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.

Issue Section:
Research Papers
Topics:
Control algorithms, Dynamics (Mechanics), Equilibrium (Physics), Pendulums, Stability, Algorithms, Robots

References

1.
Spong
,
M. W.
,
1994
, “
The Control of Underactuated Mechanical Systems I
,”
Conferencia Internacional de Mecatrónica
, México, DF.
2.
Fantoni
,
I.
, and
Lozano
,
R.
,
2002
,
Non-Linear Control for Underactuated Mechanical System
,
Springer
,
New York
.
3.
Ordaz
,
P.
,
Domínguez-Ramírez
,
O.
, and
Espinoza
,
E.
,
2008
, “
Control Based on Energy for Vertical 2 Link Underactuated Robots
,”
International Conference on Control
, UK.
4.
Maneeratanaporn
,
J.
, and
Murakami
,
T.
,
2012
, “
Anti-Sway Sliding-Mode With Trolley Disturbance Observer for Overhead Crane System
,”
International Workshop on Advanced Motion Control
, Sarajevo, Bosnia, March 25–27, pp. 1–6.
5.
Muskinja
,
N.
, and
Tovornik
,
B.
,
2006
, “
Swinging Up and Stabilization of a Real Inverted Pendulum
,”
IEEE Trans. Ind. Electron.
,
53
(
2
), pp. 631–639.10.1109/TIE.2006.870667
6.
Qing
,
X.
, and
Shu
,
C.
,
2002
,
Theory and Implementation of Fuzzy Control Scheme for Pendubot
,
Triennial World Congress
,
Barcelona, Spain
.
7.
Siuka
,
A.
, and
Schoberl
,
M.
,
2009
, “
Applications of Energy Based Control Methods for the Inverted Pendulum on a Cart
,”
Rob. Auton. Syst.
,
57
(
10
), pp.
1012
–
1017
.10.1016/j.robot.2009.07.016
Google Scholar
Crossref
Search ADS
 
8.
Zhong
,
W.
, and
Rock
,
H.
,
2001
, “
Energy and Passivity Based Control of the Double Inverted Pendulum on a Cart
,”
International Conference on Control Applications
, Mexico City, México, pp.
5
–
7
.
9.
Albahkali
,
T.
,
Mukherjee
,
R.
, and
Das
,
T.
,
2009
, “
Swing-Up Control of the Pendubot: An Impulse-Momentum Approach
,”
IEEE Trans. Rob.
,
25
(
4
), pp.
975
–
982
.10.1109/TRO.2009.2022427
Google Scholar
Crossref
Search ADS
 
10.
Ordaz
,
P.
, and
Poznyak
,
A.
,
2012
, “
The Furuta's Pendulum Stabilization Without the use of a Mathematical Model: Attractive Ellipsoid Method With KL-Adaptation
,”
51st IEEE Conference on Decision and Control
, Maui, HI, pp.
7285
–
7290
.
11.
Zhang
,
M.
, and
Tarn
,
T.-J.
,
2002
, “
Hybrid Control of the Pendubot
,”
IEEE/ASME Trans. Mechatron.
,
7
(
1
), pp.
79
–
86
.10.1109/3516.990890
Google Scholar
Crossref
Search ADS
 
12.
Åström
,
K. J.
, and
Furuta
,
K.
,
2000
, “
Swinging Up a Pendulum by Energy Control
,”
Automatica
,
36
, pp.
287
–
295
.10.1016/S0005-1098(99)00140-5
Google Scholar
Crossref
Search ADS
 
13.
Ordaz
,
P.
,
Santos
,
O.
, and
Lopez
,
V.
,
2012
, “
Toward a Generalized Sub-Optimal Control Method of Underactuated Systems
,”
Optim. Control Appl. Methods
,
33
(
3
), pp.
338
–
351
.10.1002/oca.999
Google Scholar
Crossref
Search ADS
 
14.
Bortoff
,
S. A.
,
1996
, “
Robust Swing-Up Control for a Rotational Double Pendulum
,” IFAC 96, Preprints 13th World Congress of IFAC, San Francisco, CA, Vol. F, pp.
413
–
419
.
15.
Xin
,
X.
,
She
,
J.-H.
,
Yamasaki
,
T.
, and
Liu
,
Y.
,
2009
, “
Swing-Up Control Based on Virtual Composite Links for n-Link Underactuated Robot With Passive First Joint
,”
Automatica
,
45
, pp.
1986
–
1994
.10.1016/j.automatica.2009.04.023
Google Scholar
Crossref
Search ADS
 
16.
Spong
,
M.
,
Hutchinson
,
S.
, and
Vidyasagar
,
M.
,
2006
,
Robot Modeling and Control
,
John Wiley & Sons, Inc.
, Hoboken, NJ.
17.
Athans
,
M.
, and
Falb
,
P. L.
,
1966
,
Optimal Control: An Introduction to the Theory and its Applications
,
McGraw-Hill
,
New York
.
18.
Poznyak
,
A.
, 2010,
Advanced Mathematical Tools for Automatic Control Engineers: Deterministic Techniques
,
Elsevier
,
New York
, Vol.
1
.
19.
Takeshi
,
T.
,
1990
,
Stability Theorems of Perturbed Linear Ordinary Differential Equations
,
J. Math. Anal. Appl.
,
149
, pp.
583
–
598
.10.1016/0022-247X(90)90064-M
Google Scholar
Crossref
Search ADS
 
20.
Cazzolato
,
B.
, and
Prime
,
Z.
,
2011
, “
On the Dynamics of the Furuta Pendulum
,”
J. Control Sci. Eng.
,
2011
, p. 52834110.1155/2011/528341.
Copyright © 2014 by ASME
You do not currently have access to this content.