The problem of balancing a two degree of freedom (DOF) pendulum has been a bench-mark problem in demonstrating and motivating various control design techniques. From a control design perspective, a challenging and difficult problem is presented as the system is nonlinear and the open-loop is unstable. In addition, need for a sensor system to measure the inclination angles of the pendulum contributes to the complexity of the balancing problem....[ Read more ]

The problem of balancing a two degree of freedom (DOF) pendulum has been a bench-mark problem in demonstrating and motivating various control design techniques. From a control design perspective, a challenging and difficult problem is presented as the system is nonlinear and the open-loop is unstable. In addition, need for a sensor system to measure the inclination angles of the pendulum contributes to the complexity of the balancing problem.

In this project, a series of problems about inverted pendulum were studied. First, a spherical pendulum system based on a X-Y table was designed and constructed. Then, a control model was developed by projecting the system onto the x-z and y-z planes of the inertial coordinate system. These projections were treated independently and were controlled individually by the x- axis and y- axis, respectively. Two stabilization controllers were designed for each planar inverted pendulum; one based on the state space approach using Lie theoretic tools, and the other via a simple nonlinear feedback controller. A special sensor system was developed for the contact-less measurement of the inclination angles of the pendulum. The system consists of a small magnet placed at the bottom of the pendulum, and a magneto-resistive sensor on the surface of experimental platform. Experimental results showed the feasibility of the whole system and the advantages and disadvantages of these two control strategies are provided.

The second part of this research project involved the building of a swinging up and then stabilization system for a l-DOF inverted pendulum. An energy feedback control strategy was developed to regulate the swinging energy of the pendulum. The resulting closed-loop system converged to the reference energy which is needed for bringing the pendulum from its dangling position to an upright position. The swinging up strategy was switched to a LQR control when inclination angle of the pendulum reached a feasible range near the upright position and then the pendulum was maintained at its steady balanced state.

The hardware and software packages developed in this research project were available for engineering graduate students who wish to establish and compare the practical advantages and limitations of various design methodologies.