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Article

Generalised Proportional Integral Control for Magnetic Levitation Systems Using a Tangent Linearisation Approach

1
Escuela Técnica Superior de Ingenieros Industriales de Albacete, Universidad de Castilla-La Mancha, 02071 Albacete, Spain
2
Grupo de Investigación Tecnológico en Energías Renovables Marinas (GIT-ERM), Escuela Técnica Superior de Ingenieros Navales, Universidad Politécnica de Madrid, Avda. Memoria 4, 28040 Madrid, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Carlos Llopis-Albert
Mathematics 2021, 9(12), 1424; https://doi.org/10.3390/math9121424
Received: 17 April 2021 / Revised: 9 June 2021 / Accepted: 16 June 2021 / Published: 19 June 2021
(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)
This paper applies a robust generalised proportional integral (GPI) controller to address the problems of stabilisation and position tracking in voltage-controlled magnetic levitation systems, with consideration of the system’s physical parameters, non-linearities and exogenous disturbance signals. The controller has been developed using as a basis a model of the tangent linearised system around an arbitrary unstable equilibrium point. Since the approximate linearised system is differentially flat, it is therefore controllable. This flatness gives the resulting linearised system a relevant cascade characteristic, thus allowing simplification of the control scheme design. The performance of the proposed GPI controller has been analysed by means of numerical simulations and compared with two controllers: (i) a standard proportional integral derivative (PID) control, and (ii) a previously designed exact feedforward-GPI controller. Simulation results show that the proposed GPI control has a better dynamic response than the other two controllers, along with a better performance in terms of the integral squared tracking error (ISE), the integral absolute tracking error (IAE), and the integral time absolute tracking error (ITAE). Finally, experimental results have been included to illustrate the effectiveness of the proposed controller in terms of position stabilisation and tracking performance when appreciable non-linearities and uncertainties exist in the underlying system. Comparative graphs and metrics have shown a superior performance of the proposed GPI scheme to control the magnetic levitation platform. View Full-Text
Keywords: magnetic levitation systems; generalised proportional integral (GPI) control; robust output feedback control; tangent linearisation magnetic levitation systems; generalised proportional integral (GPI) control; robust output feedback control; tangent linearisation
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MDPI and ACS Style

Belmonte, L.M.; Segura, E.; Fernández-Caballero, A.; Somolinos, J.A.; Morales, R. Generalised Proportional Integral Control for Magnetic Levitation Systems Using a Tangent Linearisation Approach. Mathematics 2021, 9, 1424. https://doi.org/10.3390/math9121424

AMA Style

Belmonte LM, Segura E, Fernández-Caballero A, Somolinos JA, Morales R. Generalised Proportional Integral Control for Magnetic Levitation Systems Using a Tangent Linearisation Approach. Mathematics. 2021; 9(12):1424. https://doi.org/10.3390/math9121424

Chicago/Turabian Style

Belmonte, Lidia M., Eva Segura, Antonio Fernández-Caballero, José A. Somolinos, and Rafael Morales. 2021. "Generalised Proportional Integral Control for Magnetic Levitation Systems Using a Tangent Linearisation Approach" Mathematics 9, no. 12: 1424. https://doi.org/10.3390/math9121424

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