Load Balancing in Control Allocation

Next-generation aircraft with a large number of actuators will require advanced control allocation methods to compute the actuator commands needed to follow desired trajectories while respecting system constraints. Previously, algorithms were proposed to minimize the l 1 or l 2 norms of the tracking error and of the actuator deflections. This paper discusses the alternative choice of the l ∞ norm, or the sup norm. Minimization of the control effort translates into the minimization of the maximum actuator deflection (min―max optimization). This paper shows how the problem can be solved effectively by converting it into a linear program and solving it using a simplex algorithm. Properties of the algorithm are also investigated through examples. In particular, the min―max criterion results in a type of load balancing, where the load is the desired command and the algorithm balances this load among various actuators. The solution using the l ∞ norm also results in better robustness to failures and lower sensitivity to nonlinearities in illustrative examples. This paper also discusses the extension of the results to a normalized l ∞ norm, where the norm of the actuator deflections are scaled by the actuator limits. Minimization of the control effort then translates into the minimization of the maximum actuator deflection as a percentage of its range of motion.