Direct tip regulation of a single-link flexible manipulator by adaptive variable structure control

Direct tip position regulation of flexible manipulators is one of the most challenging control tasks. There are mainly three problems to be addressed in order to achieve good performance. The first two control problems arise owing to the unstable zeros and complex poles in the system nominal part wh ich is dominated by a transfer function. The third problem is the existence of unstructured uncertainties owing to the truncation of high-order resona nce modes and system nonlinearities. Because of the above difficulties and in particular the non-minimum-phase nature, tip regulation task of flexible manipulators is usually solved indirectly: direct control of joint angle a nd suppression of the flexible link vibration. The aim of this study is to investigate the direct approach for tip regulation. Since the tip transfer function contains unstable zeros and the first few dominant flexible modes (complex poles), a reference model of the same order is selected which does not have any finite zero but all negative real poles. In order to force th e system to follow the reference model in the presence of the unstructured uncertainties, a variable structure controller is adopted in which the swit ching surface is derived from the reference model. When in sliding mode, th e system performs as the reference model. Hence there will be no vibration and the tip position regulation can be achieved when the system approaches steady state. To improve the system responses further, an adaptation law wi th dead-zone scheme is combined with the variable structure controller. Sim ulation results show that link vibrations have been eliminated and the cont rol profile is fairly smooth.