C(S)/R(S)=K/{S2+(1+Kτ)S+K}
ωn=K1/2,ξ=(1+Kτ)/2K1/2
ξ=In(1/σp)/{π2+(In(1/σp)2)1/2=0.456
ωn=π/tp(1-ξ2)1/2=3.53(rad/s)图4-8系统结构图
K=ω2n=12.46τ=(2ξωn-1)/K=0.178
β=arccosξ=1.097(rad)
ωd=ωn(1-ξ2)=3.14(rad/s)
td=(1+0.7ξ)/ωn=0.374(s)
tr=(π-β)/ωd=0.615(s)
ts=3.5/ξωn=2.174(s)
若取误差Δ=0.02,则调节时间为
ts=4.5/ξωn=2.796(s)