RBF neural network-based sliding mode vibration control of a flexible cantilever plate using laser displacement measurement

Abstract

This paper is concerned with active vibration control of a flexible piezoelectric cantilever plate using a nonlinear radial basis neural network sliding mode control (RBFNN-SMC) algorithm and laser displacement measurement. In order to decouple the low-frequency vibration signals of the bending and torsional modes on measurement, two laser displacement sensors are used. The decoupling method is provided. A hyperbolic tangent function is used instead of the sign function, and the chattering phenomenon is alleviated. Also, the RBFNN is utilized to adjust the switching control gain adaptively to balance the chattering phenomenon and the control effect. The controllers for bending and torsional modes are designed independently. Experimental setup of the flexible piezoelectric cantilever plate with two laser displacement sensors is constructed. Experiments on vibration measurement and control are conducted by using the decoupling method and the designed controller, compared with the classical proportional and derivative (PD) control algorithm. The experimental results demonstrate that the proposed method can decouple the low-frequency bending and torsional vibration signals on measurement. Furthermore, the designed nonlinear RBFNN-SMC can suppress both the bending and torsional vibrations more quickly than the traditional linear PD controller, especially for the small amplitude residual vibration.