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In this paper, we propose the nonlinear feedback controller design based on the phase plane behavior. The controller is to minimize the difference of two vector fields: the nonlinear closed-loop vector fields and the stabilized closed-loop vector fields of linear approximation with linear controller. The stability of the controller is guaranteed by considering the Lyapunov function on the phase plane. The effectiveness of the proposed controller is shown by the simulation of a general inverted pendulum. The results show that the stabilized domain is extended. In this model, we use the coordinate transform to extend the stabilized domain further.

Nonlinear Feedback Controller Design Based on a Geometric Consideration in the Phase Plane Behavior for Single Input Nonlinear System