Predictive Position Synchronization Control of Dual Permanent Magnet Synchronous Motor System Based on Geometric Constraints

Model predictive control (MPC) mitigates synchronous error accumulation, dynamic response mismatch, and precision-complexity trade-off in traditional multi-motor system. However, constrained numerical solutions in MPC present significant computational challenges. To address this, this paper proposes a predictive position synchronization control strategy based on geometric constraints for dual permanent magnet synchronous motor (PMSM) system. First, an incremental MPC framework is constructed, whose embedded integral action not only effectively compensates for short control horizons but also enables high-precision multi-step prediction. Second, a cost function incorporating tracking error, synchronous error and control increment is established to derive the current control increment. To reduce computational complexity, a constrained geometric mapping method is proposed: with control horizon <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> = 1, current and voltage constraints are mapped to a 2D plane to form a feasible region, converting the optimal control increment solution into determining the tangent point between the cost function's elliptic surface family and this feasible region. Rapidly localizing the tangent via real-time query and calculation of analytical solutions significantly reduces online computational load. Experimental results show the proposed strategy can improve computational efficiency by approximately 47% and dynamic response speed by approximately 57% vs traditional QP strategy, resolving the precision-complexity trade-off in multi-motor synchronization while ensuring accuracy.