In this study, a principal model of a brushed directcurrent (DC) motor that has become a benchmark is described. Then it stability program was designed based on linear quadratic optimal control theory and the controllability and observability were studied. Choosing brushed DC motor output angle θ as control variables. Simulation on this control system in Matlab/Simulink software environment was described It has been observed that the controller stabilizes the system. In addition, computer simulations show the effectiveness of the proposed approach. Parameterization of matrices, calculation of optional controller and simulations are done by using Matlab/Simulink programming.