Reduced order observers for the sliding mode control of mechanical systems with elastic joints

In this article the control of mechanical systems with elastic joints is addressed. This kind of system is characterised by a high relative degree. The mechanical control input must be designed to be continuous. Different reduced order observers are introduced and conditions are found to guarantee the exponential convergence of the observation errors. The error stability is ensured provided a certain matrix inequality has a solution. The proposed second-order sliding mode point-to-point controller based on the observed state is proven to stabilise the mechanical system with elastic joints about the desired reference position.