Simulation Study of Active Vibration Control of Cantilever Beam by Using State and Output Feedback Control Laws

Abstract

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 especially is in vogue. It 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 not possible, to theoretically construct the model of complex structures. On the other hand, it is relatively simpler to model such systems in an Finite Element (FE) environment like ANSYS©. This paper deals with the extraction of the mathematical model of a cantilever beam from its FEA model. This procedure of extraction is applicable to any mechanical system under dynamics study. Then again, the matrices thus formed are usually very large and require a lot of computational time to process. Hence an attempt is made to construct the reduced model of the system which approximates the actual model to the desired extent. In this paper, the full model of the beam is reduced by discarding those modes which do not contribute to the overall response on the basis of their dc gains in MATLAB©. 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 instead of the full model with reasonable accuracy. Design of controller is attempted using the theory of state and output feedback control laws. The controller is modeled by calculating the optimal control gain by formulating an algorithm to solve the equations involved. The transient and frequency responses of the controlled full model and reduced models are then plotted. The procedure for designing controller described in this paper may be extended to any real world system.