<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Modelling of Classical and Rotary Inverted Pendulum Systems – A Generalized Approach

Department of Cybernetics and Artificial Intelligence, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia

Journal of Electrical Engineering

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...

Modelling of Classical and Rotary Inverted Pendulum Systems – A Generalized Approach

Published Online: Mar 09, 2013

Page range: 12 - 19

DOI: https://doi.org/10.2478/jee-2013-0002

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

This content is open access.

Modelling of Classical and Rotary Inverted Pendulum Systems – A Generalized Approach

Published Online: Mar 09, 2013

Page range: 12 - 19

DOI: https://doi.org/10.2478/jee-2013-0002

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

This content is open access.

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