Vibration suppression of a beam using variable structure control with disturbance observer

A discrete variable structure control with equivalent law is proposed to suppress vibration of a flexible cantilever beam boned with piezoceramic patch and strain gauges. The finite element method and modal truncation technique is applied to obtain the dynamic model of the structure. The vibration control of structure is considered as the issue that the controller enables the system to be zero state as the system states are away from the equilibrium one due to external disturbances, that is, it is a state regulator. The error state equations are obtained according to state equation and control requirements. The discrete variable control approach with disturbance observer is applied to design the state regulator. The discrete Kalman filtering technique is employed to construct state estimator because the state variables cannot be directly measured. The first four natural frequencies and damping ratio are obtained by using experimental modal testing. Using dSPACE real-time simulation system and MATLAB/Simulink, the control system is built and the active vibration control study is carried out. The experimental results show that the proposed controller can effectively reduce the vibration response of the structure.