This research proposes to obtain a mathematical model that describes the dynamic operation of a brushed DC motor, to obtain a state function considering the electrical, mechanical, and thermal effects of the DC motor. The dynamic evolution of the proposed function is evaluated by simulation using Matlab software, and by applying different values of the step type inputs for the brushed motor excitation employing pulse width modulation (PWM) to obtain a wide range of operations. Experimental results show that the developed state function, provides a reliable approximation to estimate the voltage, armature current, mechanical torque, and temperature of the brushed DC motor, showing an error percentage of 0.2%.