Longitudinally vibration ultrasonic motor (LV-USM), a canonical nonlinear system, utilizes the inverse piezoelectric effect of piezoelectric ceramic to generate the mechanical vibration within the scope of ultrasonic frequency. However, it is very difficult to establish a strict and accurate mathematical model. Hence seeking a dynamic identifier and controller for LV-USM avoiding the accurate mathematical model becomes a feasible approach. In this paper, a novel learning algorithm for dynamic recurrent Elman neural networks is present based on a particle swarm optimization (PSO) to identify and control an LV-USM. To overcome the PSO’s global search ability, Lévy flights, a kind of random walks, are imported to improve the ability of exploration rather than Brownian motion or Gauss disturbance based on Cooperative Quantum-behaved PSO (CQPSO). Thereafter, a controller is designed to perform speed control for LV-USM along with the nonlinear identification also using this kind of neural network. By discrete Lyapunov stability approach, the controller is proven to be stable theoretically and the latter trial shows its robustness of anti-noise performance. In the experiments, the numerical results illustrate that the designed identifier and controller can achieve both higher convergence precision and speed, relative to current state-of-the-art other methods. Moreover, this controller shows lower control error than other approaches while the displacement of the rotor disc in LV-USM appears more smooth and uniform
