Model predictive control with reference tracking

An electrical system, comprising:

• an electrical converter comprising a plurality of semiconductor switches, wherein the electrical converter is adapted for generating a two-level or multi-level output voltage from an input voltage by switching the plurality of semiconductor switches, and a controller;
• wherein the controller executes a method for controlling the electrical converter comprising:
• receiving a reference electrical quantity (is*) and an actual electrical quantity (is), the reference electrical quantity being determined from measured currents, voltages, torques, and/or speeds;
• determining a sequence of future electrical quantities of the electrical converter from the actual electrical quantity;
• determining a maximal cost value based on the sequence of future electrical quantities;
• iteratively determining an optimal switching sequence for the electrical converter, wherein a switching sequence includes a sequence of future switching states for the semiconductor switches of the electrical converter;
• and
• selecting the first switching state of the optimal switching sequence as a next switching state (u) to be applied to the semiconductor switches of the electrical converter,
• wherein the optimal switching sequence is iteratively determined by:
• extending a switching sequence by appending a possible switching state to the switching sequence;
• determining a cost value for the extended switching sequence with a cost function based on the sequence of future electrical quantities, the cost function being based on a norm of a matrix equation with a triangular matrix, which is multiplied with the extended switching sequence, and the cost function is based on a difference between an unconstrained solution and the triangular matrix multiplied with the extended switching sequence, the unconstrained solution being determined from the future electrical quantities before iteratively determining an optimal switching sequence;
• and
• discarding the extended switching sequence, when the cost value is higher than the maximal cost value;
• and
• an electrical load supplied by the electrical converter.