A practical parameter tuning algorithm for super-twisting algorithm-based differentiator and its application in altitude ground test facility

The super-twisting algorithm (STA)-based robust exact differentiator (RED) proposed by Levant has been widely applied in control, observation, and fault detection. With properly set parameters, STA-RED is able to estimate exactly and robustly the derivatives of an input. With a given input signal, however, a practical parameter tuning rule still lacks. To this end, a general parameter tuning algorithm with the full stability proof for STA-RED is proposed. In particular, the time linear transformation and the coordinate transformation are performed on a given base signal, allowing the deterministic relationship between the parameters of STA-RED and the amplitude and the frequency of the input to be obtained. The full stability of the STA-RED based on the proposed parameter tunning algorithm (denoted as PSTA-RED) with perturbations is given using the Lyapunov function method. The simulations are carried out using given input signals and the pressure signals from the altitude ground test facility to illustrate the effectiveness of the proposed PSTA-RED.