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Research Papers

# Research on Swing up Control Based on Energy for the Pendubot System

[+] Author and Article Information
Patricio Ordaz

Research Laboratory,
Polytechnic University of Pachuca,
Pachuca, Hidalgo, México 43830
e-mail: patricio@upp.edu.mx

Eduardo S. Espinoza

Research Laboratory,
Polytechnic University of Pachuca,
Pachuca, Hidalgo, México 43830
e-mail: steed@upp.edu.mx

Filiberto Muñoz

Research Laboratory,
Polytechnic University of Pachuca,
Pachuca, Hidalgo, México 43830
e-mail: mupafi@upp.edu.mx

Here, the parameters represented as $θi∀i=1,..,p$ are given by classical regressor form: $D(x1)+C(x)x2+G(x1)=φ(x)θ=τ,φ(x)∈Rn×p,θ∈Rp$ in this case, the parameter $θi$ is constant and p = 5, moreover this one is not an angular position.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 20, 2013; final manuscript received January 31, 2014; published online April 11, 2014. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 136(4), 041018 (Apr 11, 2014) (8 pages) Paper No: DS-13-1242; doi: 10.1115/1.4026658 History: Received June 20, 2013; Revised January 31, 2014

## Abstract

In this paper, we present a class of nonlinear control scheme for swinging up and stabilization of an underactuated two-link robot called as Pendubot. The main objective of this paper is to present a switched control that swing up and stabilize for almost all combination of initial states given on the four equilibrium points of the double underactuated pendulum. The proposed methodology is based on two control strategies to swing up and stabilize the Pendubot system. The first one is based on Lagrangian dynamics, energy analysis, and stability theory, while the second one is based on linear quadratic regulator. Moreover, here we present a stability analysis of the switched control algorithm. In order to verify the proposed control strategy, experimental results were performed.

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## References

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## Figures

Fig. 1

The experimental environment

Fig. 2

First Pendubot's control objective

Fig. 3

Second Pendubot's control objective

Fig. 6

Pendubot's trajectories of second control shaping, from mid-up position to upright one

Fig. 7

Pendubot's trajectories of second control shaping, from mid-up position to upright one

Fig. 4

Pendubot's trajectories of first control shaping, from low position to upright one

Fig. 5

Pendubot's trajectories of first control shaping, from low position to upright one

## Errata

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