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Summary A nonlinear control algorithm for tracking dynamic trajectories using an aerial vehicle is developed in this work. The control structure is designed using a sliding mode methodology, which contains integral sliding properties. The stability analysis of the closed‐loop system is proved using the Lyapunov formalism, ensuring convergence in a desired finite time and robustness toward unknown and external perturbations from the first time instant, even for high frequency disturbances. In addition, a dynamic trajectory is constructed with the translational dynamics of an aerial robot for autonomous take‐off, surveillance missions, and landing. This trajectory respects the constraints imposed by the vehicle characteristics, allowing free initial trajectory conditions. Simulation results demonstrate the good performance of the controller in closed‐loop system when a quadrotor follows the designed trajectory. In addition, flight tests are developed to validate the trajectory and the controller behavior in real time.

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In this work, a novel nonlinear control theory design for first-order systems is developed, contributing to the improvement of the existing theory. The theory will allow a design of the open loop and closed-loop controllers that ensure the tracking of any reference, constant, or variant in time with a free initial condition where the Laplace transform was used to find all the analytical solutions, avoiding the transfer function theory. Moreover, the closed-loop control will be the best option to speed up or slow down the reference convergence rate in the desired finite time. Then, an algorithm indicating the steps for designing a closed-loop controller and achieving proper tuning for a real-time application is shown. Finally, this manuscript presents the results and discussions of the theory implemented in a prototype tank of a liquid temperature control system, where the effectiveness of the applied temperature control can be seen.

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