<p>The particle swarm optimization (PSO) algorithm is widely employed for tuning parameters in PID control systems. However, the traditional PSO approach often suffers from several limitations, including a tendency to converge prematurely to local optima, relatively low solution accuracy, and slow convergence speed. To address these drawbacks, this paper proposes a simplified dual-population PSO algorithm incorporating hyperbolic dynamic adjustment of inertia weights (HypSDPSO). The HypSDPSO sorts particles by their fitness values and divides the entire population into two subpopulations with exploitation and searching functions. The exploitation subpopulation adopts the strategies of adaptive coefficients and cross-combination of particle historical optima with the global optima of the population, thereby accelerating the convergence rate and balancing the emphasis between global exploration and local refinement. The searching subpopulation uses the optimal historical mean of all particles to guide the position updating and random mutation, which expands the diversity of particle states and strengthens the overall exploration ability. Additionally, a hyperbolic nonlinear dynamic inertia weight is proposed to balance the weights of global search and local exploitation. By comparing it with 6 other PSO algorithms on 21 test functions, the favorable improvement effect of HypSDPSO is verified. Finally, PID parameter tuning experiments on the delayed system of a permanent magnet synchronous motor are performed, which show that HypSDPSO achieves more stable convergence results than other algorithms, both under conventional control conditions and under overshoot penalty constraints.</p>