第二章 自动控制系统的数学模型
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xtwang@mail.xidian.edu.cn
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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 xtwang@mail.xidian.edu.cn
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p1p2j1 1 j 023p3z1 s=2 s=-3, s=-1+j, s = -1-j262.2 xtwang@mail.xidian.edu.cn2.2.3 G(s)
6,272.2 xtwang@mail.xidian.edu.cn2.2.3 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
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382.3 xtwang@mail.xidian.edu.cn
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 xtwang@mail.xidian.edu.cn
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)
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692.5 xtwang@mail.xidian.edu.cnMasons gain formula
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712.5 xtwang@mail.xidian.edu.cn Masons Gain Formula
722.6 MATLABxtwang@mail.xidian.edu.cn 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 MATLABxtwang@mail.xidian.edu.cn 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 MATLABxtwang@mail.xidian.edu.cn 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 = -6675xtwang@mail.xidian.edu.cn , ()() : ; ; , ; , ; 76Thank youxtwang@mail.xidian.edu.cn
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