A speed controller for permanent magnet synchronous motors (PMSMs) under the field oriented control (FOC) method is discussed in this paper. First, a novel adaptive neuro-control approach, single artificial neuron goal representation heuristic dynamic programming (SAN-GrHDP) for speed regulation of PMSMs, is presented. For both current loops, PI controllers are adopted, respectively. Compared with the conventional single artificial neuron (SAN) control strategy, the proposed approach assumes an unknown mathematic model of the PMSM and guides the selection value of parameter K online. Besides, the proposed design can develop an internal reinforcement learning signal to guide the dynamic optimal control of the PMSM in the process. Finally, nonlinear optimal control simulations and experiments on the speed regulation of a PMSM are implemented in Matlab2016a and TMS320F28335, a 32-bit floating-point digital signal processor (DSP), respectively. To achieve a comparative study, the conventional SAN and SAN-GrHDP approaches are set up under identical conditions and parameters. Simulation and experiment results verify that the proposed controller can improve the speed control performance of PMSMs.