Significant payload variations often occur in many practical tasks for robotic applications. But its adequate control is a formidable challenge to control designers, and previous research works have exhibited either limited performance or noticeable difficulties in implementation. In this article, we have proposed an adaptive PID control that is simple, model-free, and robust against payload variations. These advantages, already verified from the adaptive time-delay control (TDC), have been inherited to the proposed PID control through the equivalence relationship between the two controls. As a result, the proposed PID shares the simplicity, robustness, and the model free property, as well as the high levels of stability and performance with the adaptive TDC. In particular, the selection of its gains becomes especially simple and straightforward, while the adaptation becomes efficient under substantial payload variations. These positive attributes have been verified through simulations and experiments on robots under substantial payload variation. In particular, the proposed PID control was applied to the control of a WAM robot holding a baseball bat, with a result better than a standard PID control.