General form of discrete optimal tracking differentiator

For the problem of the traditional discrete optimal tracking differentiator (TD) with complex expressions and large phase delay, a more general and terse discrete optimal tracking differentiator without chattering is proposed. By introducing a phase adjusting gene, a new optimal control synthesis function is deduced. The phase characteristic of the tracking differentiator can be adjusted and the mathematic expression of the differentiator is terser. The traditional discrete optimal tracking differentiator is only an especial case of the new tracking differentiator (when the gene is equal to zero). The numerical simulation validated the effectiveness of the proposed approach.