Synthesis of PI- and PID-Regulators in Control Systems Derived by the Feedback Linearization Method

The work proposes a comprehensive approach to the synthesis of the coefficients of PI- and PID-controllers, as well as the coefficients of feedback based on the state variables of the system, using the feedback linearization method for the synthesis of control influences. This approach considers not only the static but also the dynamic characteristics of the system, allowing for higher control accuracy. The feedback linearization method facilitates the transformation of nonlinear systems into linear ones, simplifying their further analysis and controller design. The research shows that the new methodology for synthesizing the coefficients of controllers provides improved system stability, reduces sensitivity to external influences, and decreases the response time of the system to changes in operating conditions. A comparison of the proposed approach with the classical feedback linearization method demonstrates significant advantages in adaptability and accuracy. Specifically, the new methodology accounts for real-time changes in system parameters, which is critically important for complex automated processes. Using a two-mass system as an example, the practical application of this approach for synthesizing a control system is demonstrated, allowing for greater precision in control and reduced energy costs. The results of experimental studies confirm the effectiveness of the proposed methodology, indicating its ability to ensure stable system operation under variable loads and external influences. The analysis showed that the new approach can be utilized not only in traditional automated systems but also in a wide range of applications, such as robotics, industrial automation, and electric drive control systems. This research opens new horizons for the further development of adaptive control methods and can serve as a foundation for future studies in this field.