Long-Horizon Direct Model Predictive Control: Modified Sphere Decoding for Transient Operation

Abstract

In this paper, we present modifications to the sphere decoder initially introduced in the work of Geyer and Quevedo and modified in the work of Karamanakos et al. that significantly reduce the computation times during transients. The relative position of the unconstrained solution of the integer quadratic program underlying model predictive control (MPC) with respect to the convex hull of the (truncated) lattice of integer points is examined. If it is found that the unconstrained solution does not lie within the convex hull—a phenomenon that is observed mostly during transients—then a projection is performed onto the convex hull. By doing so, a new sphere that guarantees feasibility and includes a significant smaller number of candidate solutions is computed. This reduces the computation time by up to three orders of magnitude when solving the optimization problem at hand. Nonetheless, the reduction of the computational burden comes at a cost of (mild) suboptimal results. The effectiveness of the proposed algorithm is tested with a variable speed drive system consisting of a three-level neutral point clamped voltage source inverter and a medium-voltage induction machine. Based on the presented results, the sphere decoding algorithm with the proposed refinements maintains the very fast transient responses inherent to direct MPC. Moreover, it is observed that the occasional implementation of suboptimal solutions does not lead to a deterioration of the system performance.