State-Space Modelling of a Rocket for Optimal Control System Design

In this study, we present the derivation of the mathematical model for a rocket’s autopilot in state-space. The basic equations defining the airframe dynamics of a typical six-Degree-of-Freedom (6DoF) are non-linear and coupled. Separation of these nonlinear coupled dynamics is presented as lateral and longitudinal dynamic equations. The need to determine aerodynamic coefficients and there derivative components are brought to light here, which is the crux of the equations. Methods of obtaining such coefficients and their derivatives in a sequential form are also put forward. After the aerodynamic coefficients and their derivatives are obtained, the next step is to trim and linearize the decoupled non-linear 6DoFs. In a novel way, we presented the linearization of the decoupled 6DoF equations in a generalized form. This provides a lucid and easy way to implement trim and linearization using any computer program.