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We have already proposed high order tuner (HOT) which uses a smooth projection algorithm to ensure the positive definiteness of an estimated inertia matrix for realizing a stability and a good transient response of adaptive tracking control system based on  for a rigid link robot arm. Also, we proposed a HOT capable to constrain adjustable parameters into hyper-parallelogram region [8, 9]. In this paper, an adaptive control scheme for a 2 DOF flexible link robot arm is proposed. The controller is composed of an adaptation law using smooth projection algorithm [8, 9] and a control law based on dynamic certainty equivalent principle [7, 14]. The effectiveness of the proposed scheme is illustrated by a theoretical analysis and simple numerical simulation results.