Reduced-order observer for mechanical systems with elastic joints

The paper considers an example of mechanical system with high relative degree: a fully actuated robot with elastic joints and the related control problem. The considered system is characterized by a uniform relative degree five, assuming as available output only the joints´ angles. Two different strategies can be exploited to address this control problem. A first possibility is to use a full order observer and to exploit the observer´s state instead of the actual system´s state to design the feedback control law. A second methodology consists in introducing differentiators to reduce the system´s relative degree. In the paper the presented strategy is a compromise between the two approaches. The adopted criterion to stop the differentiation procedure is given by the existence of a global solution of a reduced order matrix inequality and by designer´s capability to compute such a solution.