請問一下控制系統公式的推導

令 r = %OS/100.由 r = e^{-ζπ/√(1-ζ^2)}, 取對數, 得
ln(r) = -ζπ/√(1-ζ^2)
所以,
ζ/√(1-ζ^2) = - ln(r)/π
兩邊平方, 得
ζ^2/(1-ζ^2) = [-ln(r)/π]^2
解得
ζ^2 = [-ln(r)/π]^2/{1+[-ln(r)/π]^2}
= [-ln(r)]^2/{π^2+[ln(r)]^2}
開平方根, 取適當正負號, 得
ζ = -ln(r)/√{π^2+[ln(r)]^2}



2012-12-10 19:08:56 補充：
ζ^2/(1-ζ^2) = [-ln(r)/π]^2　　如何變成　　 ζ^2 = [-ln(r)/π]^2/{1+[-ln(r)/π]^2}　　的


ζ^2/(1-ζ^2) = A 則 ζ^2 = A(1-ζ^2) 則 ζ^+Aζ^2 = A 則 ζ^2= A/(1+A).
把 A = [-ln(r)/π]^2 代入上式.

公式在哪...XD

雖然控制系統這東西我應該不會 :P