H∞ Loop Shaping Using Polytopic Weights and Pole Assignment to Missile Autopilot

Modern missiles must deal with stringent performance requirements and ensure robustness across a wide range of operating conditions during flight time. Classic gain-scheduling designs have been successful in practice, but do not provide theoretically ensured bounds on both performance and robustness. Controllers are interpolated at intermediate operating conditions and switching them may cause instability. On the other hand, polytopic linear parameter-varying (LPV) controllers avert this switching and use real-time information about the plant, in order to smooth out the gain scheduling. We hereby propose a novel procedure to yield an output feedback LPV controller that ensures robust $\text{H}_{\infty} $ performance to a missile longitudinal autopilot. Our novel approach considers the four-block loop-shaping $\text{H}_{\infty} $ control theory with polytopic LPV weights that use polytopic coordinates of the LPV plant. One is capable of adjusting the singular values of the open-loop plant individually at the polytope vertices, and benefits from a trade-off between linear matrix inequalities (LMI) based optimization tools and the designer experience. This can be construed as a natural extension of the traditional $\text{H}_{\infty} $ loop-shaping method that uses linear time-invariant (LTI) weights. Assuming the scheduling variables are frozen, we also include LMI conditions for assigning closed-loop poles and hence circumvent controller order reduction. Nonlinear simulations assess the proposed autopilot, and results show an improved robust stability margin, in addition to an improved response to the acceleration command, concerning the LTI-based approach.