A backstepping-based procedure with saturation functions to control the PVTOL system

Abstract

In this study, we present a control strategy to solve the regulation problem for a simplified version of a PVTOL system strongly coupled. The strategy is split into two control actions that act simultaneously: one stabilizes asymptotically the vertical position; the other stabilizes both the horizontal and the angle positions. The first controller uses a simple feedback linearization procedure in conjunction with a saturation function. This controller assigns a quasilinear behavior to the vertical displacement. The second controller is based on a suitable backstepping procedure, and its task is to force the remaining variables converge asymptotically to the origin. In short, the resulting control is a nonlinear state feedback, whose performance is demonstrated by numerical simulations. The convergence analysis, based on the Lyapunov method, turned out to be quite simple if compared to other control methods found in the literature.

Robust Stabilization of Nonlinear PVTOL Aircraft with Parameter Uncertainties

“…The above simulation examples show that the control scheme proposed in can only work for the PVTOL aircraft with known model parameters. However, our control scheme always works well for the PVTOL aircraft no matter whether the parameters are known or not.…”

“…, showing that the position error y − y d is not convergent to zero but divergent with time under small mass uncertainty. Combination of the two examples indicates that the control scheme provided in is not robust against the model parameters.…”

“…Closed‐loop response of a PVTOL aircraft with mass parameter uncertainty under the control strategy in . [Color figure can be viewed at wileyonlinelibrary.com]…”

“…Considering unmeasurable velocities and bounded external disturbances, Cardenas [6] designed an output feedback control scheme by sliding-mode technique, which guaranteed local finite time stability of the closed-loop PVTOL aircraft system. Secondly, some researchers were aware that the coupling coefficient should be taken into account (hence viewed as nonzero) for gaining a better control performance [8][9][10][11][12][13][14][15][16][17][18][19]. In [9], the receding horizon control method was used to design a globally asymptotical stabilization controller with a low computational cost.…”

“…The input transformation in [13], by contrast with those in [11,12], was valid for both the nonzero and the zero coupling coefficients. Then, many schemes, dependent on the converted aircraft model proposed by Olfati-Saber, were developed, see [14][15][16][17][18][19] for details. Wood modified the control law in [13], and gave a new controller [14] by minimizing the interconnection term between closed-loop subsystems.…”