Abstract
Multiple input multiple output active vibration control architectures pose some common challenges to designers, such as the optimization of the number and of the position of sensors and actuators, and of the controller parameters. At a more fundamental level, however, the modeling of the electromechanical structure under control is a preliminary step necessary to perform all the optimizations described above. While some control algorithms try to prescind from a detailed modeling, some models are always required to simulate numerically the performance of the control.
Finite element or reduced order models are often employed to simulate and to estimate the relationship between electrical and mechanical inputs and outputs. However, building these models can rapidly become onerous, even for relatively simple bidimensional structures, for example composite beams, plates and shells. Therefore, an experimental method was developed for the determination of the electromechanical coupling matrices. Simple experimental modal analyses were performed to obtain parameters such as natural frequencies, damping ratios, modal shapes and frequency response functions. Afterwards, a least square error algorithm, implemented in MATLAB and in Python, was used to determine the matrices that correlate transducer voltages, generalized coordinates and modal coordinates. Modal coordinates are especially useful for the construction of multiple input multiple output active vibration control algorithms that operate in the modal space; however, in these cases the inversion or the pseudo-inversion of the participation matrices had to be performed as well.
The proposed method was tested on one cantilever sandwich beam and on one sandwich plate with free edges, equipped with two collocated couples of sensors and actuators and four non-collocated couples of sensors and actuators respectively. In particular, piezoelectric patches operating in flexural mode were employed as transducers. The method simulated correctly the uncontrolled electromechanical response of either structure, and its performance in this regard compared favorably with that of the finite element method.
Afterwards, multiple input, multiple output positive position feedback active vibration control algorithms based on these participation matrices were built for either system, and tuned according to established method described in the relevant literature. In either case, a number of modes double with respect to that of the couples of installed actuators and sensors was controlled satisfactorily. The controllers resulted stable and negligible spillover on uncontrolled modes was observed.
