Title: Modelling and stability analysis of the 155 mm spin-stabilised projectile equipped with steering fins

Authors: Spilios Theodoulis; Yannick Morel; Philippe Wernert

Addresses: Guidance, Navigation and Control Department, French-German Research Institute of Saint-Louis, Saint-Louis 68300, France. ' Guidance, Navigation and Control Department, French-German Research Institute of Saint-Louis, Saint-Louis 68300, France. ' Guidance, Navigation and Control Department, French-German Research Institute of Saint-Louis, Saint-Louis 68300, France

Abstract: The presented work concerns the modelling and stability analysis of 155 mm spin-stabilised projectiles equipped with steering fins. While a large roll rate provides the projectile with interesting stability properties, it also renders the steering control problem very difficult due to the need for very fast fin actuator dynamics. Reciprocally, this control problem can be facilitated by reducing the projectile|s roll rate using differential fin steering. This paper presents a technique allowing to assess to what extent roll rate can be reduced without jeopardising trajectory stability. First, a non-linear mathematical model for the considered class of projectiles is presented. This model is then linearised along a reference trajectory, thus, yielding a linear time-varying (LTV) model that can be used to facilitate stability analysis through frozen-time eigenvalue computation. The stability of the projectile|s trajectory is then analysed under various, and successively steeper, decreasing roll rate profiles, obtained through two proposed adaptive control schemes for the roll rate channel. The presented stability analysis technique can then be used in order to find a minimum limit for the roll rate, below which the projectile trajectory becomes unstable.

Keywords: modelling; simulation; spin-stabilised projectiles; trajectory linearisation; LTV systems; adaptive control; frozen-time stability analysis; finned projectiles; steering fins; steering control; fin actuator dynamics; roll rate; trajectory stability; nonlinear models; mathematical modelling; linear time-varying models.

DOI: 10.1504/IJMIC.2011.042655

International Journal of Modelling, Identification and Control, 2011 Vol.14 No.3, pp.189 - 204

Available online: 23 Sep 2011 *

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