I have the following transfer function:
and this is a transfer function of a plant with two poles in the origin. So I want to desing a controller with two poles in the origin in order to have zero steady state error. So the controller I want to desing is of the type:
now, I want to find the k such that the closed loop is stable, but I am having some problems in doing so. I am using the Routh criterion, and I have that the closed loop is:
and the table for the Routh criterion:
and where I have omitted terms it means that there is a zero and the bar $|$ has been used to say that these numers are in different columns.
By doing this I obtain that the closed loop is stable if $k>0$ and $k<-4$, but if I use these values I have that the closed loop is unstable.
And also I would like to ask if there is a simpler way to find the value of $k$ instead of using the Routh Criterion, for example using Matlab.
What am I doing wrong?