Grey-box modeling of an inverted pendulum system via identification of a PD-LTI system

Abstract

A rotary-type unstable inverted pendulum system is modeled by means of a parameter-dependent lineartime-invariant (PD-LTI) system. The pendulum systems operating at upright and downright positions are modeled by a PD-LTI system with a scheduling parameter that is fixed in each operation. The unknown parameters are estimated by taking a grey-box modeling approach to the pendulum system operating at the downright position. The obtained model is verified by designing an H ∞ controller.

Grey-box Modeling of an Inverted Pendulum System Based on PD-LTI System

“…We derive a PD-LTI system from the rotary-type pendulum systems at the upright and downright positions, by using (8) and (14).…”

“…We will further verify the model by designing a stabilizing controller. It should be noted that the material of this paper was partially presented at SSS'15 [14], and the difference between the manuscript and this paper is to consider how to choose a model structure by taking numerical condition into account. Also, the partial idea of taking numerical conditions into account has been presented by the authors [15] but has not described models for the system in this paper.…”