Optimization of the State of an Inverted Pendulum System Using Kalman Filter in the Presence of Gaussian and Poisson Noise

Pourmir, Mohammadreza

doi:10.22034/cas.2025.496057.1045

Optimization of the State of an Inverted Pendulum System Using Kalman Filter in the Presence of Gaussian and Poisson Noise

Document Type : Original Article

Author

Mohammadreza Pourmir

Computer Engineering Department, Faculty of Engineering, University of Zabol, Zabol, Iran

https://doi.org/10.22034/cas.2025.496057.1045

Abstract

The inverted pendulum problem is an interesting equilibrium problem because the uncontrolled system is unstable and if the base does not move to maintain the vertical position, the pendulum will simply fall and its dynamics are also nonlinear. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) solution of the least squares' method. The Kalman filter supports the estimation of past, present, and even future states, and can perform the estimation well even when the exact nature of the modeled system is unknown. This paper aims to estimate the state of the system to optimize the state created by the base in the inverted pendulum problem model so that the pendulum remains in the upright state. The generated random noise signals are added to the real measurement data generated using the system dynamics and these data are used to estimate the system states using the Kalman filter and the extended Kalman filter. The results of these estimates are analyzed and compared.

Graphical Abstract