Hello experts,
I'm trying to apply one-step nonlinear model predictive control (NMPC) for 3 degree of freedom nonlinear model of the ships(the system is nonlinear affine). The state weighting matrix is selected to be diagonal. The problem i face is that the controller can not track the position states due to the zeros corresponding to them in the control matrix g(x) (see the attachment).
i think changing the matrix Q, may lead to a solution but i couldn't do that by trail and error and i don't know any technique for selecting it.
Thanks in advance
As a general advice I would say: when you are setting your MPC problem up you should choose your weighting matrices based on the following criteria:
- stability and feasibility of the underlying problem should be achieved.
- elements of the weighting matrices should be first normalized and then magnified based on their importance.
Generally for the first criterion there is no solid theory in the context of "NMPC" based on my best knowledge, although some results may be found in the literature.
Regarding the second factor the simplest way is to consider physical features of all states and obtain the maximum and minimum values they will achieve in the normal operations. Alternatively, you can first design a simple controller (e.g. PID) and run the system in different points, then you can estimate min/max of each state. Finally, you can first normalize all states and so on....
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