Robust control methodology applied in inverted pendulum system considering polytopic uncertainty

Inverted pendulum systems are used in the academic world due to their numerous applications in industrial and control engineering that are used as a benchmark, e.g., modern robots and others. These systems investigate several challenges, such as stability analysis and control design, focusing on robust stability and performance when considering polytopic uncertainties. This paper proposes a robust control methodology considering polytopic uncertainties in an inverted pendulum tracking problem. The proposed method combines the cascade control structure and the LMI approach with polynomial uncertainty theory. The proposed methodology consists of the inner loop design based on LMI theory. Then, the outer control loop is based on Kharitonov’s theorem to ensure robust stability and performance under parametric uncertainties. The proposed methodology is compared with the other three classic control techniques: LQR, PID+LQR, and robust tracking and disturbance rejection (RTDR)). Many simulations and experimental tests showed that the proposed methodology outperforms the other classic approaches when the system is subject to parametric variations (i.e., rod length and mass variations), ratifying the proposed method’s robustness, effectiveness, and accuracy.