Frameworks for double hyperbolic function‐based robust sliding mode differentiator and observer for nonlinear dynamics

Abstract

This paper puts forward contemporary designs of sliding mode differentiator and state observer for evaluation of unknown nonlinear signal derivatives and unknown internal system states, respectively, by the virtue of tangential and inverse sinusoidal hyperbolic functions. The utility of the proposed frameworks is that it bestows smooth and robust estimation without inciting unacceptable oscillations (chattering), unlike high gain discontinuous function-based preliminary observers/differentiators. Moreover, the employed double hyperbolic functions would drive the various deviations in estimations of signals or states to a very close neighborhood of origin in finite time which is substantiated via Lyapunov's energy function. To demonstrate the efficiency of the introduced techniques, two examples for estimating the derivatives of a nonlinear signal and internal states of motor are also illustrated with time varying uncertainties. At last, the attained simulation outcomes of the proposed differentiator are further compared with formerly formulated designs such as higher-order sliding mode differentiator (HOSMD) and uniformly convergent differentiator (UCD).

Analysis and implementation of second order differentiators in embedded systems

“…Observing equation (23) and the integration algorithm observed in equation (13), it follows that the position x1 , velocity x2 and acceleration ẋ2 estimations can be constructed by the recursive expression Aditionally, just as stated in equation ( 21), a low pass filter can be used to improve the acceleration estimation as…”