Due to their low mass and conformability, actuators and sensors made of active materials can be used in the vibration control of inflatable structures. In this study, we model piezoelectric patches attached to an inflated toroidal shell as actuators and sensors. Using Sanders' shell theory in the presence of initial stresses, the generalised forces due to the piezoelectric actuators are derived for the inflated toroidal shell assuming quasi-static conditions. The derivations are given for both unimorph and bimorph configurations. Effects of the mass and stiffness of the patches are incorporated in the equations of motion. Thereafter, a sensor equation is presented. Within linear shell theory, the methodology is quite general in nature and can be applied easily to other types of shells and membranes. To demonstrate this, we specialise the actuator and sensor equations for a circular cylinder. Using the formulations for the inflated toroidal shell, the modal forces and modal sensing constants are calculated for different sizes and locations of the piezoelectric patches. Along with this, controllability and observability indices are calculated to quantify the performance of the actuators and sensors. A study of the stiffness and mass effects of the piezoelectric patches is performed using frequency response function.