Adaptive estimation of velocity and acceleration with high gain input observer

The design of an ideal differentiator is a difficult and a challenging task. In this paper, we propose two types of differentiators to estimate the time-derivative of an output signal. To begin with, a velocity estimator is proposed based on the adaptive identification method and compared with the exact differentiator proposed by Levant. Then, an acceleration estimator is proposed with the non-passifiable adaptive schemes. Finally, the proposed differentiators are applied to the estimation of the speed and acceleration of the mass-spring system. The simulation results show that the proposed differentiators are robust to additive noises.