18-08-2012, 12:12 PM
Inverted Pendulum
Inverted Pendulum.pdf (Size: 2.11 MB / Downloads: 57)
Introduction
• Inverted pendulum - center of mass is
above its point of suspension
• Achieving stabilisation – pendulum
suspension point vibrating!
• Principal parameters:
• lenght
• frequency
• amplitude
Experimental approach
• Apparatus
• Construction
• Measurements:
• Pendulum angle in time
• Stabilisation conditions:
amplitude vs. pendulum length
amplitude vs. frequency
• Double pendulum
Measurements
• Stability – pendulum returns to upward
orientation
• measurements of boundary conditions:
frequency vs. amplitude
length vs. amplitude
angle in time (two cases);
• inverted pendulum
• “inverted” inverted pendulum –
for drag determination
Theoretical approach
• Pendulum – tends to state of minimal energy
• Upward stabilisation possible if enough energy
is given at the right time
• Formalism – two possibilities:
• equation of motion
• energy equation – Lagrangian formalism
• Forces approach –more intuitive:
Conclusion
we determined and experimentaly prove
stability parameters
• mass is not a parameter
• theoretical analisismatch with results
• we managed to stabilisemultiple inverted
pendulum