PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES
Abstract
A cubic Bezier curve formulation is used for generating phase portrait of an inverted pendulum system. Assuming that the cart and pendulum masses, pendulum length, and friction coefficient values in the inverted pendulum model are unknown, its finite number of experimentally obtained trajectories are utilized as a basis for generating the experimentally unavailable trajectories. It is shown that both the experimentally obtained and the remaining computationally generated trajectories can be formulated as an overlapping sequence of cubic Bezier curves in a computationally efficient manner. In the case of having no model of system dynamics, cubic Bezier curve formulation accurately relates experimentally obtained trajectories to the computationally generated trajectories corresponding to different initial conditions. A case study presented in this manuscript verifies that the computational approach using a cubic Bezier curves formulation has far better approximation performance compared to the ones obtained by the linear interpolation.
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