Adaptive pre-compensator for rejecting output disturbances in non minimum phase SISO systems

We have presented an adaptive pre-compensator for rejecting output disturbance in nonminimum phase SISO systems assuming only knowledge of the polynomial´s degree of the disturbance generator. This adaptive pre-compensator is a generalized approximation of the nonproper adaptive pre-compensator developed in Bonilla et al (1994). The proposed controller is inspired on an ideal nonproper controller. However the control law is a proper approximation of the ideal controller, i.e, can be implemented using only integrators. The basic structure of such an approximation is studied. The user can choose the degree of approximation with a single parameter E. The choice of E can be done to establish a trade-off between deterministic disturbance rejection and robustness of the control scheme with respect to other noises. The parameter p gives the rate of convergence to the ideal solution. We have selected a gradient adaptation algorithm because of: (i) it is the simplest one with the minimum desired convergence properties, and (ii) it is well adapted to our control law since high gains tend to derivative actions