Adaptive robust sliding-mode control of a flexible beam using PZT sensor and actuator

This work presents an adaptive robust sliding-mode control scheme based on Lyapunov´s direct method for active vibration control of a flexible beam using PZT (lead zirconate titanate) sensor and actuator. PZT, a type of smart materials, has the advantages of high reliability, high bandwidth and solid state actuation and is adopted here in forms of surface-bond PZT patches for vibration control. Two adaptive robust sliding-mode controllers for vibration suppression are designed: one uses a discontinuous bang-bang robust compensator and the other uses a smooth compensator with a hyperbolic tangent function. Both controllers guarantee asymptotic stability as proved by the Lyapunov´s direct method. Experimental results showed that both controllers suppress vibrations of the flexible beam with the PZT sensor and actuator. However, the bang-bang robust compensator causes small-magnitude chattering because of the discontinuous switching actions. With the smooth compensator, vibration is quickly suppressed and no chattering is induced. Furthermore, the robustness of the controllers is successfully demonstrated by adding mass to the flexible beam.