Hybrid control of vibrations of a smart von Kármán plate

Abstract

The suppression of large vibrations of a smart thin elastic rectangular von Kármán's plate is considered. The plate is subjected to external disturbances and generalized control forces produced by electromechanical feedback. The considered nonlinear initial-boundary value problem is spatially discretized by means of the time spectral method. The implicit Newmark-β iterative method is employed for the time integration of the obtained system of nonlinear equations of motion. Nonlinear controllers are designed, based on a fuzzy inference system. Two numerical algorithms involving a general control of displacement/velocity and a direct control of the Fourier coefficients are proposed. The techniques have been implemented within MATLAB environment with the use of the fuzzy logic toolbox. Numerical examples are presented.

Adaptive Neuro-Fuzzy vibration control of a smart plate

“…For simplicity we will omit the denomination "characteristics" for w ij N (t) and w ij t,N (t), and index N below. For solving the resulting equations (15) we apply the implicit Newmark-β technique with iterations ( [12]) and for the linear model the Newmark formulas. 4.…”

“…The plate is subjected to external disturbances and generalized control forces, which are produced by the electromechanical coupling effects. The behaviour of the structure is described by a nonlinear control model for large deflections [12]. The mechanical model is an extension of the von Kármán plate system ( [2,5] etc.)…”

“…The equations are spatially-discretized by a time spectral method ( [10]). The obtained system of nonlinear ordinary differential equations (ODEs) is solved by the implicit iterative Newmark-β method [12]. The nonlinear controller is designed using the Sugeno-type Fuzzy Inference System (FIS) and optimized by using Adaptive Neuro-Fuzzy Inference System (ANFIS).…”

“…[4,14,19,20,16]). Two effective computational procedures with the use of Mamdani-type FIS in Fuzzy Logic Toolbox of MATLAB are outlined in [11] and [12], respectively. An active vibration control of a simply supported rectangular plate using fuzzy logic rules have also been considered in [16], where the comparison of the results with the classical proportional integral derivative (PID) controller demonstrates the efficiency of the fuzzy controller.…”

Optimal design of smart structures with intelligent control

“…A hybrid control scheme, based on fuzzy techniques, for the suppression of vibrations of a smart von Karman plate is presented in (Muradova & Stavroulakis, 2015). Namely, the suppression of large vibrations of a smart thin elastic rectangular von Kármán plate is studied.…”