Phonation results from the passively induced oscillation of the vocal folds in the larynx, creating sound waves that are then articulated by the mouth and nose. Patients undergoing laryngectomy have their vocal folds removed and thus must rely on alternative sources of achieving the desired vibration of artificial vocal folds. Existing solutions, such as voice prostheses and the Electrolarynx, are limited by producing sufficient voice quality, for instance. In this paper, we present a mathematical analysis of a physical model of an active vocal fold prosthesis. The inverse dynamical equation of the system will help to understand whether specific types of soft actuators can produce the required force to generate natural phonations. Hence, this is referred to as the active actuation model. We present the analysis to replicate the vowels /a/, /e/, /i/, and /u/ and voice qualities of vocal fry, modal, falsetto, breathy, pressed, and whispery. These characteristics would be required as a first step to design an artificial vocal folds system. Inverse dynamics is used to identify the required forces to change the glottis area and frequencies to achieve sufficient oscillation of artificial vocal folds. Two types of ionic polymer-metal composite (IPMC) actuators are used to assess their ability to produce these forces and the corresponding activation voltages required. The results of our proposed analysis will enable research into the effects of natural phonation and, further, provide the foundational work for the creation of advanced larynx prostheses.