A fast system estimation algorithm for a discontinuous dynamical model with coefficients coupling

Abstract

For a discontinuous dynamical system with multi-degree-of-freedom, the coefficients of the established model may be coupled and the response can be also non-smooth, which bring difficulties to estimating the system under fast convergence requirement. In this paper, a nonlinear observer based on super-twisting sliding mode method is designed to evaluate the difference between the prediction of the model and the actual system dynamics. The pseudoinverse and Newton-Raphson iteration are firstly integrated to achieve the fast and reliable estimation of the coefficients of the model including the coupled ones. The event-triggered mechanism is specifically designed to detect the singularity of the dynamics for such a discontinuous system, such that the measured response which is used for the proposed algorithm can be divided into different segments. The experimental validation is conducted, which shows that the proposed method can gain more accurate estimations than pseudoinvese-based comparison method. The switching time between free motion and collision, as well as the collision force can also be predicted accurately based on the model with the estimated coefficients.