Position Control of Flexible Joint Carts Using Adaptive Generalized Dynamics Inversion

This paper presents the design and implementation of Adaptive Generalized Dynamic Inversion (AGDI) to track the position of a Linear Flexible Joint Cart (LFJC) system along with vibration suppression of the flexible joint. The proposed AGDI control law will be comprised of two control elements. The baseline (continuous) control law is based on principle of conventional GDI approach and is established by prescribing the constraint dynamics of controlled state variables that reflect the control objectives. The control law is realized by inverting the prescribed dynamics using dynamically scaled Moore-Penrose generalized inversion. To boost the robust attributes against system nonlinearities, parametric uncertainties and external perturbations, a discontinuous control law will be augmented which is based on the concept of sliding mode principle. In discontinuous control law, the sliding mode gain is made adaptive in order to achieve improved tracking performance and chattering reduction. The closed-loop stability of resultant control law is established by introducing a positive define Lyapunov candidate function such that semi-global asymptotic attitude tracking of LFJC system is guaranteed. Rigorous computer simulations followed by experimental investigation will be performed on Quanser's LFJC system to authenticate the feasibility of proposed control approach for its application to real world problems.