Matching in the method of controlled Lagrangians and IDA-passivity based control

Blankenstein, Guido and Ortega, Romeo and Schaft van der, Arjan J. (2006) Matching in the method of controlled Lagrangians and IDA-passivity based control. In: Nonlinear and Adaptive Control: Tools and Algorithms for the User. World Scientific, Singapore, pp. 79-114. ISBN 9781860946172

Preview

PDF
322Kb

Abstract:	This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler-Lagrange system, respectively Hamiltonian system, by searching for a stabilizing structure preserving feedback law. The conditions under which two Euler-Lagrange or Hamiltonian systems are equivalent under feedback are called the matching conditions (consisting of a set of nonlinear PDEs). Both methods are applied to the general class of underactuated mechanical systems and it is shown that the IDA-PBC method contains the controlled Lagrangians method as a special case by choosing an appropriate closed-loop interconnection structure. Moreover, explicit conditions are derived under which the closed-loop Hamiltonian system is integrable, leading to the introduction of gyroscopic terms. The $\lambda$ -method as introduced in recent papers for the controlled Lagrangians method transforms the matching conditions into a set of linear PDEs. In this paper the method is extended, transforming the matching conditions obtained in the IDA-PBC method into a set of quasi-linear and linear PDEs.
Item Type:	Book Section
Copyright:	© 2006 World Scientific
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Link to this item:	http://purl.utwente.nl/publications/66801
Export this item as:	BibTeX EndNote HTML Citation Reference Manager

Show download statistics for this publication

Repository Staff Only: item control page

Metis ID: 237838