The inverted pendulum error analysis with MATLAB simulation and validation

Abstract

This article contains error analysis and stability margin study by using linear and non-linear model analysis. The dynamic differential equation is established to study the state of parameters and to simulate the system; then the error between the linear and non-linear system is performed. The result indicated a 12° deflection angle of the inverted pendulum is an acceptable margin of simulation. Invert pendulum problem is a classical example in the traditional control theory. To simplify the mathematical analysis, a linear approximation is introduced which generates error from the original non-linear mathematical model. The discussion in this article provides specific quantitative error deviation between the linear model and non-linear model. This article is focused to find the relationship between control error and the linearity angle within 12 degrees. By comparing the linear model and the original non-linear model, and using PID control method to verify the presumed maximum angular range, we obtain the comparison of performance between the two mathematical models and draw the results in this article.