This paper presents the co-simulation of the self-adjusting fuzzy PI controller to control a two-axes system. Each axis was driven by a permanent magnet linear synchronous motor (PMLSM). The position and speed controller used the fuzzy PI algorithm with parameters adjusted by a radial basis function neural network (RBFNN). The vector control was applied to the decoupled effect of the PMLSM. The field programmable gate array (FPGA) was used to control both axes of the system. The very high-speed

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... integrated circuithardware description language (VHDL) was developed in the Quartus II software environment, provided by Altera, to analyze and synthesize designs. Firstly, the mathematical model of PMLSM and fuzzy PI was introduced. Secondly, the RBFNN adjusted the knowledge base of the fuzzy PI. Thirdly, the motion trajectory was introduced for testing the control algorithm. Fourthly, the implementation of the controller based on FPGA with the FSM method and the structure of co-simulation between Matlab/Simulink and ModelSim were set up. Finally, discussion about the results proved the effectiveness of the control system, determining the exact position and trajectory of the XY axis system. This research was successful in implementing a two-motor controller within one chip. Keywords: FPGA Fuzzy PI controller Radial basis function neural network Simulation XY-axis This is an open access article under the CC BY-SA license.