In this paper, the synchronous rotor speed control problem of multiple permanent magnet synchronous motors (PMSMs) with port-Hamiltonian (PH) dynamics is investigated. First, the synchronous rotor speed problem is reformulated as an optimization problem and a distributed controller is proposed for each PMSM. Then, the stability of the closed-loop system is analyzed, and it is proven that its equilibrium aligns with the optimum of the value function derived from the optimization problem. Based on the proposed distributed controller, PMSMs exchange the estimated average rotor speed with their neighbours, rather than the direct rotor speed, which benefits the protection of the sensitive state variables. Finally, a simulation example is presented to validate the effectiveness of the proposed distributed controller.