The feedback control algorithm is developed to suppress oscillations caused by high resolution schemes. The stable propagation of the shock of the nonlinear advection equation is studied using the Lax-Wendroff and Warming-Beam second- rder schemes. It is shown that the addition of one and the same control artificial term in both schemes results in efficient suppression of oscillations. The switch on/off the control is studied to demonstrate the role of the control in the stable monotonic shock propagation.