Modal control of a plate using a fuzzy logic controller

This paper presents fuzzy logic based independent modal space control (IMSC) and fuzzy logic based modified independent modal space control (MIMSC) of vibration. The rule base of the controller consists of nine rules, which have been derived based upon simple human reasoning. Input to the controller consists of the first two modal displacements and velocities of the structure and the output of the controller is the modal force to be applied by the actuator. Fuzzy logic is used in such a way that the actuator is never called to apply effort which is beyond safe limits and also the operator is saved from calculating control gains. The proposed fuzzy controller is experimentally tested for active vibration control of a cantilevered plate. A piezoelectric patch is used as a sensor to sense vibrations of the plate and another piezoelectric patch is used 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 the plate. For experimentation, the first two modes of the plate are observed using a Kalman observer. Real-time experiments are performed to control the first mode, the second mode and both modes simultaneously. Experiments are also performed to control the first mode by IMSC, the second mode by IMSC and both modes simultaneously by MIMSC. It is found that for the same decibel reduction in the first mode, the voltage applied by the fuzzy logic based controller is less than that applied by IMSC. While controlling the second mode by IMSC, a considerable amount of spillover is observed in the first mode and region just after 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 both with fuzzy logic based MIMSC as well as with direct MIMSC, but there is a considerable amount of spillover in the off-resonance region. This may be due to the sub-optimal location and/or an insufficient number of actuators. So, another smart plate with two piezoelectric actuators and one piezoelectric sensor is considered. Piezoelectric patches are fixed in an area where modal strains are high. With this configuration of the smart plate, experiments are conducted to control the first three modes of the plate and it is found that spillover effects are greatly reduced.