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


Blankenstein, Guido and Ortega, Romeo and Schaft, Arjan J. van der (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

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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
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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