Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: Design and experiments

The aim of this article was to determine control strategy for balance control of rotary double inverted pendulum system, which is highly nonlinear and unstable under-actuated system. The complexities involved in rotary double inverted pendulum dynamics make this system a useful engineering test bed to test and verify newly designed controllers. In this article, a constraint-based control approach titled robust generalized dynamic inversion is designed and implemented for robust stabilization of rotary double inverted pendulum system. The robust generalized dynamic inversion control is designed in two stages; in the first stage, constraint differential equations of the controlled state variables are prescribed, which encompasses the control objectives. To enforce the constraint dynamics, the equivalent control is realized by means of Moore–Penrose generalized inversion. To enhance robustness, the switching (discontinuous) control is introduced in second stage, whose design principle is based on classical sliding mode control theory. Finally, the controllers obtained in two stages are augmented to form the resultant robust generalized dynamic inversion control law. The proposed controller ensures robustness along with improved time domain performance regardless of system nonlinearities, uncertainties, and unwanted disturbances. The stability analysis is presented for guaranteeing semi-global asymptotically stable closed loop performance via Lyapunov stability criteria. Numerical simulation and experimental investigations are carried out along with comparative analysis, to demonstrate the effectiveness of robust generalized dynamic inversion control algorithm over other conventional control methods.