Adaptive nonlinear boundary control of a flexible link robot arm

In this paper, we consider the problem of designing a boundary controller for a flexible link robot arm with a payload mass at the link's free-end. Specifically, we utilize a nonlinear, hybrid dynamic system model (the model is hybrid in the sense that it is comprised of a distributed parameter, dynamic field equation coupled to discrete, dynamic boundary equations) to design a model-based control law which asymptotically stabilizes the link displacement while driving the actuator hub's position to a desired setpoint. We then illustrate how the control law can be redesigned as an adaptive controller which achieves the same control objective while compensating for parametric uncertainty including unknown payload mass. The control strategy is composed of a boundary control torque applied to the actuator hub and a boundary control force at the link's free-end. Experimental results are presented to illustrate the performance of the proposed control laws.