Control allocation approaches

The control allocation problem is defined in terms of solving or approximately solving a system of linear equations subject to constraints for redundant actuator control variable commands. There is one equation for each controlled axis. The constraints arise from actuation rate and position limits. An axis priority weighting is introduced when the equations cannot be solved exactly because of the constraints. A actuator command preference weighting and preferred values are introduced to uniquely solve the equations when there are more unknowns than equations. Several approaches to this problem are discussed. The approaches are broadly grouped into linear and quadratic programming approaches. While the linear programming approach is well suited to solving the general problem a computationally faster but approximate solution was found with the quadratic programming approach. Example results based on tailless aircraft flight control are presented to illustrate the key aspects of the approaches to control allocation. Conclusions and recommendations are stated relative to the various approaches.