Modal properties and control system design for two-link flexible manipulators

The vibration modes of a generic two-link flexible manipulator are studied as a function of the link rotor and tip (stator/payload) mass distribution. Necessary and sufficient conditions are developed for all vibration modes to exhibit a node at the manipulator endpoint. A rigorous treatment of the relevant kinematics and dynamics shows that this property can be closely achieved for large tip/link mass ratio and sufficiently small rotor inertia. The major impacts of this result on feedforward/feedback controller design are uncovered. First, the nonlinear joint torque to end-effector motion dynamics become essentially equivalent to those of the rigid case. Second, an output involving the endpoint rates and elastic motions is shown to possess the passivity property for suitably defined inputs. This permits the design of simple controllers that furnish endpoint stabilization with simultaneous vibration suppression. A numerical example is used to illustrate the results and demonstrate the achievable performance using the controller design concepts.