The real stability and stabilizability radii of the multi-link inverted pendulum system

A multi-link inverted pendulum with an arbitrary number of v links and controlled by a single torque input is considered in this thesis. The nonlinear and linearized dynamics are derived for a general v. It is then shown that the linearized model of the system is controllable for all v ≥ 1. Although this implies from linear control theory that one can locally stabilize the system with any number of links, it is well known that it is experimentally difficult to do so as the number of links increases. Such a difficulty is illustrated by three "real-life" simulations. It is believed that the primary reason for such an increase of difficulty is the pendulum system's poor stabilizability properties as additional links are added. Using the real stabilizability radius, this thesis performs a robustness study to confirm this conjecture.