Disturbance attenuation using proportional integral observers

In this paper, we first propose a proportional integral observer design for single-output uncertain linear systems which permit us to attenuate either measurement noise or modelling errors. We show that, when only sensor noise is present in the system, an integral observer alone suffices to achieve good convergence and filtering properties. On the other hand, when modelling errors and sensor noise are present, we show that, for some classes of linear systems, the proportional integral observer allows us to decouple completely the modelling uncertainties while keeping satisfactory convergence properties. A comparison of the classical proportional observer to the proposed observers are given via academic simulation examples. We next extend the design to the class of single-output uniformly observable non-linear systems. We show through a practical simulation example, dealing with a flexible joint robot, that the non-linear proportional integral has very satisfactory disturbance attenuating properties.