A multivariable adaptive control approach for stabilization of a cart-type double inverted pendulum
type: Item
instance of: scholarly article
title: A multivariable adaptive control approach for stabilization of a cart-type double inverted pendulum
zbMATH Open document ID: 1213.93113
DOI: 10.1155/2011/970786
author: A. Nejadfard
author: M. Zadi
author: Iraj Hassanzadeh
published in: Mathematical Problems in Engineering
publication date: 2011-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/222635
review text: Summary: This paper considers the design and practical implementation of linear-based controllers for a cart-type double inverted pendulum (DIPC). A constitution of two linked pendulums placed on a sliding cart, presenting a three Degrees of Freedom and single controlling input structure. The controller objective is to keep both pendulums in an up-up unstable equilibrium point. Modeling is based on the Euler-Lagrange equations, and the resulted nonlinear model is linearized around up-up position. First, the LQR method is used to stabilize DIPC by a feedback gain matrix in order to minimize a quadratic cost function. Without using an observer to estimate the unmeasured states, in the next step we make use of LQG controller which combines the Kalman-Bucy filter estimation and LQR feedback control to obtain a better steady-state performance, but poor robustness. Eventually, to overcome the unknown nonlinear model parameters, an adaptive controller is designed. This controller is based on Model Reference Adaptive System (MRAS) method, which uses the Lyapunov function to eliminate the defined state error. This controller improves both the steady-state and disturbance responses.
Mathematics Subject Classification ID: 93C42
zbMATH DE Number: 5904931
MaRDI profile type: Publication
OpenAlex ID: W2075020434
Wikidata QID: Q58693681
cites work: Q4353661
cites work: Q4401802
cites work: Nonlinear systems.
description: scientific article; zbMATH DE number 5904931