Comparative study of motion control methods for a nonlinear system

We designed and fabricated a two-link inverted pendulum, and learned about the relationships and the tradeoffs that exist in it. In the context of controlling an inverted pendulum, the ideas presented relate to i) the design of a fuzzy logic controller; ii) the design of a neural-network controller; and iii) experimental implementation of a nonlinear controller based on differential-geometric notions. A comparative study presented compares five different control schemes; a PD controller, a linear quadratic controller, a nonlinear controller, a neural network controller and a fuzzy logic controller. We show how the controllable portion of the four dimensional space of control variables changes with the different control schemes. While the superiority of the neural network controller is borne out by both the simulations and the experiments, the former overemphasizes the advantage by a wide margin. Also the simulation study would have us believe that a linear quadratic controller should be our second best choice, a conclusion not supported by actual experiments. The differences between the experiments and the simulations can be attributed to the difficulty of capturing in a simulation phenomena such as friction, motor dynamics. etc