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.
In this paper is presented a new technique to design trajectories with finite time convergence properties for precision tracking maneuvers in unmanned vehicles. This technique allows the finite time positioning on sequentially distributed points, the properties for the trajectory guarantee to start in an initial point with velocity and acceleration zero, and position itself on the subsequent point with finite time convergence, again with velocity and acceleration zero. Such trajectory depends exclusively of the time and of the initial and last position. In addition, this technique could be used to design open loop controllers to be implemented in mobile robotics applications that require long accuracy. To show the controllers feasibility we considering the kinematic car model with finite time properties, obtaining an open loop control for the car’s velocity and steering the vehicle to desired trajectory, where simulation results present the control performance and effectiveness.
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