Nonminimum Phase Unstable Systems?
Have you ever dealt with nonminimum phase unstable systems? Especially in practice.
If so, what was your aproach to deal with such a problem?
I know that nonminum phase systems (without instability) has the restriction on the controller gain, as a high gain will eventuell drag the stable poles from the LHP to the instable zero positions on the RHP according to the Root Locus of the open loop transfer function.
More problematic is when the system is additionally unstable. And even more problematic when the RHP pole lies right to the RHP zeros. So untill you place a zero/pole after the RHP pole, that path remains within root locus path and thus instability is not compensated.
Is it sound, to draw such conclusions based on Root Locus only? Can a output feedback controller stabilize such a system somehow?
I personally see no other way than using a state feedback controller to shape the dynamics of the whole system by placing the eigenvalues in desired locations. Am I overseeing something minor maybe?
Would like to hear your experience with such systems.