(s),F(s)f(t),Lf(t)
f(t)F(s) F(s)f(t), f(t)F(s) 142.2 [email protected] L513467
152.2 [email protected]
22 L
5
1
3
4
6
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162.2 [email protected](t)c(t)c(t)LsR(s)C(s)sC(s) L-1 1) 2)s 3)s 172.2 [email protected]
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L-1182.2 3) [email protected]
4)
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202.2 [email protected]
1 G(s) 2 s3 4
212.2 [email protected]
EG1, RLC
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222.2 [email protected] EG5.EG3RLC
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232.2 [email protected] (a) (b) (c)(d) (e)(f)s n m(g)h ,
242.2 [email protected]:
1 2 3 (2)s1 M(s)=0N(s)=0zi(i=1,2,,m)pj(j=1,2,,n),k(2.24)1,i(i=1,2,,m)Tj(j=1,2,,n), K 252.2 [email protected]
(chaper4)2 EG
p1p2j1 1 j 023p3z1 s=2 s=-3, s=-1+j, s = -1-j262.2 [email protected] G(s)
6,272.2 [email protected] 1. c(t) = K r(t) G(s) = K C(s) = G(s) R(s) = K/s c(t) = K1(t) r(t)=1(t)c(t)r(t)1c(t)t0K
282.2 [email protected] 2.()
: , , , j 01/T
292.2 [email protected] 2.()
: 0tc(t)0.6320.8650.950.9821.0T2T3T4T
302.2 3., ,
r(t)t01c(t)t01T 1/T
312.2 [email protected]
G(s)=Ts
c(t) = T(t)t = 0t = 0r(t)t01c(t)t0T,
322.2 5.RLC
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332.2 5.RLC
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c(t) t 01=cos1342.2 [email protected]
r(t)t01c(t)t01 : , 352.3 [email protected]
362.3 [email protected] : 1,
(2)
372.3 [email protected].
382.3 [email protected]
R(s)C(s) E(s), B(s)C(s)= G(s)*E(s)E(s)= R(s)-B(s)B(s)= H(s)*C(s)C(s)= G(s)*E(s)C(s)= G(s)*(R(s)-B(s))C(s)= G(s)*[R(s)-H(s)*C(s)]B(s)E(s)
392.3 [email protected]
R(s)C(s) E(s), B(s)C(s)= G(s)*E(s)E(s)= R(s)-B(s)B(s)= H(s)*C(s)1B(s)E(s)
AE(s)B(s)A2C(s)E(s)
31
402.3 [email protected], , R(s)N(s)
N(s),R(s)=0, ,, ,R(s),N(s)=0,
412.3 [email protected]
R(s)N(s)
, R(s)N(s),()C(s) : 422.3 [email protected] (1) (2) (3)
432.3 [email protected]. RC R C u1 u2 i (1)
2U1(s)+U2(s)UR(s)1RI(s)UR(s)U2(s)1CsI(s)
442.3 [email protected]. 2-8(a),Ur(t)Uc(t),
IIIIi1u1IIi2uc
, (1) , (2) , (3) ; , (4) ,
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542.3 [email protected] 2-9 ,C(s)/R(s)
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56
2.3 [email protected](s)G4(s)H3(s)(2-21(b)),
57
G2(s)G34(s)H2(s)1/G4(s)
582.4 [email protected]
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622.4 [email protected](2)
abcd-g-f-e632.4 [email protected](2)
abcd-g-f-e
642.5 [email protected],
P (, ); k ; Pk k; 652.5 [email protected] ,, , :
,L(1); L(2) L(3); L(m)m; k kPk, Pk 662.5 [email protected](Mason)
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682.5 [email protected](d)(e)(f)(g)2x2x2x2x3x3x4x4x5x5x32231aaL=4234232aaaL=443aL=524534234aaaaL=5235235aaaL=44322312aaaL=4452352325aaaaL=
692.5 [email protected] gain formula
3
546154612=GGGGP
2-24 2-11702.5 [email protected]
712.5 [email protected] Masons Gain Formula
722.6 [email protected] 2-17
MATLAB MATLAB: num=12 24 12 20; den=2 4 6 2 2; G=tf(num, den) Transfer function: 12 s^3 + 24 s^2 + 12 s + 20 2 s^4 + 4 s^3 + 6 s^2 + 2 s + 2, 0,3s21,MATLAB num=3 0 1; ,MATLABconv( ) 732.6 [email protected] 2-18
MATLAB MATLAB: num = 4*conv(1 2, conv(1 6 6, 1 6 6)); den = conv([1 0], conv([1 1], conv([1 1], conv([1, 1], [1 3 2 5])))); G = tf(num, den)conv( ), :Transfer function: 4 s^5 + 56 s^4 + 288 s^3 + 672 s^2 + 720 s + 288 s^7 + 6 s^6 + 14 s^5 + 21 s^4 + 24 s^3 +17 s^2 + 5 s 742.6 [email protected] 2-19
P = [1, 3, 0, 4];R = roots(P);
R= -3.3553 0.1777 + 1.0773i 0.1777 - 1.0773i
P = poly(R)
P =1.000 3.000 0.000 4.000 2-20 2-21 s=-5
N = conv([3, 2, 1],[1, 4])Value = polyval(n, -5)
Value = [email protected] , ()() : ; ; , ; , ; 76Thank [email protected]
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C(s)