Implementation and comparison of different alternatives to remove steady state errors in a time-domain ℓ1 controller

The ℓ₁ controller is an interesting one, since it minimizes the deviation of the controlled variables (system outputs z), in presence of unknown but bounded disturbances (system inputs w). Being defined in the time domain, this controller also allows taking into account constraints such as maximum deviations of controlled variables (z) and control action variables (u). When applied to a river or an irrigation canal this can correspond, for example, to water levels, discharges or gate openings. But, by default, like many others, this controller does not include integral effects. Several options allow forcing this effect. The paper deals with this issue and shows how a time-domain template can solve this problem, in a better way compared to other more classical options.