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A Power Series Based Controller for the Stabilization of a Single Inverted Pendulum on a Cart: Analysis and Real-Time Implementation

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Figure

Fig. 1. Single inverted pendulum diagram.
Fig. 2. Simulated state response and control effort for the power series based controller with various initial angles, and x0 = 0, ˙α0 = 0, ˙x0 = 0.
Fig. 3. Simulated state response and control effort for the LQR controller with various initial angles, and x0 = 0, ˙α0 = 0, ˙x0 = 0.
Fig. 10. Stability region estimate for the LQR controller for various initialcart positions, pendulum angles, and angular velocities with zero initial cartvelocity.
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