This paper discusses the balancing of a nonlinear triple inverted pendulum, sometimes described as a gymnastic robot due to its simple simulation of the action of a human acrobat. This three-joint robot is mounted on a freely rotated high bar. The first joint is passive, being unpowered, while the second and third joints are powered. Managing the action of the first joint thus presents the most significant challenge in balancing the gymnastic robot in the vertical plane. Linear Quadratic Regular (LQR) optimal control theory was thus used throughout this work to balance the gymnastic robot. However, while the weighting matrices for Q and R are generally determined using trial and error, this is both time consuming and inaccurate. An optimization algorithm known as Gray Wolf Optimization (GWO) was thus used in this case to obtain the ideal control parameters, with superior results for all three links (first, second, and third) obtained in terms of overshot (26.12%, 1.62%, 31.22%), rise time (0.02506s, 0.0501s, 0.050s), and setting time (2.732s, 3.258s, 3.058s) as compared to those produced using the trial-and-error method.
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