Closed-loop analysis with incremental backstepping controller considering measurement bias

In this paper, closed loop system characteristics with an incremental backstepping controller are investigated through theoretical analysis when both measurement biases and model uncertainties exist. Incremental backstepping algorithm is proposed in previous studies to reduce model dependency of classical backstepping algorithm with additional measurements about state derivatives and control surface deflection angles. This research enables to have following critical understandings especially about the effects of biases on these additional measurements to system characteristics with incremental backstepping method. First, these biases do not affect a characteristic equation, so they do not have any influence about a condition for absolute stability. Second, these biases cause a steady state error, and model uncertainty in control effectiveness information starts to have an impact to it when these biases are additionally considered.