Self-adaptive vibration control of simply supported beam under a moving mass using self-recurrent wavelet neural networks via adaptive learning rates

A self-recurrent wavelet neural network (SRWNN) is used to control suppression of vibration of an Euler–Bernoulli beam under excitation of a moving mass traveling along a vibrating path. The proposed control structure uses one SRWNN as an identifier and one as a controller. The SRWNN identifier is trained to model the dynamic behavior of the process and provide the SRWNN controller with information about system sensitivity. The SRWNN controller uses the sensitivity information provided by the SRWNN identifier to update weights and produce a signal that controls beam vibration. The gradient descent method and adaptive learning rates (ALRs) are used to update all SRWNN weights. The ALRs are obtained using the discrete Lyapunov stability theorem which guarantees the convergence of the proposed control structure. The performance and robustness of the proposed controller are evaluated at different mass ratios of moving mass to beam and for dimensionless velocity of a moving mass. The simulations verify the effectiveness and robustness of the controller.