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

Abstract

This chapter is the first of two others that will follow (a three-chapter series). Here we present the derivation of the mathematical model for a rocket's autopilots in state space. The basic equations defining the airframe dynamics of a typical six degrees of freedom (6DoFs) are nonlinear and coupled. Separation of these nonlinear coupled dynamics is presented in this chapter to isolate the lateral dynamics from the longitudinal dynamics. Also, the need to determine aerodynamic coefficients and their derivative components is brought to light here. This is the crux of the equation. 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 nonlinear 6DoFs. In a novel way, we presented the linearization of the decoupled 6DoF equations in a generalized form. This should provide a lucid and easy way to implement trim and linearization in a computer program. The longitudinal model of a rocket presented in this chapter will serve as the main mathematical model in two other chapters that follow in this book.