This paper proposes a method for near energy optimal allocation of control effort in dual-input over-actuated systems using a linear time-invariant (LTI) controller. The method assumes a quadratic energy cost functional, and the non-causal energy optimal control ratio within the redundant actuation space is defined. Near energy optimal control allocation is addressed by using a LTI controller to align the control inputs with a causal approximation of the energy optimal control ratio. The use of a LTI controller for control allocation leads to low computation burden compared to techniques in the literature which require optimization at each time step. Moreover, the proposed method achieves broadband, near optimal control allocation, as opposed to traditional allocation methods which make use of a static system model for control allocation. The proposed method is validated through simulations and experiments on an over-actuated hybrid feed drive system. Significant improvements in energy efficiency without sacrificing positioning performance are demonstrated.
A Framework for Optimal Control Allocation with Structural Load Constraints
