Modeling and control of low frequency dynamics of a smart system

Background/Objectives: Active vibration control is an important aspect in mechatronic system dynamics and control. The objective of this manuscript is to present a classical PI controller in order to control the vibrations of a piezoelectric laminate flexible cantilever beam when excited by various signals. Methods/Statistical analysis: Finite element modeling techniques are employed to analytically develop the mathematical model of the smart system which replicates the low frequency system dynamics. The sensor, exciter and control actuator dynamics are modeled as well. The programming platform selected for developing the math model is MATLAB. The developed model was exported to SIMULINK platform for the controller design wherein classical PI control technique is implemented. Findings: The developed model is verified for its accuracy from its frequency response to free vibration condition which showed a close match between the resonant frequencies of the model with that derived from theory of vibrations. PI controller is the most commonly used controller worldwide due to its ease in computation as well as cost effectiveness. Its efficiency is proved in this manuscript when the system was subjected to free vibration in open loop as well as with the controller in loop. Further, as in practical cases, the system was also subjected to harmonic excitations at the dominant resonant frequencies and here as well, the controller was highly efficient in damping out the vibrations. Application/Improvements: The work presented in this manuscript can be extrapolated to any fixed-free system in aerospace, defence as well as heavy industries. The performance of the active controller can be further improved by opting for math intensive robust control strategies.