I am working with a control system which has an unstable pole in the process. So I have the following transfer functions for the controller and for the process:
G = 10/((s+10)*(s-1)); K1 = K*(s+1)/s;
where G is the process and K1 is the controller. In the controller I have to choose a gain K such that the system is stable, and using the Routh Criterion I have found that it is stable for $K>1.125$, so I have chosen has value 4 because it gives me good performances. Now, I have that if I do the root locus I have:
L1 = K1*G; figure; rlocus(L1)
so I have a pole in the RHP. But I have that with an appropriate value of the gain of the controller we have a stable system. But in this case the pole should be in the LHP, not in the RHP.
So, what I don't understand is how it is possible that the system is stable even if it is present a pole in the RHP?
Can soebody help me?