The first part of the paper deals with the theoretical foundations of a DC motor with independent excitation and speed control by changing the armature voltage to the rated speed. Then, a theoretical analysis of a single-phase thyristor rectifier, its operating modes, and the control and output characteristics of the rectifier was performed. It is important to emphasize that the output voltage from a single-phase thyristor rectifier is connected to the armature winding of a DC motor. This armature voltage is controlled by the control angle of the rectifier, i.e. by reducing or increasing the control angle, the speed of the DC motor is increased or decreased at a constant mechanical load. The ratio of the control angle to the armature voltage (speed) is the basis on which speed control is based. When the mechanical load of the motor is variable and there is a need for the speed to follow the reference speed and to maintain system stability and reduce unwanted system oscillations, then there is a need for speed control. In this paper, a cascade control system for two-quadrature operation with PI controllers is used for speed control. To analyze the speed control of a DC motor with independent excitation, a simulation model of the control system in MATLAB - Simulink was used. The simulation model is described with its basic parts and the communication windows of the model used for simulation are explained. At the end of the work, simulations of the characteristic operating modes of the DC motor were performed in MATLAB - Simulink and the effects of selected system parameters on the behavior of system variables were analyzed.