As an important part of aesthetic education, music is the artistic expression of human emotions. It has a crucial impact on the cultivation of individual music perception ability, music aesthetic ability, music creation ability, etc. The degree of influence of emotions and values in music runs through the individual. This study introduces a method to independently design a predictive controller using the theoretical framework of the state-space method. Since the same results as DMC can be derived, it can be regarded as an understanding of DMC in the time domain. We take the asymptotically stable object of SISO as the model and use the step response coefficient to directly model, but this method makes the control uncontrollable, so we use the method of adding the correction parameter to make the observable process more effective. The advantages of one-time online optimization can reduce the amount of calculation and greatly enhance the robustness in the control process. In order to study the dynamic characteristics of the system, an internal model control system is introduced. By studying the closed-loop stability of the internal model system, the internal model structure of the dynamic matrix control system is studied, and its dynamic characteristics are further studied. When analyzing the dynamic characteristics, we can know that the dynamic characteristics of the system only depend on the object characteristics and control strategies, and have nothing to do with the model length. This study introduces the basic structure, main properties, and design method of the internal model controller. On the basis of conventional internal model control, an enhanced internal model control method is introduced. Through the analysis of the sensitivity function and the complementary sensitivity function, the robust performance and robust stability of the enhanced internal model control system are studied. Music learning psychology is related to the effect of music teaching. Since individual psychological development is dynamic and controllable, by grasping students’ music learning motivation and music psychological ability, we can well practice the concept of contemporary new curriculum standards and implement high-quality music courses. This study mainly discusses the music learning psychology itself, the analysis of real-time measurement results, and the analysis of teaching countermeasures, and does some research on music theory and teaching practice. Through real-time measurement research, it can be concluded that the real-time measurement results are relatively optimistic, which shows that teachers can maintain students’ learning well as long as they use teaching methods that conform to students’ learning psychology. The nonlinear dynamic incremental internal model algorithm can improve students’ various music psychological abilities and achieve the expected music teaching goals.