Non-linear Control of Inverted Pendulum

Presented is a study of non-linear control for an inverted pendulum system. The inverted pendulum system is a great example of an underactuated, non-minimum phase, and highly unstable system. The objective of this research paper is to derive non-linear control laws for an inverted pendulum system. First, dynamic equations of the inverted pendulum are derived by utilizing the Lagrange's equations and then it is linearized around an unstable upright position. Secondly, the corresponding analysis uses the standard linear stability arguments and the traditional Lyapunov method. The non-linear sliding mode control and feedback linearization control laws are then derived The feedback linearization control law is used to transform the non-linear system into an equivalent linear system such that a suitable feedback control law can be proposed. The stabilization of the initial condition and reference tracking is studied in this paper. I demonstrate the effectiveness of the proposed non-linear control strategies using MATLAB/Simulink software.