MODELLING OF CLASSICAL AND ROTARY INVERTED PENDULUM SYSTEMS – A GENERALIZED APPROACH

Slávka Jadlovská – Ján Sarnovský

   The purpose of this paper is to present the design and program implementation of a general procedure which yields the mathematical model for a classical or rotary inverted pendulum system with an arbitrary number of pendulum links. Lagrange equations of the second kind with an integrated Rayleigh dissipation function are employed in model design, and the energetic balance relations, derived for the base and all pendulum links in a generalized (n-link) classical and rotary inverted pendulum system, are implemented in form of symbolic MATLAB functions and a MATLAB GUI application. The validity and accuracy of motion equations generated by the application are demonstrated by evaluating the open-loop responses of simulation models of classical double and rotary single inverted pendulum.

Keywords: inverted pendulum systems, automated mathematical modelling, Lagrange mechanics, symbolic MATLAB functions, classical double inverted pendulum, rotary single inverted pendulum

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