This study presents the design and real-time applications of an Interval Type-2 Fuzzy PID (IT2-FPID) control system on an unmanned aerial vehicle (UAV) with a flexible cable-connected payload in comparison to the PID and Type-1 Fuzzy PID (T1-FPID) counterparts. The IT2-FPID control has significant stability, disturbance rejection, and response time advantages. To prove and show these advantages, the DJI Tello, a commercial UAV, is used with a flexible cable-connected payload to test the robustness of PID, T1-FPID, and IT2-FPID controllers. First, the optimal coefficients of the compared controllers are found using the Big Bang–Big Crunch algorithm via the nonlinear UAV model without the payload. Second, once optimised, the controllers are tested using several scenarios, including disturbing the payload and the coverage path planning area to examine their robustness. Third, the controller performance results are evaluated according to reference achievement and point-based tracking under disturbances. Finally, the superiority of the IT2-FPID controller is shown via simulations and real-time experiments with a better overshoot, a faster settling time, and good properties of disturbance rejection compared with the PID and the T1-FPID controllers.