Given a transfer function, how can you find a K for closed loop stability, that minimizes the settling time?
This is for a Mechanical Control Systems class.
The usual from of analysis for a mechanical control system is
M*a(t) = K*x(t) + B*v(t)
Where
a = vector acceleration
v = vector velocity
x = vector position
M = Mass
K = spring constant
B = damping factor
B is usually considered the term that is to be used to modify the system to control stability and minimize settling time.
Are we discussing the same control function?
Niel Leon
Community Developer – Engineering.com
Without know the equation it is difficult to provide you with any assistance.
Did the Wikipedia provide any guidance towards your solving this problem?
Niel
It’s not in the form of an equation of motion. It’s an equation with K in the numerator and a 4th order poly in the denominator. This equation is defined as the transfer function of the system output/input.
Given that transfer function, we’re supposed to find a range of K that minimized the settling time.
I am assuming that the value for the function is the Settling Time that you are looking for.
Have you tried to graph the function holding “s” as a constant and varying K?
Have you tried to take the derivative of the function to find the deflection points that would determine the maximum and minimum settling times?
It has been over 30 years since I did this type of analysis, but that would be how I would start.
Niel
The equation itself is:
T(s) = [ (.63K) / ( 1.74×10^(-10)*s^4 +2.086×10^(-8)*s^3 + .000027*s^2 + .00134*s + 1) ]
So the num = .63K
The denominator is the 4th order polynomial
