<p>Proportional Integral Derivative (PID) controllers are <a href="http://www.thesaurus.com/browse/extensively">extensively</a> used in practical industries to control the speed of DC Motors. The single weakness of PID controllers is their sensitivity to variation in parameters and operating conditions; thus, tuning the controller gains to adapt with these variations presents a practical challenge. In this paper, an adaptive mechanism that utilizes a Recursive Least Square (RLS) algorithm, with rate limiters, is implemented to perform an online self-adjusting of each of the PID gains in order to achieve Adaptive PID (APID) controller that will accommodate to system variations. MATLAB/ Simulink software is used to implement and simulate APID control of a Chopper-Fed DC motor. A conventional PID control system is also designed and simulated to obtain results that can be used to judge the performance of the APID controller. Results proved that the APID controller forced the motor speed to track the reference input with <a href="http://www.thesaurus.com/browse/insignificant">insignificant</a> tracking error, and also managed to attain the motor speed at its desired value, regardless of the load changes inflected on the motor. This enhances both transient and steady-state speed responses.</p>