Output feedback control of TORA — A benchmark underactuated nonlinear system

In this paper the problem of output feedback stabilization of Translational Oscillator with Rotational Actuator (TORA) — a benchmark underactuated nonlinear system is discussed. Proposed method utilizes an Extended High Gain Observer (EHGO) based Sliding Mode Control technique for output stabilization of the entire system. Starting with Lagrangian model of the nonlinear dynamical system and using a suitable coordinate transformation, a normal form representation of the system is derived. The normal form decouples complex nonlinear dynamics into an internal and external system. The dynamics of internal system is utilized to derive an auxiliary system and the full order EHGO thus obtained is used for estimation of system states as well as for derivative(s) of the system output. The actual and estimated system states are then utilized to design a state feedback and an output feedback controller respectively. It is shown that the proposed output feedback controller stabilizes the system and that the estimated states with suitable choice of observer parameters, converge to that of actual states arbitrarily fast. The efficacy of the proposed control scheme is demonstrated and validity of the analytical results is shown by simulation.