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Cylinder on beam PID control system
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PID control system of a frictionless cylinder rolling without slipping on a beam with a controlled inclination. This PID system is Hamiltonian and loopless. The non-autonomous Hamiltonian system is simulated using Hamilton's equations and the error associated with the time-dependent control variable is expressed analytically by ODEs as opposed control loops and feedback mechanisms using global memory.
The system is generally unstable for periodic and uncontrolled beam inclinations. Proportional or derivative gains stabilize the system for a certain set of initial conditions. Non-zero proportional and derivative gains can be used to approach a certain reference or desired cylinder coordinate on the beam. The effect of derivative and proportional gains are demonstrated. Integral gain has no practical benefit in this frictionless and noiseless system, and generally only slows the convergence toward the set cylinder coordinate.
0:00 unstable / diverging
0:26 proportional gain
0:58 derivative gain
1:10 complete PID
The system was simulated using high order explicit symplectic integrators and was rendered in real time.
🎵 "Payment Day" / "Turrican 3 Main title" by "Chris Huelsbeck" | not affiliated with/endorsed by.
The system is generally unstable for periodic and uncontrolled beam inclinations. Proportional or derivative gains stabilize the system for a certain set of initial conditions. Non-zero proportional and derivative gains can be used to approach a certain reference or desired cylinder coordinate on the beam. The effect of derivative and proportional gains are demonstrated. Integral gain has no practical benefit in this frictionless and noiseless system, and generally only slows the convergence toward the set cylinder coordinate.
0:00 unstable / diverging
0:26 proportional gain
0:58 derivative gain
1:10 complete PID
The system was simulated using high order explicit symplectic integrators and was rendered in real time.
🎵 "Payment Day" / "Turrican 3 Main title" by "Chris Huelsbeck" | not affiliated with/endorsed by.
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