Nonlinear Controller for an Inverted Pendulum Using the Trigonometric Function

Abstract

In this paper, a nonlinear controller (TR) for an inverted pendulum using the trigonometric function is presented. The TR controller is a new proposal, which is represented by a simple mathematical formula. TR operation does not require complex calculations, so it can be applied even to the simplest microcontrollers. Tuning the TR controller is very simple, and the range of stable operation is very wide. Simulation tests of the TR controller showed that the controller is effective even for deviations exceeding 50∘. The TR controller tests were compared to the results of a PID controller. The TR controller is designed to stabilise an inverted pendulum in the equilibrium point, a state in which the pendulum is in a upright position. Stabilisation for other deflection-angle set points was not taken into account. During the research, steps were taken to simulate phenomena characteristic of real solutions. An inertial block and a disturbance were introduced into the test system. Despite the introduced difficulties, the TR controller effectively stabilised the pendulum without the need to retune the controller settings. Consequently, the TR controller is an attractive alternative to previously applied solutions for the stabilisation of an inverted pendulum.