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Robust gain-scheduled autopilot design with anti-windup compensation for a guided projectile


This article deals with the control design of a dual-spin projectile concept, characterized by highly nonlinear parameter-dependent and coupled dynamics, and subject to uncertainties and actuator saturations. An open-loop nonlinear model stemming from flight mechanics is first developed. It is subsequently linearized and decomposed into a linear parameter-varying system for the roll channel, and a quasi-linear parameter-varying system for the pitch/yaw channels. The obtained models are then used to design gain-scheduled \(\mathcal {H}_\infty\) baseline autopilots, which do not take the saturations into account. As a major contribution of this paper, the saturation nonlinearities are addressed in a second step through anti-windup augmentation. Three anti-windup schemes are proposed, which are evaluated and compared through time-domain simulations and integral quadratic constraints analysis. Finally, complete guided flight scenarios involving a wind disturbance, perturbed launch conditions, or aerodynamic uncertainties, are analyzed by means of nonlinear Monte Carlo simulations to evaluate the improvements brought by the proposed anti-windup compensators.

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  1. Using a more standard \(\mathcal {H}_\infty\) soft goal of the form \(\Vert {W_M(s) \mathcal T_{\varvec{n}_{zy,g} \rightarrow \varvec{e}_{zy,ref}}(s)}\Vert_\infty\), as with the roll channel, led to less robust margins, as well as less smooth gain surfaces when performing the synthesis over the flight envelope.

  2. Thus, the \(\mathcal {H}_2\) norm of G(s)/s corresponds to the energy of the step response of G(s).


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This research is supported by the French-German Research Institute of Saint-Louis, and ONERA, the French Aerospace Lab.

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Correspondence to Sovanna Thai.

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Thai, S., Theodoulis, S., Roos, C. et al. Robust gain-scheduled autopilot design with anti-windup compensation for a guided projectile. CEAS Aeronaut J 14, 765–786 (2023).

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