Given the transfer function \$G(s)=\frac{(1-\frac{s}{3})}{(\frac{s}{0.1}+1)(\frac{s}{100}+1)^2}\cdot 10\$, I would like to calculate the settling time.
From what I've learned, this is a third-order system, and the settling time can be calculated as \$T_{a}=\frac{3}{\zeta\omega_{n}}\$ (the same as a second-order system correct me if I'm wrong), where \$\omega_n\$ is the natural frequency, \$\zeta\$ is the damping factor.
However, there are no imaginary poles and I'm struggling to really understand the fundamentals. What's the "right" intuition/approach?
The relative bode diagram:
Update: I am also looking for solutions that involve simpler calculation than finding the Laplace inverse.