Assignment Problem: Figure shows a schematic of an inverted pendulum on a cart. The cart is driven by a DC motor, attached to the wheels, whose specs are provided as an attachment.
(1) Derive the state-space model of the system, including motor's dynamics.
(2) Design an MPC controller for keeping the pendulum in an upward configuration, and tracking a position set point on the cart, simultaneously (i.e., an inverted pendulum control problem). Set constraints on the pendulum angle and cart position as: |θ| << 30 degrees, and |X| << 0.5 meters.
(3) Repeat (2) when adding a full-state observer. Design proper observer gains and explain your design process.
Physical parameters of the system:
Mass of the cart (M) = 0.5 kg
Mass of the pendulum (m) = 0.2 kg
Coefficient of friction for cart (b) = 0.1 N/m/sec
Length of pendulum center of mass (l) = 0.3 m
Mass Moment of inertia of the pendulum (I) = 0.006 kg.m2
Radius of the wheels (r) = 0.10 m.
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