Advanced Generalized Modelling of Classical Inverted Pendulum Systems

The purpose of this paper is to present the design and program implementation of expansions made to the existing general algorithmic procedure which yields the mathematical model for a classical inverted pendulum system with an arbitrary number of pendulum links. The expansions include the option to define the reference position of the pendulum in a planar coordinate system, to choose the reference direction of pendulum rotation and to select the shape of a weight attached to the last pendulum link. The underlying physical formulae based on the generalized inverted pendulum concept are implemented in the form of a symbolic MATLAB function 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 the classical single and double inverted pendulum system using the newly-developed MATLAB blocks and applications.