Naturally, a pendulum wants to oscillate about the bottom position (stable equilibrium). A real control challenge is to balance a pendulum vertically about its unstable equilibrium. The system shown in the videos uses a brushed DC motor under a closed feedback loop to stabilize the pendulum in its vertical position. An encoder at the pivot point of the pendulum is used to directly measure the angular position and estimate the angular velocity of the pendulum. The information is fed back into a LabView program which, in collaboration with a MyRio (microcontroller), is used to send current to an actuator driver that sends the appropriate command to the motor. An LQR controller is used to control the system with full-state feedback. Full-state feedback allowed for a system that was both robust to external disturbances (taps *see videos below*) and strong in tracking a command (minimal vibrations once vertically balanced).

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Both linear and non-linear models were created in Simulink to test the system dynamics. A Solidworks model was created to capture the physical parameters and inertia of the plant. Significant parameter identification was completed for the motor to correctly characterize the torque constant, viscous damping, friction torque, shaft moment of inertia, internal resistance, inductance, and actuator driver gain.