If the steady-state error of the proportional-plus-derivative-plus acceleration system is to be less than 10% determine a suitable value for Kp.
The input of the system is: v
The output of the system is: y
The transfer function of the system including the controller is:
(23(Kp+4s+s^2)) / (s^3+19s^2+48s+96+23Kp)
The Attempt at a Solution
With steady state: s = 0
Therefore: y steady state = v x (23Kp / (96 + 23Kp))
The error of the system is: v-y
Therefore: error = v - (23Kp / (96+23Kp))v
error = 96v / (96 + 23Kp)
How can I correctly substitute the error of 10% now in this equation.
I think (v-y)/y = 0.1 [error]
But this will leave 3 variables in the equation...
Thanks in advance!