An Equivalent Linearized Discrete-Time Realization of Optimal Control Based Tracking Differentiator

The discrete-time optimal control (DTOC) based tracking differentiator (TD) is first proposed by Han (named fHan-TD). As for a nonlinear differentiator, it is difficult to evaluate the stability of the system containing fHan-TD. The application of the fHan-TD is also constrained by complex computation. Hence, in this article, a linearized TD is proposed for the fHan-TD based on the frequency-domain characteristics of fHan-TD and the Sanathanan–Koerner iterative method. The linearized fHan-TD, abbreviated as linear-TD, shows the same frequency-domain characteristics as fHan-TD. The theoretical proof of the linear-TD is derived from the DTOC principle. Meanwhile, a sufficient but not necessary condition for the linearization is given. Both the analysis of frequency-domain characteristics and the principle of DTOC show that the conventional fHan-TD can be replaced by the proposed linear-TD with a simple structure and no loss in convergence time. A DSP28379D based testbed is used to verify the characteristics of linear-TD, thus validating the equivalence of fHan-TD and linear-TD. Moreover, experiment results demonstrate that the computational resources required for linear-TD are only 24.4% of fHan-TD. Finally, the effectiveness of the proposed method is verified through experiments on grid-forming inverter.