Analysis of discrete time schemes for milling forces control under fractional order holds

In this paper, discrete time model reference control schemes for practical milling using different discretization of the continuous-time plant are presented. First, a basic controller scheme is addressed where a fractional order hold with pre-fixed value of the gain is used. Secondly, a multi-model scheme, which outputs different discretization in parallel with the continuous-time milling system transfer function under a fractional order hold (FROH) of correcting β ∈ [−1, 1], is dealt with. Then, an intelligent design framework is designed as a supervisory scheme with two hierarchical levels in order to find the most appropriate value for the gain β. For choosing the value of β, a tracking performance index is designed. It evaluates each pre-defined discretization of the continuous time milling transfer function and the scheme chooses the one with the smallest value of the index in order to generate the real control input to the plant. Two different methods of adjusting this value are presented and discussed. The first one selects a β-value among a fixed pre-defined set of possible values, while the second one the value of β is updated by adding or subtracting a small quantity.