In this paper, first, the dynamic behavior of a nonlinear friction driven oscillator subjected to harmonic external excitations and supported by limited power supply is studied. Dynamic analysis of the system through the variation of excitation frequency reveals that the system has chaotic motion near the fundamental natural frequency. After analyzing the dynamic response of the system, the control of chaotic motion of this system using tuned liquid column dampers (TLCD) and magneto-rheological tuned liquid column damper (MR-TLCD) are analyzed. Time-delay feedback control strategy is used in order to have real-time semi-active vibration control of the block with MR-TLCD. Simulation results show the high performance of both of the proposed methods for chaos elimination and improving the system operation. It is also concluded that the system transient time in semi-active control using MR-TLCDs and based on the new proposed control strategy is less than conventional TLCDs.