Pendulum Dynamics
13
ESE 447 Dynamics of the Single- Link Inverted Pendulum.
description
robotics lab dynamics notes
Transcript of Pendulum Dynamics
ESE 447
Dynamics of the Single-Link Inverted Pendulum.
Right Handed Coordinate system
Counter-clockwise positive direction of rotation
Skeletel Diagram of theSingle-Inverted Pendulum.
Generalized Coordinates
Single Link Rotary Inverted Pendulum
q_1, q_2 – Joint Angles
Lagrangian Dynamics
Link 1 Kinetic Energy:
Link 1 Potential Energy:q1
q2
Lagrangian Dynamics
q1
q2
x
Velocity is obtained by taking the time derivative
Lagrangian Dynamics
q1
q2
x
Total Kinetic Energy of link 2 is obtained by integratinginfinitesimal Kinetic energies along link2.
Lagrangian Dynamics
Total Kinetic Energy of system:
Physical Parameters of the system.
Lagrangian Dynamics
Potential Energy:
q1
q2
lc2
Lagrangian Dynamics:
Lagrangian Dynamics
Actuator Effects (DC Motor)
Gear Transfer:
Ideal PowerTransfer:
qm, tm q1, t1
Friction Effects
Friction acts opposite to the direction of motion
Assume no Static FrictionDynamic Friction is proportional to velocity
joint 1:
joint 2:
Langrangian Dynamics with Friction and Actuator Effects
