Summary In this work, we introduce a simple stability analysis to justify, under some suitable assumptions, the active disturbance rejection control method, used in the feedback regulation of a substantially uncertain plant. A criterion is obtained that allows us to define under what conditions closed‐loop stability can be assured. When the plant is mostly unknown, the criterion allows us to guarantee exponential convergence for the output‐feedback regulation problem, in the presence of a constant external perturbation, and practical stability when the external perturbation and the tracking reference signal are both time‐varying. In the latter case, the confinement error can be made as small as desired. To carry out the corresponding stability analysis, we derive the tracking error equation, and the observation error equation. To decouple these error equations, we use the Sylvester equation. Finally, we applied the direct Lyapunov method to analyze the corresponding convergence of the observation error and of the tracking error. Copyright © 2017 John Wiley & Sons, Ltd.

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.

This study presents a feedback control strategy for the regulation of a planar vertical takeoff and landing aircraft. To this end, two controllers that work simultaneously were designed. The first controller is devoted to stabilizing the vertical variable and is based on a simple feedback-linearization procedure in combination with a saturation function. The second controller -based on a combination of the traditionally PD-controller and a sliding mode controller -stabilizes both the horizontal and angular variables to the desired rest position. The performance of the closed-loop system is demonstrated through simulation results.

We introduce a control strategy to solve the regulation control problem, from the perspective of trajectory planning, for an uncertain 3D overhead crane. The proposed solution was developed based on an adaptive control approach that takes advantage of the passivity properties found in this kind of systems. We use a trajectory planning approach to preserve the accelerations and velocities inside of realistic ranges, to maintaining the payload movements as close as possible to the origin. To this end, we carefully chose a suitable S-curve based on the Bezier spline, which allows us to efficiently handle the load translation problem, considerably reducing the load oscillations. To perform the convergence analysis, we applied the traditional Lyapunov theory, together with Barbalat’s lemma. We assess the effectiveness of our control strategy with convincing numerical simulations.

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