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Modeling, analysis and control of a single stage linear inverted pendulum

In this paper, modeling, analysis and real-time stabilization of a cart pendulum system is performed. The cart pendulum system is the typical benchmark example of the underactuated system and has been used for examine different control schemes. Cart pendulum system represents a wide range of realistic systems like rocket propeller, tank missile launcher, self-balancing robot, biped walking, etc. The main aim of this work is to investigate the performance of controller in stabilizing the inverted pendulum at the unstable equilibrium point. The work is done in both analytical and experimental manners for validation of results. LQR (Linear-Quadratic-Regulator) controller is developed to address the regulation problem of the cart pendulum system. The experimental work is done on Googoltech Linear Inverted Pendulum (GLIP) setup. The analytical results are performed using MATLAB and the results are found in the closed agreement of the experimental results. Thus, the mathematical model is validated on the basis of real-time experiment. Experimental and analytical results are demonstrating that the LQR controller is able to effectively stabilize the cart pendulum system at its unstable equilibrium point.