Abstract: Automatic control of robots with flexible links has been a pivotal subject in control engineering and robotics due to the challenges posed by vibrations during repetitive movements. These vibrations affect the system?s performance and accuracy, potentially causing errors, wear, and failures. LQR control is a common technique for vibration control, but determining the optimal weight matrices [Q] and [R] is a complex and crucial task. This paper proposes a methodology based on genetic algorithms to define the [Q] and [R] matrices according to design requirements. MATLAB and Simulink, along with data provided by Quanser, will be used to model and evaluate the performance of the proposed approach. The process will include testing and iterative adjustments to optimize performance. The work aims to improve the control of robots with flexible links, offering a methodology that allows for the design of LQR control under the design requirements of controllers used in classical control through the use of genetic algorithms.

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