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Automated Controller Design for a Missile Using Convex Optimization

The focus of the present master thesis is the automation of an existing controller design for a missile using two aerodynamic actuating systems. The motivation is to evaluate more missile concepts in a shorter period of time.The option used is trimming and linearization of a highly nonlinear missile at specfic conditions.

According to these conditions, either a two-dimensional operating point grid defined by Mach number and height or three-dimensional operating point grid defined by Mach number, height and angle of attack is generated for the whole operating range of the missile.

The controllers are designed at these points using convex optimization. The convex set defines the pole placement area which is constrained by linear matrix inequalities according to the dynamic behavior of the missile at the operating point conditions. These controllers describe a validity area where the missile can be stabilized. This area consists all neighboring operating points and defines therefore the grid density which can differ at specfic regions of the operating range. Controlling the missile to the target make sit necessary to apply gain-scheduling in order to get the manipulated variable by interpolation of adjacent operating points.

During this blending of the controllers a problem called windup can occur when an actuator is saturated. This might lead to instability in worst case but can be counteracted by a model-recovery anti-windup network which guarantees stability in the presence of saturation. Thisanti-windup design is automated by an ane linear parameter dependency of the grid parameters and has the same validity area like the controllers.

The whole design was successfully developed and tested in MATLAB/Simulink on missiles using one or two aerodynamic actuating systems. The controllers have a good performance at small and high acceleration steps and the anti-windup keeps the missile stable even though the actuators are saturated. Stability and robustness of the controllers and anti-windup networks was verfied as well as an air defense maneuver where the missile starts at the ground and intercepts at high altitude was successfully simulated for different grids and missiles.
Source: Luleå University of Technology
Author: Auenmüller, Christoph

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