Model free adaptive control under Sigmoid Function and newton method for estimation of the pseudo-partial-derivative in nonlinear systems

The Model Free Learning Adaptive Control (MFLAC) is based on the pseudo-partial-derivative (PPD) calculated from the input and output signals of the system to be controlled and also using a fixed penalty factor that weights the control energy to provide a good behavior to the feedback process. This paper presents two new adaptation algorithms to adjust the PPD, based on the Sigmoid Function (SF) and another on the Newton Method (NM). With these proposals, alternative control designs are obtained for the on-line tuning of the PPD, ensuring good stability and robustness for the closed-loop system. Simulations on a nonlinear coupled liquid-tank plant and a laboratory apparatus on a damped pendulum show the efficiency and superiority of the proposed adaptive controllers when using estimation mechanisms to adjust these parameter over the standard MFLAC. Performance indices are used to show the improvement of the behavior of the proposal control algorithms.