Adaptive discrete-time inverse model control using generalized holds

In this paper, an adaptive digital implementation of an inverse model based control scheme for a system with parametric uncertainty is proposed using generalized sampling and hold functions. The implementation of the control law using this kind of holds allows overcoming the difficulties related to the presence of unstable zeros in the continuous-time model and the usual appearance of unstable discretization zeros in the discrete model when a ZOH is applied. The generalized sampling and hold functions allows obtaining a discrete model of the plant with all its zeros stable which allows performing an exact inverse model of the plant in comparison to the use of a classical ZOH which only allows, in general, an approximate inversion of the plant. The stability and asymptotic properties of the general adaptive scheme are established. Also, simulation examples showing the scope and application of the method are presented.