Stabilization control of the inverted pendulum on a self-balancing cart
DOI:
https://doi.org/10.5902/2179460X92185Keywords:
Inverted pendulum, Self-balancing cart, LQR controller, Nonlinear control systems, Dynamic stabilizationAbstract
The inverted pendulum is one of the most challenging systems in control theory, serving as a key model for real-world applications that require dynamic balance, such as biped robots, autonomous vehicles, and aerospace systems. Its highly nonlinear, unstable, and underactuated nature poses significant challenges, demanding advanced control strategies. This study adopts the inverted pendulum system on a self-balancing cart as the object of analysis, conducting a dynamic study based on Lagrangian mechanics to derive the equations of motion, which are later reformulated into state-space form. For the stabilization phase, the Linear Quadratic Regulator (LQR) is employed, offering advantages such as full-state feedback, minimal control effort, fast settling time, and smooth system response, characteristics obtained through the minimization of a cost function assigned to each state and control variable. This work proposes an effective methodology for modeling, linearization, and control of nonlinear dynamic systems, applied to an inverted pendulum mounted on a self-balancing cart, aimed at applications in autonomous systems, robotics, electrical engineering, mechanical engineering, and aerospace engineering.
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