Active vibration control of cantilever beam by using PID based output feedback controller

Undesired noise and vibrations have a detrimental effect in many areas. Hence the control of vibrations has become a relevant technological challenge. Active vibration control of structures using smart materials is especially in vogue. This involves sensing the motion of the structure using sensors, generating a control signal using a controller and applying a control force on the structure using actuators. To design the control system of any vibrating structure, the mathematical model of the system is required. However, it is difficult to theoretically construct a model of complex structures. On the other hand, it is relatively simpler to model such systems in a Finite Element (FE) environment like ANSYS^©. This paper deals with the extraction of the full and reduced mathematical models of a cantilever beam into MATLAB^© from its FE model. The full model of the beam is reduced by discarding those modes which do not contribute to the overall response. It is found that the frequency and transient responses of the full and reduced models match closely. Hence the reduced model may be used to represent the system which in turn reduces the computational time. The controller is designed using proportional-integral-derivative theory with output feedback. SIMULINK^© is then used to create a working block diagram of the control system and perform the control action. The transient responses of the controlled full and reduced models are then plotted which are found to be in close agreement. The procedure for the design of the controller described in this paper may be extended to control the vibrations of any real life system.