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Open AccessFeature PaperArticle

Discrete-Inverse Optimal Control Applied to the Ball and Beam Dynamical System: A Passivity-Based Control Approach

1
Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Carrera 7 No. 40B-53, Bogotá, D.C 11021, Colombia
2
Laboratorio Inteligente de Energía, Universidad Tecnológica de Bolívar, km 1 vía Turbaco, Cartagena 131001, Colombia
3
Grupo GIIEN, Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Campus Robledo, Medellín 050036, Colombia
4
Facultad de Ciencias Básicas, Universidad Tecnológica de Pereira, Pereira 660003, Colombia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(8), 1359; https://doi.org/10.3390/sym12081359
Received: 5 August 2020 / Accepted: 12 August 2020 / Published: 14 August 2020
(This article belongs to the Special Issue Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems)
This express brief deals with the problem of the state variables regulation in the ball and beam system by applying the discrete-inverse optimal control approach. The ball and beam system model is defined by a set of four-order nonlinear differential equations that are discretized using the forward difference method. The main advantages of using the discrete-inverse optimal control to regulate state variables in dynamic systems are (i) the control input is an optimal signal as it guarantees the minimum of the Hamiltonian function, (ii) the control signal makes the dynamical system passive, and (iii) the control input ensures asymptotic stability in the sense of Lyapunov. Numerical simulations in the MATLAB environment allow demonstrating the effectiveness and robustness of the studied control design for state variables regulation with a wide gamma of dynamic behaviors as a function of the assigned control gains. View Full-Text
Keywords: discrete-inverse optimal control; ball and beam dynamical system; asymptotic stability; passivity-based analysis; Hamiltonian and Lagrangian functions; state variables regulation discrete-inverse optimal control; ball and beam dynamical system; asymptotic stability; passivity-based analysis; Hamiltonian and Lagrangian functions; state variables regulation
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MDPI and ACS Style

Danilo Montoya, O.; Gil-González, W.; Ramírez-Vanegas, C. Discrete-Inverse Optimal Control Applied to the Ball and Beam Dynamical System: A Passivity-Based Control Approach. Symmetry 2020, 12, 1359. https://doi.org/10.3390/sym12081359

AMA Style

Danilo Montoya O, Gil-González W, Ramírez-Vanegas C. Discrete-Inverse Optimal Control Applied to the Ball and Beam Dynamical System: A Passivity-Based Control Approach. Symmetry. 2020; 12(8):1359. https://doi.org/10.3390/sym12081359

Chicago/Turabian Style

Danilo Montoya, Oscar; Gil-González, Walter; Ramírez-Vanegas, Carlos. 2020. "Discrete-Inverse Optimal Control Applied to the Ball and Beam Dynamical System: A Passivity-Based Control Approach" Symmetry 12, no. 8: 1359. https://doi.org/10.3390/sym12081359

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