Given the control accuracy problem of the resonant acoustic mixer's acceleration, a radial basis function neural network (RBFNN) PID optimized by an improved sparrow search algorithm (ISSA) method is proposed to control acceleration. Firstly, the acceleration model is identified through the step response curve. Secondly, the sparrow search algorithm is enhanced by introducing a Tent chaos initializing population and a linear dynamic inertial weight method for updating the discoverer's position. Thirdly, ISSA is then applied to optimize the parameters of the RBFNN. Finally, the optimized RBFNN-PID is employed for the simulation test of acceleration and compared with other traditional algorithms. The simulation results show that the convergence speed and optimization ability of the developed ISSA are superior to other algorithms. It is found that the RBFNN-PID acceleration control optimized by ISSA can effectively suppress system overshoot and improve system control speed, accuracy, and stability. Experimental results show that, compared with the comparison algorithms, the RBFNN-PID acceleration control system optimized by ISSA demonstrates superior control performance and adaptive capability, providing a great practical value for the acceleration control of the resonant acoustic mixer.