Model predictive control with fatigue-damage minimization through the dissipativity property of hysteresis operators

In this paper, we propose an approximation method for the well-known fatigue-damage estimation of rainflow counting (RFC) using the dissipativity property of hysteresis operators that can be embedded in model predictive control (MPC) frameworks. Firstly, we revisit results that establish the equivalence between RFC to an energy dissipation property of an infinite-dimensional operator of the Preisach hysteresis model. Subsequently, we approximate the Preisach model using a finite-dimensional differential Duhem hysteresis model and propose an extended MPC scheme that takes into account the dissipated energy of Duhem hysteresis model as a damage proxy in the optimization problem formulation. Lastly, we present an example of control design for damage minimization in the shaft of a wind turbine where we illustrate the proposed strategy.