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.

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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.

This work proposes a robust controller to solve the trajectory-tracking control problem of planar vertical take-off and landing (PVTOL) aircraft under crosswind. The controller combines input-output feedback linearization and active disturbance rejection control techniques. The former linearizes the PVTOL dynamics and the latter actively estimates and compensates for the crosswind effects. Numerical simulations assess the effectiveness of the proposed approach.

SUMMARYWe present a simple control scheme for changing the position of a microscopic particle immersed in a viscous medium and trapped by optical tweezers. We derive a simple feedback controller under the consideration that the particle mass is so small that it can be discarded from the motion equations. This approximation is well justified in practice, since the inertial force produced by the motion of a micronscaled trapped particle is completely dominated by the medium viscous drag force. Finally, we formally prove that the obtained controller is able to globally asymptotically stabilize the system when the particle mass is considered, if some suitable values of some control parameter are used. The stability analysis of the controlled system was carried out by using the standard Lyapunov stability theory. Also, by means of numerical simulations, we show that the obtained closed-loop system is robust when random thermal noise is presented.