Robust ripple-free tracking and regulation under uncertainties of physical parameters for ramp-exponential signals

In asymptotic tracking of a continuous-time plant using digital control, the undesirable ripple which may arise between sampling instants may become unacceptable, and should be avoided; this is achieved if a continuous-time internal model of reference signals is included in the forward path of the feedback control system. In this paper, a method for obtaining such a continuous-time internal model for sinusoidal-exponential reference signals and disturbance functions containing a linear function of time as a factor, is derived for the case when the only uncertainties about the description of the plant concern the values of some "physical" parameters. Such a method allows the control requirements to be robustly satisfied, at least in a neighbourhood of the nominal "physical" parameters of the plant to be controlled and, in particular, a continuous-time null steady-state error response to be guaranteed for all the values of the physical parameters in such a neighbourhood of the nominal ones-together with a ripple-free dead-beat error convergence at the nominal parameters. This can be obtained under conditions which are weaker than the Davison one, and are expressed in terms of the description of the original continuous-time plant