Furuta Pendulum Simulation by George Cakiades and Christopher Hildebrand for ECE431 Dr. Timothy Chang The goal of this project was to simulate and balance a rotary inverted pendulum a.k.a. the Furuta pendulum. Its inherent unstable nature lends to the challenge of balancing the pendulum. Using state equations given by K. Furuta and collegues, the pendulum was simulated in MATLAB with Simulink. The simulation was then animated using Ansim. Torque is supplied by a motor attached to the pivot of the pendulum which is controlled by a microprocessor. A resolver measures the angle b and feeds this information back to the microprocessor which in turn balances the pendulum.

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Differential Equations The differential equations above define the motion of the pendulum. As seen in the previous screen, a is the angle measured between the rotary arm and its initial position, and b is the angle measured between the pendulum and its critically stable position. The variable U defines the contribution of the motor to the motion of the pendulum; it is essentially the balancing force that is dictated by the microprocessor.

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The coefficients above are derived by finding the stable points of the system. Notice how the coefficients are completely defined in terms of b, as this is the only variable fed back to the microprocessor.

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The coefficient B and the constant E are both defined in terms of b as well.

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Simulink Model Above is the model as it was implemented in Simulink. Please click on the image for a larger picture.

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Ansim Animation

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