Brushed DC motors are still widely used in industrial automation, robotics, and mechatronic systems due to their simplicity, easy implementation, and fast response. They are sensitive to load variations, and therefore, precise load control of speed is essential for stable operation. This paper provides an example of modeling, design, and simulation of a closed-loop speed control system for a brushed DC motor using a Proportional–Integral–Derivative (PID) controller. The paper begins with a thorough explanation of the motor operating principle and the construction of its mathematical model both for its electrical and mechanical subsystems. Then the PID controller is designed and controlled so that the difference between the reference speed and motor speed is minimized to ensure good robustness in cases of disturbances. The system is simulated and tested with MATLAB/Simulink, which enables the transient and steady-state responses to be studied under different operating conditions. Simulation results reveal that the PID-controlled motor responds with short rise time, minimum overshoot, and even zero steady-state error in spite of changing load torque. The study underscores the advantage of PID controllers in finding a balance between simplicity, performance, and flexibility over advanced approaches such as fuzzy logic or model predictive control. The study introduces a low-cost, pragmatic, and scalable solution to speed control in small- to medium-scale industrial processes, which will experience more usage of automation technologies. Electric motors are simple devices in the modern industry, powering a huge range of applications from production devices and robots to transportation and household appliances.