Root locus of dynamic equation

I have an expression (characteristic equation) of the form

a*s^4 + (a^2)*3*(s^3) + 45*s^2 + 12 = 0

I need to get the locus of all poles of characteristic equation (locus of solution of above equation) when a varies from 0 to 10.

This is not as simple as "rlocus" since System transfer function, as shown above, is not static but dynamic due to presence of a.

Can anyone help?

Answer 1

[Mischa Kim]

Satyajit, you could simply compute the root loci in a loop for different values of a and plot them in 3D ( plot3 ). The root loci would lie in planes parallel to the xy -plane, with a on the z-axis.

[Satya C]

Well 'a' is not an axis. When a changes, we get 4 complex roots of above equation. I need to show how these poles vary without showing a explicitly. Just as in root locus we just show poles movement without showing gain value.

[Mischa Kim]

So you are saying you would like to get the roots for a in [0,10] with keeping s fixed? Or, since you emphasize 'dynamic', have a=a(t) vary as a funtion of time?