Comparative analysis of observer-based LQR and LMI controllers of an inverted pendulum

Nura Musa Tahir, Mustapha Muhammad, Musa Idi, Salinda Buyamin, Ladan Maijama’a, Sa’id Musa Yarima


An inverted pendulum is a multivariable, unstable, nonlinear system that is used as a yardstick in control engineering laboratories to study, verify and confirm innovative control techniques. To implement a simple control algorithm, achieve upright stabilization and precise tracking control under external disturbances constitutes a serious challenge. Observer-based linear quadratic regulator (LQR) controller and linear matrix inequality (LMI) are proposed for the upright stabilization of the system. Simulation studies are performed using step input magnitude, and the results are analyzed. Time response specifications, integral square error (ISE), integral absolute error (IAE) and mean absolute error (MAE) were employed to investigate the performances of the proposed controllers. Based on the comparative analysis, the upright stabilization of the pendulum was achieved within the shortest possible time with both controllers however, the LMI controller exhibits better performances in both stabilization and robustness. Moreover, the LMI control scheme is effective and simple.


Inverted pendulum; Linear matrix inequality; Linear quadratic regulator; Nonlinear system; Opserver; Robustness

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