Скачать или смотреть Unstable inverted pendulum: modelling, linearization, free response (Laplace)

This video presents a pendulum model using Newton's equations and torque balances.

As the goal is analysing the behaviour close to its inverted (unstable) equilibrium position, $\sin\alpha\approx \alpha$ is then linearized in said upper equilibrium.

A Laplace transform of the pendulum ODE is then performed, obtaining the transfer function representation of the system (the input is a manipulable torque at the lower joint) + initial conditions term (dependent on the initial position and velocity at the start of the experiment/simulation).

This representation in the Laplace domain of the linearized model is used to calculate the free response from non-zero initial conditions and zero input, verifying that it, obviously, tends to infinity (unstable response). This does not occur in the real nonlinear system, but the linearized model is only locally valid for small angular deviations around the upper vertical position.
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PDF/code/notes at: https://personales.upv.es/asala/YT/V/...
#mechanics #differentialequations #controltheory
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Antonio Sala, UPV
University lectures
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