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A new filtering method for discrete-time delay control

This paper presents a new filtering method for the discrete-time delay control (DTDC) method. The DTDC estimates unknown dynamics of a system using a time delay estimator (TDE). The TDE is based on the past expected unknown dynamics which is delayed by one sampling period. Therefore, the DTDC cannot properly compensate for the high frequency components of unknown dynamics. Moreover, the transfer gain of the TDE from unknown dynamics to the TDE error is more than 0 dB in the high frequency ranges. This means that the high frequency components of unknown dynamics can be amplified in the TDE error. A conventional solution of the high frequency unknown dynamics is applying a recursive structure to the DTDC law. The effect of the recursive structure is the same as that of a low-pass-filter, which attenuates the high frequency components of the DTDC law. However, the recursive structure may make the system response slow. This paper presents a new filtering method which attenuates the high frequency components of the estimated unknown dynamics only. The update law of the TDE is separated from the DTDC law and a recursive scheme is applied to this update law. Simulation results show that the proposed method can attenuate the high frequency components of the estimated unknown dynamics without slowing the system response down.