MODELLING AND CONTROL OF A TWO-AXIS ROBOT WITH FLEXIBLE LINKS

For robots with flexible links different decoupling and linearizing controls have been presented using models obtained by different spatial discretization methods: Finite Element, Static Mode Method. Here each flexible beam is modelized using the Assumed Mode Method with force-free boundary conditions, then the beams are assembled by the Modal Synthesis Method in order to obtain the model of a two-axis robot with two flexible links. In a first time the continuous-time control is commented. Indeed the considered model exhibits an interesting property: the decoupling matrix is constant which implies the existence of the control law on the whole domain of validity of the model. Moreover the closed-loop system is commented with respect to its minimum phase properties. In a second time two approximate discrete controls are compared. First a discrete control law is deduced by sampling and holding the continuous control; simulation results illustrate how this control may lead the robot to instability. Then, following a recent approach successfully applied to a spacecraft with flexible appendices a refined discret control strategy is proposed to the robot model.