II. PROBLEM FORMULATION
This section introduces first the PH formulation of both the
SPMSM and the mechanical elevator which is used for system
energy description. Then, the system constraints and cost are
described.
A. SPMSM and Mechanical system model
As detailed in [3], the PH model is a combination of the
DC/AC inverter, of SPMSM (Park transform and SPMSM
model on d-q frame) and of mechanical system with the
following specifications: linear regime of machine, symmetry
in the machine construction, non-friction in mechanical system
and constant length of the elevator rope. In this paper the
simplified model, component of the mechanical part and of the
SPMSM model on d-q frame, is investigated for the control
design convenience. Likewise, the resistance is constant, and
the control port connection matrix is unit (see the standard
form in [4]). Therefore, the machine PH model is written in a
simple form as following:
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