Fuzzy logic based modal space control of a cantilevered beam instrumented withpiezoelectric patches

Abstract

In this paper, a control law for controlling the vibrations of a cantilevered beam isestablished using fuzzy logic based independent modal space control and fuzzy logic basedmodified independent modal space control. The effect of this modification is that anactuator is never called upon to apply effort which is beyond safe limits and the operatordoes not have to calculate control gains. The inputs to the fuzzy logic based control arethe modal displacements and modal velocities of the modes to be controlled. Afuzzy rule base consisting of nine simple rules based on modal displacements andvelocities is used. The controller is implemented experimentally on a test beamand the first two modes are satisfactorily controlled. The experimental set-upconsists of a cantilevered beam on which a piezoelectric sensor–actuator pair isfixed near the root, in a collocated fashion. For experimental implementation,the size of the problem is reduced using a modal reduction technique. Modaldisplacements as well as the velocities of the first two modes are observed using a realtime Kalman observer. Real time implementation of fuzzy logic based control hasalways been a challenge because a given set of rules has to be executed in everysampling interval. Results in this paper establish the feasibility of experimentalimplementation of the fuzzy logic based controller presented for active vibration control.