The most critical parameter of audio and video information output is the playback speed, which affects many viewing or listening metrics, including when learning using tutoring systems. However, the availability of quantitative models for personalized playback speed control considering the learner's personal traits is still an open question. The work aims to develop a model to control the personalized playback speed of audio information for beginners and experienced learners for intelligent tutoring systems. Analysis of the data from the experimental study using traditional machine learning methods did not allow us to classify the preferred playback rate with accuracy higher than 60%. Therefore, we developed the three-level hierarchical logistic model that predicts the preferred playback speed of audio material on the scale from "very low speed" to "high speed" for beginners and experienced learners with 80% accuracy. The model uses a combination of cognitive and psychomotor traits of individual learners and aims to maximize audio listening convenience and satisfaction. We explained the influence of the learners' selected personal traits on the preferred speed of audio playback. We calculated the convenience of listening to the audio materials without and with the model. By using the model, the convenience of listening to audio materials increased by an average of 13% at a low speech speed and 37% at a high speech speed. The model extends the control theory of multimedia information in e-learning systems by describing the influence of selected psychophysiological traits of learners on the preferred playback speed of audio materials.