Performance analysis of input shaped model reference adaptive control for a single-link flexible manipulator

Motion control for flexible link manipulators will have a great influence on their overall performance. Conventional control systems have the problem that they cannot compensate for the presence of uncertainty due to a variety of factors such as a change in the system itself-payload variations, degradation and modelling uncertainty. In addition, the underdamped structure of these systems entails motion-induced transient deflection and residual vibration. On the contrary, adaptive control, in particular Model Reference Adaptive Control (MRAC), has therefore been proposed to handle problems of this type dealing with other systems such as cranes, steering stability control for ground vehicles, airplanes and so on. This study presents a review and discussion on the MRAC and some individual issues of MRAC for these flexible link manipulators are addressed to specify: the state tracking error, the limitation of the adaptation values corresponding to the control gains and the control effort. Dealing with the last one, this work proves that shaping the command input to a Model Reference Adaptive Control (IS-MRAC) reduces the control effort necessary for the plant to follow the reference model and also mitigates the detrimental effects of flexibility. The IS-MRAC is implemented in a Single-Link Flexible Manipulator whose natural frequencies, experimentally and analytically estimated using the Transfer Matrix Method plus symbolic computation, vary significantly depending on payload mass and position. To this structured or parametric uncertainty, the proposed Lyapunov control law using the states associated with the low mode is designed for asymptotic stability and accommodates correctly. The state tracking, vibration suppression and control effort reduction performances of the proposed IS-MRAC combined controller are analysed via numerical simulations and experiments.