Modelling of self-oscillations of a controlled pendulum with respect to a friction torque depending on a normal reaction in a joint

The paper presents a mathematical model of a controlled pendulum under the assumption that friction in a joint is a sum of Coulomb and viscous friction. Moreover, it is taken into account that the Coulomb friction torque depends on the value of normal reaction force in a joint. The control torque is chosen as a function that depends only on the sign of the angular speed of the pendulum. Via the Pontryagin approach for near-Hamiltonian systems, the program law is constructed for test self-oscillations. Test self-oscillations are to be used for identification of friction coefficients. Bifurcation diagrams are constructed that describe the dependence between amplitudes of self-oscillations and values of the control torque. The proposed approach to the identification of parameters of the friction requires information about amplitudes of test selfoscillations but does not require information about the trajectory of motion as a function of time. Numerical simulation of the motion of the system is carried out. The range of parameter values is described for which the method proposed in the paper is quite accurate.