Generalized Control Coupling Effect of Spinning Guided Projectiles

Abstract

This article focuses on the analysis of generalized control coupling effect of spinning guided projectiles. A concept of so-called equivalent dynamics is first proposed in this article to avoid nonlinearity and facilitate understanding of control coupling for spinning guided projectiles. First, the coupling induced by an arbitrary-order dynamic is formulated. Two useful theorems showing the property of the concept are presented standby. Second, considering the main elements involved in the control loop, i.e., autopilot, actuator, and inertial measurement unit, a comprehensive model in the spinning frame is established for spinning guided projectiles. With aid of the second theorem, the equivalent dynamics of the multiple elements are introduced into the model, in which the closed-loop characteristic equation is described with the complex summation method. Then, the closed-loop complex steady gain is analyzed and an integrated decoupling is applied to eliminate the coupling effects completely. This can be implemented readily via presetting a leading angle in engineering. Furthermore, it is noted that for this high-order system, numerical method solving the characteristic equation is the only way to obtain dynamic stability conditions. Finally, a case study is conducted to demonstrate the effectiveness and robustness of the decoupling approach. In addition, the stability problem is figured out with numerical method.