Comparative Study of Motion Control Methods: A Case Study for a Nonlinear System

Abstract

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 neural-network controller; and iii) implementation of a nonlinear controller based on differential- geometric notions. These novel ideas are presented in a comparative setting where five different control schemes are compared: a proportional and derivative controller, a linear quadratic controller, a nonlinear controller, a neural network controller, and a fuzzy logic controller. The paper shows how the controllable portion of the four dimensional space of control variables changes with the different control schemes. This is done 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. The overall conclusion may be summarized by the following values of the effectiveness coefficient for the five different control schemes:

Keywords

Linear controller nonlinear controller neural controller fuzzy controller differential geometry.

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