Modal control of a plate using a fuzzy logic controller

Abstract

This paper presents fuzzy logic based independent modal space control (IMSC) and fuzzylogic based modified independent modal space control (MIMSC) of vibration. The rule baseof the controller consists of nine rules, which have been derived based upon simple humanreasoning. Input to the controller consists of the first two modal displacements andvelocities of the structure and the output of the controller is the modal force to be appliedby the actuator. Fuzzy logic is used in such a way that the actuator is never calledto apply effort which is beyond safe limits and also the operator is saved fromcalculating control gains. The proposed fuzzy controller is experimentally testedfor active vibration control of a cantilevered plate. A piezoelectric patch is usedas a sensor to sense vibrations of the plate and another piezoelectric patch isused as an actuator to control vibrations of the plate. For analytical formulation,a finite element method based upon Hamilton’s principle is used to model theplate. For experimentation, the first two modes of the plate are observed usinga Kalman observer. Real-time experiments are performed to control the firstmode, the second mode and both modes simultaneously. Experiments are alsoperformed to control the first mode by IMSC, the second mode by IMSC andboth modes simultaneously by MIMSC. It is found that for the same decibelreduction in the first mode, the voltage applied by the fuzzy logic based controller isless than that applied by IMSC. While controlling the second mode by IMSC, aconsiderable amount of spillover is observed in the first mode and region justafter the second mode, whereas while controlling the second mode by fuzzy logic,spillover effects are much smaller. While controlling two modes simultaneously,with a single sensor/actuator pair, appreciable resonance control is observed bothwith fuzzy logic based MIMSC as well as with direct MIMSC, but there is aconsiderable amount of spillover in the off-resonance region. This may be due to thesub-optimal location and/or an insufficient number of actuators. So, another smartplate with two piezoelectric actuators and one piezoelectric sensor is considered.Piezoelectric patches are fixed in an area where modal strains are high. Withthis configuration of the smart plate, experiments are conducted to control thefirst three modes of the plate and it is found that spillover effects are greatlyreduced.