ACCURATE MODELLING OF A FLEXIBLE-LINK PLANAR MECHANISM BY MEANS OF A LINEARIZED MODEL IN THE STATE-SPACE FORM FOR DESIGN OF A VIBRATION CONTROLLER

Vibration control of flexible link mechanisms with more than two flexible links is still an open question, mainly because defining a model that is adequate for the designing of a controller is a rather difficult task. In this work, an accurate dynamic non-linear model of a flexible-link planar mechanism is presented. In order to bring the system into a form that is suitable for the design of a vibration controller, the model is then linearized about an operating point, so as to achieve a linear model of the system in the standard state–space form of system theory. The linear model obtained, which is valid for whatever planar mechanism with any number of flexible link, is then applied to a four-bar planar linkage. Extensive simulation is carried out, aimed at comparing the system dynamic evolution, both in the open- and in the closed-loop case, using the non-linear model and the linearized one. The results prove that the error made by using the linearized system instead of the non-linear one is small. Therefore, it can be concluded that the model proposed in this work can constitute an effective basis for designing and testing many types of vibration controllers for flexible planar mechanisms.