Determining the range of a controller for a stable system

[MattH150197]

Homework Statement

The controller K(s) = Kp, determine the range of Kp over which the closed loop system is stable.

Homework Equations

I found the transfer function of system = Y(s)/V(s)=Kp/(1.5s^2 + 2.5s - 1 + Kp)

The Attempt at a Solution

So i know (1.5s^2 + 2.5s - 1 + Kp) is the characteristic equation is been a while since I've done these i think i remember that all roots of the polynomial for a stable system must be negative real parts and i know its probably obvious but i just can't remember how to find the range of Kp. Thanks!

 

[FactChecker]

Solve for the roots of the denominator. It's only second order, so you can use a formula.

 

[MattH150197]

yeah it's just the Kp being part of the denominator that's throwing me a bit, how do I include that in the quadratic formula

 

[gneill]

yeah it's just the Kp being part of the denominator that's throwing me a bit, how do I include that in the quadratic formula

Um, by including it in the quadratic formula? Treat Kp as a constant and write out the formula. Then see how the value of Kp affects the roots. What range of values for Kp will satisfy your requirements? Be discriminating

 

[LvW]

... how do I include that in the quadratic formula

As far as I can see IT IS included in the formula (see your own post).

 

[MattH150197]

Yeah I got it now, cheers guys.