This paper presents a mathematical representation of a system composed of a rigid link manipulator under PID trajectory-tracking control. The representation describes the system as a two-port network that accepts the external force (including the gravity) and the desired velocity as the inputs and produces the actuator force and a motion-related quantity as the outputs. The input-output causality between the desired velocity and the actuator force is reversible by exploiting the fact that they are connected through a feedthrough term. The model is shown to be state-strictly and output-strictly passive in the semiglobal sense by using a storage function suggested by Wen and Murphy  as a Lyapunov function for a PID-controlled robot. The new model allows the analysis of a class of controllers that are represented as an interconnection of a PID controller and another controller such as a sliding mode controller. In addition, it leads to an alternative proof for the semiglobal stability of PID set-point control.