Filter‐Based Adaptive Control for a Flexible String Under an Unknown Exosystem

ABSTRACT This article proposes that the measurable outputs encompass not only the tracking error but also its perturbed time derivative, which is influenced by an unknown output disturbance. For the flexible string, an exosystem with an unknown matrix generates both the disturbances and the reference. In case where the perturbed derivative is collocated with the control input, we require only a single set of filters for designing adaptive control. Conversely, when the derivative is non‐collocated with the input control, two sets of filters are designed to account for both the unknown reference and the output disturbance. This approach eliminates the need for designing an observer for the exosystem. We then demonstrate that the tracking error converges to zero in an exponential manner, illustrated by two simulation examples.