TY - JOUR
T1 - The Lyapunov direct method for the stabilisation of the ball on the actuated beam
AU - Aguilar-Ibanez, Carlos
N1 - Funding Information:
The author wants to thank to the IPN, SIP, COFAA and CIC for supporting this work under the research grant 20091430. Also, the author is thankful for the reviewers’ comments that helped to improve the quality of this work.
PY - 2009/12
Y1 - 2009/12
N2 - This article deals with the stabilisation of a ball on an actuated beam independently of whether or not the force acts on the non-actuated coordinate. The feedback control law is deduced via application of the traditional Lyapunov stability method. The balancing strategy consists of shaping a convenient energy function that allows us to derive the required asymptotic stabilising controller. To this end, we introduce an auxiliary control input variable in order to algebraically obtain the kinetic metric and the potential energy of the entire system. The formed positive energy function along with the proposed feedback controller assures that the overall system is a dissipative one.
AB - This article deals with the stabilisation of a ball on an actuated beam independently of whether or not the force acts on the non-actuated coordinate. The feedback control law is deduced via application of the traditional Lyapunov stability method. The balancing strategy consists of shaping a convenient energy function that allows us to derive the required asymptotic stabilising controller. To this end, we introduce an auxiliary control input variable in order to algebraically obtain the kinetic metric and the potential energy of the entire system. The formed positive energy function along with the proposed feedback controller assures that the overall system is a dissipative one.
KW - Euler-Lagrange equations
KW - Lyapunov direct method
KW - Lyapunov stability
KW - Under-actuated mechanical systems
UR - http://www.scopus.com/inward/record.url?scp=70449109960&partnerID=8YFLogxK
U2 - 10.1080/00207170902874033
DO - 10.1080/00207170902874033
M3 - Artículo
SN - 0020-7179
VL - 82
SP - 2169
EP - 2178
JO - International Journal of Control
JF - International Journal of Control
IS - 12
ER -