Proxy-Based Optimal Control Allocation for Dual-Input Over-Actuated Systems

Over-actuated systems are characterized by a larger number of actuators compared with the degrees of freedom to be controlled. In such systems, it is often desirable to allocate control effort dynamically (i.e., over a broad range of frequencies) in an optimal manner, without sacrificing control performance. At present, this goal is achieved through computationally intensive real-time optimization or by using static redundancy models, which could significantly sacrifice optimality and/or control performance. In the context of dual-input, single-output over-actuated systems, this paper proposes a proxy-based approach for optimal dynamic control allocation without need for real-time optimization. Using factorization, a causally implementable optimal relationship between two control inputs is derived. It is shown that control energy is minimized indirectly by minimizing the deviation of control inputs from the derived relationship, which can be achieved using classical or advanced feedforward (FF) and/or feedback (FB) control techniques. A classical FF and FB approach for implementing the proposed proxy-based allocation scheme, alongside an approach for handling input constraints, is detailed and validated in simulations and experiments on an over-actuated hybrid feed drive. In comparison with an existing static-model-based dynamic allocation approach, large reductions in control energy without sacrificing control performance are demonstrated.