Control allocation for an over-actuated Satellite Launch Vehicle

Dynamic equations governing the short period dynamics of an over-actuated Satellite Launch Vehicle (SLV) with a typical eight-actuator configuration have been modeled in a separable form. Two rigid body models have been developed – one including the slosh dynamics, the other neglecting it. Effects of differential thrust, mounting misalignment and thrust misalignment are modeled as disturbances. The controller design and the allocation task have been taken up separately. The state feedback controller is designed for the virtual control inputs through H ∞ disturbance rejection with pole restricted to a specified region formulated using Linear Matrix Inequality (LMI) approach. The partial state feedback control strategy is applied to the rigid body model of SLV including slosh by feeding back the states, available for measurement. The dynamic allocation is carried out by formulating a separate LMI optimization problem where the weighting matrices are selected considering the actuator priorities during allocation. The combined algorithm on controller design and allocation is tested on an attitude control problem of the SLV. The response to a step command of 2° applied to pitch, yaw and roll has been tracked. The allocation algorithm distributed the three control inputs to the eight actuators by satisfying the rate and position saturation bounds.