"基于LQR控制的二级倒立摆系统研究与优化"

ng coupling and fast motion. It is an ideal model to test the effectiveness of various new control theories and methods. During the control process, it can effectively reflect many key issues such as stability, robustness, agility, and tracking. This paper mainly focuses on the LQR control method for a double inverted pendulum. Firstly, the mathematical model of the double inverted pendulum is established. Then, the control design for the mathematical model of the double inverted pendulum is conducted. Genetic algorithm is applied to determine the weighting matrices Q and R in the performance index function of the system, obtaining the state feedback control matrix. MATLAB is used for system simulation. After several attempts with different values for the Q matrix, the response of the system was not satisfactory. Therefore, genetic algorithm is used to optimize the Q matrix. Simulation results prove that the system response after genetic algorithm optimization can better meet the design requirements. Finally, experiments are conducted on the test bench to validate the results obtained from MATLAB simulation. The results from the experiment confirm the findings from the simulation. In conclusion, the research on the double inverted pendulum using LQR control method with genetic algorithm optimization shows promising results in improving the system response to meet the design requirements. The study provides insights into the control of complex and unstable systems like the double inverted pendulum, and the combination of LQR control method with genetic algorithm optimization proves to be effective in enhancing the system performance.