Active Vibration Suppression of a Smart Flexible Beam Using a Sliding Mode Based Controller

Abstract

This article investigates robust active vibration suppression of a flexible beam with a low dominant frequency using piezoceramic sensor and actuators. The piezoceramic sensor and actuators are in patch form and are surface-bonded to the cantilevered end of the flexible beam. The robust sliding mode control, which has the advantages of being robust to plant parameter variation, insensitive to the unmodeled dynamics, and easy to implement, is adopted in this article for active vibration control of the flexible beam. Unlike other commonly used vibration suppression methods, such as positive position feedback control, strain rate feedback control, and lead compensation, the sliding mode controller requires almost no knowledge of the flexible beam. To avoid the chattering problem commonly associated with sliding mode control, a smooth switching function employing a hyperbolic tangent function is used. A low pass filter is applied to the output of the sliding mode controller to avoid excitation of the higher modes of the flexible beam. To demonstrate the advantage of sliding mode based active vibration reduction, its experimental results are compared with those of Proportional plus Derivative (PD) control and lead compensation. The comparison shows that the sliding mode controller reduces vibration of the flexible beam much more rapidly. To verify the robustness of the proposed sliding mode controller, vibration suppression of the beam is conducted for a case where the modal frequency of the beam is changed by adding masses. In addition, vibration suppression of the beam when subjected to a multi-modal excitation is also conducted. Experimental results demonstrate the robustness of the proposed controller with respect to varying model parameters and even the dynamics of higher modes.