Interpolation schemes in the control of systems with unknown dynamics

Time-delay control for systems with unknown dynamics involves estimations. In its present form, these estimations include not only the interpolation of a time-varying function but also its derivative between data points. Presently, the control law is reformulated, taking into account the computation delay. A window-shifting scheme is then devised to view n data points as they are sampled in order to perform the function estimation. At each new sampling time, the window shifts to include the new data point as well as the last n-1 points. Several interpolation methods are considered. These methods use data points from a sampled function to construct a polynomial estimate of the function. The control system performance was experimentally tested using a servosystem. The results show that a Newtonian interpolation provided best results when the computation time was 0.4 times the sampling period.