DYNAMICS AND STABILITY STATE-SPACE OF A CONTROLLED INVERTED PENDULUM

A study is conducted into the dynamics of an inverted pendulum under t he regulation of a linear-feedback control system. Analysis of the res ulting dynamic equations indicates the presence of stable regions with in the four-dimensional state space of the system, which are confirmed through simulation. System trajectories are,examined in this state sp ace, and complex, apparently chaotic behaviour is observed outside the stable regions of the state space. An algorithm is developed to map t he boundaries of the stable state-space hyper-volume; this algorithm i s broadly applicable to the study of other systems. Results are presen ted, generated by executing the algorithm on the inverted pendulum dyn amics. These comprise a series of three-dimensional plots, outlining t he four-dimensional stability volume. The boundaries of this volume ar e seen to exhibit a jagged, possibly fractal, morphology.