Linearization of Digital Derived Rate Algorithm for Use in Linear Stability Analysis

The digital derived rate (DDR) algorithm is used to calculate the rate of rotation of the Centaur upper-stage rocket. The DDR is a highly nonlinear algorithm, and classical linear stability analysis of the spacecraft cannot be performed without linearization. The performance of this rate algorithm is characterized by a gain and phase curve that drop off at the same frequency. This characteristic is useful in many applications. This paper deals with the investigation of a linearization technique for the DDR algorithm. The linearization method is described. Examples of the results of the linearization technique are illustrated, and the effects of linearization are described. A linear digital filter may be used as a substitute for the DDR in classical linear stability analyses, while the DDR itself may be used in time response analysis.