Mathematical modelling, numerical simulations and experimental verification of bifurcation dynamics of a pendulum driven by a dc motor

A mathematical model of a system consisting of a dc motor, mechanism converting the rotational motion to the linear one and a single physical pendulum with the joint horizontally driven is developed. Constant angular velocity of the crank is assumed. The parameters of the model are estimated using the experimental data consisting of five solutions corresponding to the five different values of constant input voltage. Different versions of the mathematical model, with different details concerning friction and damping modelling, are tested. A good agreement between real and simulated behaviour of the system is obtained. Moreover the model is validated by testing its ability to predict critical values of the bifurcation parameter.