In current work, a comprehensive study on control algorithms with the presence of soil-structure interaction (SSI) effects is presented. Algorithms used in this study are Clipped-Optimal Control (COC), Lyapunov, Bang-Bang and Fuzzy with two Passive-On (P-On) and Passive-Off (P-Off) cases. Furthermore, characteristics of soil including four cases of fixed base, dense, medium and soft soil are investigated. In order to evaluate the efficiency of these algorithms in determining the appropriate voltage of the Magneto-rheological Damper (MR) and the corresponding control force, a 5-story linear shear building under 21 ground motions is selected. Earthquake records used in this paper contain 3 sets of 7 ground motions including far-fault and near fault records with fling step and forward directivity. Important effects such as nonlinear behavior of MR damper, actuator dynamics and damper saturation are also considered in this study. Mean and standard deviation of structural responses for the 3 sets of presented records show that the reduction in structural responses increases with reducing the stiffness of the base of the structure. Moreover, COC and Bang-Bang algorithms presented better performances than the other considered control algorithms and provide a robust method for semi-active control of structures equipped with MR dampers.