ACTIVE VIBRATION CONTROL OF A PIEZOELECTRIC BEAM USING PID CONTROLLER: EXPERIMENTAL STUDY

Abstract

      VIBRATION SUPPRESSION OF SMART BEAMS USING THE PIEZOELECTRIC PATCH STRUCTURE IS PRESENTED IN THE PRESENT WORK. THE SMART SYSTEM CONSISTS OF A BEAM AS THE HOST STRUCTURE AND PIEZOCERAMIC PATCHES AS THE ACTUATION AND SENSING ELEMENTS. AN EXPERIMENTAL SET-UP HAS BEEN DEVELOPED TO OBTAIN THE ACTIVE VIBRATION SUPPRESSION OF SMART BEAM. THE SET-UP CONSISTS OF A SMART CANTILEVER BEAM, THE DATA ACQUISITION SYSTEM AND A LABVIEW BASED CONTROLLER. EXPERIMENTS ARE PERFORMED FOR DIFFERENT BEAM SPECIMEN. THE COUPLED EFFICIENT LAYERWISE (ZIGZAG) THEORY IS USED FOR THEORETICAL FINITE ELEMENT MODELING. THE FINITE ELEMENT MODEL IS FREE OF SHEAR LOCKING. THE BEAM ELEMENT HAS TWO NODES WITH FOUR MECHANICAL AND A VARIABLE NUMBER OF ELECTRIC DEGREES OF FREEDOM AT EACH NODE. IN THE THICKNESS DIRECTION, THE ELECTRIC FIELD IS APPROXIMATED AS PIECEWISE LINEAR ACROSS AN ARBITRARY NUMBER OF SUB-LAYERS IN THE PIEZOELECTRIC LAYERS. CUBIC HERMITE INTERPOLATION IS USED FOR THE DEFLECTION, AND LINEAR INTERPOLATION IS USED FOR THE AXIAL DISPLACEMENT AND THE SHEAR ROTATION. UNDAMPED NATURAL FREQUENCIES ARE OBTAINED BY SOLVING THE EIGEN VALUE PROBLEM USING SUBSPACE ITERATION METHOD FOR CANTILEVER BEAM. A STATE SPACE MODEL CHARACTERIZING THE DYNAMICS OF THE PHYSICAL SYSTEM IS DEVELOPED FROM EXPERIMENTAL RESULTS USING PID APPROACH FOR THE PURPOSE OF CONTROL LAW DESIGN. THE EXPERIMENTAL RESULTS OBTAINED BY USING THE ACTIVE VIBRATION CONTROL SYSTEM HAVE DEMONSTRATED THE VALIDITY AND EFFICIENCY OF PID CONTROLLER. EXPERIMENTS ARE CONDUCTED TO COMPARE THE CONTROLLING OF VARIOUS CANTILEVER BEAMS OF DIFFERENT SIZES. IT SHOWS THAT THE PRESENT ACTUATOR AND SENSOR BASED CONTROL METHOD IS EFFECTIVE AND THE LABVIEW CONTROL PLOTS FOR VARIOUS BEAMS CAN BE USED AS A BENCHMARK FOR ANALYTICAL WORK. THE RESULTS ARE COMPARED WITH ABAQUS SOFTWARE AND 1D FINITE ELEMENT FORMULATION BASED ON ZIGZAG THEORY.