Unknown input functional observers for vector second order structural systems

Abstract

This paper considers a class of linear time invariant systems that describe the dynamics of mechanical systems. Due to their algebraic structure, the dynamics of such systems are written in their natural second order framework in order to exploit this structure with the obvious computational benefits in controller and observer design. A functional observer along with an unknown input observer are combined and are presented for this class of systems. The additional advantage of this combined observer is that when certain conditions are imposed, it reduces to the standard natural second observer. This translates to guaranteeing that the derivative of the estimated position vector coincides with the estimate of the velocity vector, a case not always ensured when such system is brought in a first order realization. An added benefit resulting from the second order formulation is the minimum order compensator whose order is dictated by the rank of the control input matrix, when the proposed functional estimate is used in place of a full state control signal.