In this paper, two control allocation algorithms have been proposed for overactuated systems. The algorithms are developed by formulating constrained control allocation problem into an equivalent fixed point framework. The first algorithm follows sequential solving method while the other one involves a zero finding technique by the Newton method. In order to consider limiting constraints, the saturation function has been taken into account that leads to a nonsmooth zero finding problem and the proposed method guarantees superlinear convergence. The second algorithm is easy to implement and faster than the algorithm developed based on the sequential solving technique. To demonstrate the effectiveness of the proposed algorithms, a detail simulation study has been carried out, in which one example considers both the actuator rate and amplitude constraints.