ControlSystems - Easy way to simplify Closed Loop Equation?

[jdoe10]

Homework Statement

$G_{OL} = \frac{5}{s}$
$G_{CL} = \frac{KG_{OL}}{1+KG_{OL}}$

Homework Equations

The Attempt at a Solution

It's pretty easy when the equation is so simple
$G_{CL} = \frac{K\frac{5}{s}}{1+K\frac{5}{s}}$
$G_{CL} = \frac{5K}{s+5K}$

If the open loop equation is really long, is there an easy way to simplify it?

 

[LvW]

What is the emaning of K?
If it is the feedback factor, the expression for Gcl is false.

 

[donpacino]

Homework Statement

$G_{OL} = \frac{5}{s}$
$G_{CL} = \frac{KG_{OL}}{1+KG_{OL}}$

Homework Equations

The Attempt at a Solution

It's pretty easy when the equation is so simple
$G_{CL} = \frac{K\frac{5}{s}}{1+K\frac{5}{s}}$
$G_{CL} = \frac{5K}{s+5K}$

If the open loop equation is really long, is there an easy way to simplify it?

If youre referring to a non-computer based technique not really. You just need to power through the algebra, you'll get used to it.

You can use tools such as MATLAB that have the capability to do simplification.