Resolving actuator redundancy — Control allocation vs. linear quadratic control

When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give exactly the same design freedom in distributing the control effort among the actuators. The main benefit of using a separate control allocator is that actuator constraints can be considered, which is illustrated with a flight control example.