My answer for (i)
Given that C =35 in this question.

G(s) = θ(s) / F(s) = 1 / (s^2 - α )

α = (10 + C) / 1000 = 45 / 1000 = 9 / 200

System pole can be found at s


Thus , it tells me that it is a real and district roots and when input signal is applied , output signal from the space booster will be a exponentially growing transient response.

ii. Sketch the impulse response, θ(t).

My answer for (ii)




Question 2



My answer for (i)
I let A = kp + kd s + ki / s and B = 1 / (s^2 - α )

To obtain the closed-loop transfer function with respect to a specific point , we assume that all other inputs are zero. Thus , for θ(s) / θr(s) , we take D(s) = 0 and θ(s)/D(s) , we take θr(s) = 0

Hence, Gr(s) = (AB) / (1 + AB) and Gd(s) = B / (1-AB)

Gr(s) = (kp + kd s + ki / s ) / (s^2 - α + kp + kd s + ki / s )
Gd(s) = 1 / (s^2 - α - kp - kd s - ki / s )

Is my answer correct?

 

The question also asks the order of the booster rocket control system. So based on my result of Gr(s) , it is a second order system?

 

Hi,

A quick note here...

I did not go over your equations but from the last set Gr and Gd it does not look like you have them in the right form in order to determine the order of the system. You can do it that way, but it's better to get it into the ratio of two polynomials.
Try doing that and then see if you can figure out the order (it's simple really).