The Design of a Rocket Angular Stabilization System Based on Stability and Performance Indices Using the Coefficient Method

This paper proposes a coefficient-based method for designing a rocket angular stabilization system that yields an explicit, direct solution for determining the parameters of a PID control law from specified stability and performance indices. Linearized equations of motion in the yaw channel with a PID law are formulated, and the system transfer function and its characteristic polynomial are obtained. Quantitative stability and performance indices are introduced, defined via the coefficients of the characteristic polynomial, and expressed directly through the control law parameters. Based on sufficient conditions for stability and performance, resolving inequalities are derived for the control parameters that meet the prescribed stability and performance requirements. It is shown that the solution set of these inequalities is non-empty; i.e., the problem of finding the required control law parameters always has a solution. In the control-parameter space, the boundaries of the system’s stability and performance regions are explicitly described. A decomposition method and its extension are proposed for the design problem by the required transient process shape and transient time, splitting it into two sequential subproblems: obtaining the required shape and obtaining the required speed. A simple and effective adaptive algorithm is proposed to maintain constant stability and performance indices under variable engine thrust. The results of applying the proposed design methods to the development of a rocket angular stabilization system test stand are presented. Numerical experiments convincingly demonstrate the high effectiveness of the proposed coefficient-based design method—combining sufficient stability and performance conditions with the decomposition approach—for designing the test stand system.