- #1

- 3

- 0

Member advised to use the homework template for posts in the homework sections of PF.

Hi,

Having a bit of trouble with this question: "Assuming a proportional controller is used, determine the gain to achieve a damping ratio of 0.5, for the following transfer function. Hence calculate the associated natural frequency and oscillation period. G(s) = -4(s+0.4) / s^2+1.6s+14."

I would normally try and solve this using root locus method, but the question explicitly says not to use root locus. The furthest I've been able to go is determining the zeros and poles of the transfer function as -0.4, and -1.6+/-3.66i respectively. Some additional data is given: "Data that may be required: (s-2.38)(s+4.14-2.60i)(s+4.14-2.60i)=s^3+5.9s^2+4.24s-56.82" I think I recognise the left hand side of that equation coming from the characteristic equation of a state space model but I'm really not sure how I could use this.

Can anyone lend a hand? Thanks.

Having a bit of trouble with this question: "Assuming a proportional controller is used, determine the gain to achieve a damping ratio of 0.5, for the following transfer function. Hence calculate the associated natural frequency and oscillation period. G(s) = -4(s+0.4) / s^2+1.6s+14."

I would normally try and solve this using root locus method, but the question explicitly says not to use root locus. The furthest I've been able to go is determining the zeros and poles of the transfer function as -0.4, and -1.6+/-3.66i respectively. Some additional data is given: "Data that may be required: (s-2.38)(s+4.14-2.60i)(s+4.14-2.60i)=s^3+5.9s^2+4.24s-56.82" I think I recognise the left hand side of that equation coming from the characteristic equation of a state space model but I'm really not sure how I could use this.

Can anyone lend a hand? Thanks.