It's an interesting question.

Not necessary for all systems

I think it depends on the system's characteristics, like stability, dynamics, etc.

Hi Chitta,

Do you talk about a linear or a nonlinear system? And what is the control task you are referring to: stabilization or tracking?

In abstract terms you need to verify that the required set-point is reachable. Controllability of linear systems and absence of constraints directly implies that for any set-point. However, if you are only interested in stabilization, let's say of the origin, than stabilizability is sufficient.

For nonlinear systems checking these conditions can be though. In that case you might simply try and see if the simulated MPC is able to stabilizes your set-point or not.

Regards,

Thanks...what about tracking a set point for nonlinear system? In this case is it necessary to check controllability of nonlinear system??

Hey Chitta,

The answer depends on what you want to do. Do you want verify stability conditions for a given system? In that case typical stability conditions (e.g. terminal region constraints) imply reachability properties. So often you check controllability properties implicitly when you verify stability conditions. However, in practice many people would skip terminal regions and simply try via simulations whether the controller is stabilizing or not. In this case you also implicitly verify a kind of controllability or stabilizability property.

However, in any case I would always check whether the required set-point is admissible for your system and the given constraints. In other words, you should check whether the system admits a steady state corresponding to your set-point.

Regards,

If you talk about a linear system, then control authority can be checked graphically using root locus or nyquist. From Bode plot you can decide controllability if there is a sequence between poles and zeros.

It depends on the system. It is not a must but it is better to check.Timm Faulwasser is exactly right.