Predictive control of a Linear Motor for tracking of constant references

This paper deals with the application of a model predictive controller (MPC) for tracking to a real system: a linear motor. The MPC formulation used in this paper in a novel approach to track piecewise constant references recently presented by the authors. The main novelties of this controller are: (i) the addition of an artificial steady state and input as decision variables, (ii) the minimization of a modified cost function which penalizes the error with the artificial steady and the distance from the artificial to the desired steady state and (iii) the usage of an extended terminal constraint. The obtained MPC ensures the admissible convergence to any admissible set point for any feasible initial state. The optimization problem associated to this MPC technique results to be a quadratic programming problem parametrized in the current state and the desired steady state. Thus, well-known techniques to compute the control law explicitly based on multiparametric programming can be used, which allows us to apply this control technique to fast systems. We have applied an explicit MPC for tracking to a synchronous linear motor with permanent magnets using a sampling time of 10 ms. This system has been modelled as a linear system with constraints in the input and states. The control objective is to steer the motor at any admissible position in an admissible evolution. The explicit controller has been coded as a search tree for its implementation on a dSPACE Card. The obtained experimental results are satisfactory and show the properties of the predictive controller