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LQR Control of inverted pendulum on moving
cart with friction
April 16, 2012 compiled on — Wednesday July 06, 2016 at 08:28 AM
The linear quadratic regulator LQR method is used to generate a control force that brings an inverted
pendulum from an initial condition back to the upright position in an optimal way. The state space
is used to represent the dynamics of the system. Static and Coulomb friction
forces act as external disturbances. Coulomb friction causes an oscillation of the cart position around the
equilibrium position .
When only viscous friction is present, LQR brings the pendulum to the upright position since viscous
friction is included in the state matrix, while Coulomb friction is included in neither the nor the
matrix.
A standard friction model is used and is described below. The eigenvalues of the closed loop state
matrix (where is the gain vector generated by LQR are all located in the left side of the
complex plane, showing that the resulting system is stable.