Understandings of classical and incremental backstepping controllers with model uncertainties

This paper suggests closed-loop analysis results for both classical and incremental backstepping controllers considering model uncertainties. First, transfer functions with each control algorithm under the model uncertainties, are compared with the ones for the nominal case. The effects of the model uncertainties on the closed-loop systems are critically assessed via investigations on stability conditions and performance metrics. Second, closed-loop characteristics with classical and incremental backstepping controllers under the model uncertainties are directly compared using derived common metrics from their transfer functions. This comparative study clarifies how the effects of the model uncertainties to the closed-loop system become different depending on the applied control algorithm. It also enables understandings about the effects of additional measurements in the incremental algorithm. Third, case studies are conducted assuming that the uncertainty exists only in one aerodynamic derivative estimate while the other estimates have true values. This facilitates systematic interpretations on the impacts of the uncertainty on the specific aerodynamic derivative estimate to the closed-loop system.