This paper proposed novel direct design methods from closed loop measured data to estimate faults and design controllers. When imposing the lower and upper bounds constrain conditions on the faults, a fast gradient method was applied to solve it. Based on fault estimations, the subspace predictive control was proposed to solve an optimization problem with linear matrix inequality constraint. To this optimization problem in the subspace predictive control under fault estimations, a class of estimation sequences were constructed to use the fast gradient method. The helicopter simulation shows that the algorithm proposed is reliable and effective.