LAUSR

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.