What led to the novel ideas, some of them theoretical, presented in this paper is our highly experimental approach to nonlinear control. We actually designed and fabricated a two-link inverted pendulum, and learned about the relationships and the trade offs that exist in such a device. In the context of controlling an inverted pendulum, the novel ideas presented in this paper relate to i) the design of a fuzzy logic controller; ii) the design of a neuralnetwork controller; and iii) experimental implementation of a nonlinear controller based on differential-geometric notions; etc. etc. These novel ideas are presented in a comparative setting. The comparative study presented compares, experimentally and by simulation, five different control schemes. We compare 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. We do this by defining an effectiveness coefficient that is the ratio of the portion of the size of the controllable region to the size of the overall space as spanned by the position variables. Our overall conclusion may be summarized by the following values of the effectiveness coefficient for the five different control schemes: Simulation Experiment PD Controller: 0.324 0.022 Linear Quadratic Controller: 0.524 0.234 Neural Network Controller: 0.785 0.272 Non-linear Controller: 0.248 0.203 Fuzzy Logic Controller: 0.349 0.262 It is interesting to note that 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.
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