On Convergence Performance of Discrete-Time Optimal Control Based Tracking Differentiator

Time optimal control (TOC) based tracking differentiator (TD) was first proposed by Han as a practical solution to avoid setpoint jump in active disturbance rejection control. In practice, the discrete-time optimal control (DTOC) is implemented in the form of state feedback for a double-integral system, which is widely used to design controllers, observers and noise-tolerant differentiators. The convergence of the DTOC-TD, however, has not been fully understood. This article provides a rigorous full convergence analysis of the DTOC-TD. It then illustrates the frequency-domain characteristics of this DTOC-TD in signal-tracking filtering and differentiation acquisition, giving a rule of thumb for regulating the parameters. Finally, the case studies including comparison simulations and experiments on processing gap sensor' signals in the suspension system of maglev train are carried out to verify the effectiveness of the DTOC-TD.