Acosta Rodríguez, José ÁngelOrtega, RomeoAstolfi, AlessandroMahindrakar, A.D.2025-09-022025-09-022005-12Acosta Rodríguez, J.Á., Ortega, R., Astolfi, A. y Mahindrakar, A.D. (2005). Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one. IEEE Transactions on Automatic Control, 50 (12), 1936-1955.https://doi.org/10.1109/TAC.2005.860292.00189286https://hdl.handle.net/11441/176586Interconnection and damping assignment passivity-based control is a new controller design methodology developed for (asymptotic) stabilization of nonlinear systems that does not rely on, sometimes unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with a desired energy function - that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. We prove in this paper that for a class of mechanical systems with underactuation degree one the partial differential equations can he explicitly solved. Furthermore, we introduce a suitable parametrization of assignable energy functions that provides the designer with a handle to address transient performance and robustness issues. Finally, we develop a speed estimator that allows the implementation of position-feedback controllers. The new result is applied to obtain an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling, and a controller for the pendulum in a cart that can swing-up the pendulum from any position in the upper half plane and stop the cart at any desired location. In both cases we obtain very simple and intuitive position-feedback solutions. © 2005 IEEE.application/pdf20 p.engEnergy shapingHamiltonian systemsNonlinear-controlPassivityUnderactuated mechanical systemsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1109/TAC.2005.860292