Analysis of a Time Delay Controller Based on Convolutions

Time Delay Control has been proposed as an effective control method for a class of systems with unknown dynamics and unpredictable disturbances. The control algorithm uses recent past data to estimate the uncertain dynamics and disturbances in the system. This paper presents a convolution method to attenuate the noise amplification in the calculation of the estimated functions. The method suggests a delay time to be much larger than the sampling period. Through the accuracy analysis, an extrapolation scheme is found to be useful to improve the performance while keeping the delay time at an appropriate level. Stability analysis shows that a trade-off exists between robustness and performance. For a special class of systems with slow changing dynamics during the delay time, the convolution method with an extrapolation scheme is shown to provide a very satisfactory performance.