An improved tracking differentiator based on discrete-time optimal control and its application for electromagnet suspension control in active vibration isolation system

The differentiator is one way to extract the derivative of the signal. However, it is challenging to achieve both accuracy and robustness in the differentiator design when the input signal is subject to noise. In this article, an improved tracking differentiator (TD) based on discrete-time optimal control (DTOC) is proposed to address this issue. Firstly, for the discrete double-integral system, a novel control law of DTOC (denoted as Fntd algorithm) is designed, which is based on an introduced line with a slope of \(-h\) $-h$ (the sampling period). Subsequently, the new TD is constructed based on this control law. Frequency domain analysis of TD indicates that its tracking characteristic approximates a low-pass filter, and its differentiation characteristic behaves like a band-pass filter. Finally, the simulation results demonstrate its good performance in signal tracking and differentiation acquisition. The experimental results on obtaining the velocity signal of the position signal in the electromagnet suspension control for active vibration isolation system validate the effectiveness of the proposed TD in filtering out noise and acquiring derivative signals.