Spatial system identification of a simply supported beam and a trapezoidal cantilever plate

Dynamic models of structural and acoustic systems are usually obtained by means of modal analysis or finite element modelling. To their detriment, both techniques rely on a comprehensive knowledge of the system's physical properties. Experimental data and a nonlinear optimization is often required to refine the model. For the purpose of control, system identification is often employed to estimate the dynamics from disturbance and command inputs to a set of outputs. Such discretization of a spatially distributed system places further unknown weightings on the control objective, in many cases, contradicting the original goal of optimal control. This paper introduces a frequency domain system identification technique aimed at obtaining spatially continuous models for a class of distributed parameter systems. The technique is demonstrated by identifying a simply supported beam and trapezoidal cantilever plate, both with bonded piezoelectric transducers. The plate's dimensions are based on the scaled front elevation of a McDonnell Douglas FA-18 vertical stabilizer.