To tackle the difficulty in tuning the parameters of sliding mode differentiator (SMD), an improved adaptive notch filter based real-time parameter tuning scheme (denoted as ANF-SMD) is presented. Specifically, the integral feedback of the system output errors is introduced in constructing the cost function for the adaptive notch filter so as to estimate the real-time amplitude and frequency of given inputs. Then, upon the deterministic formula between the parameters of the SMD and the input signals, the parameters of the SMD can be adjusted adaptively as inputs vary. Simulation results show that the proposed ANF-SMD scheme performs well in signal filtering and differentiation estimation. The effectiveness of the proposed ANF-SMD is further experimentally verified on the pressure signal processing for the altitude ground test facility.
In this work, an alternative solution to the tracking problem for a SISO nonlinear dynamical system exhibiting points of singularity is given. An inversion-based controller is synthesized using the Fliess generalized observability canonical form associated to the system. This form depends on the input and its derivatives. For this purpose, a robust exact differentiator is used for estimating the control derivatives signals with the aim of defining a control law depending on such control derivative estimates and on the system state variables. This control law is such that, when applied to the system, bounded tracking error near the singularities is guaranteed.