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Volume 11
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10.3390/math11041067
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Article

A Differential Flatness-Based Model Predictive Control Strategy for a Nonlinear Quarter-Car Active Suspension System

by
Daniel Rodriguez-Guevara
1,
Antonio Favela-Contreras
1,*,
Francisco Beltran-Carbajal
2,
Carlos Sotelo
1 and
David Sotelo
1
1
Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Mexico
2
Departamento de Energía, Universidad Autónoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa Tamaulipas, Mexico City 02200, Mexico
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(4), 1067; https://doi.org/10.3390/math11041067
Submission received: 25 January 2023 / Revised: 9 February 2023 / Accepted: 11 February 2023 / Published: 20 February 2023
(This article belongs to the Special Issue Mathematical Methods for Nonlinear Control)
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Abstract

Controlling an automotive suspension system using an actuator is a complex nonlinear problem that requires both fast and precise solutions in order to achieve optimal performance. In this work, the nonlinear model of a quarter-car active suspension is expressed in terms of a flat output and its derivatives in order to embed the nonlinearities of the system in the flat output. Afterward, a Model Predictive Controller based on the differential flatness derivation (MPC-DF) of the quarter-car is proposed in order to achieve optimal control performance in both passenger comfort and road holding without diminishing the lifespan of the wheel. This formulation results in a linear optimization problem while maintaining the nonlinear behavior of the active suspension system. Afterward, the optimization problem is solved by means of Quadratic Programming (QP), enabling real-time implementation. Simulation results are presented using a realistic road disturbance to show the effectiveness of the proposed control strategy.
Keywords: differential flatness; model predictive control; automotive suspension; nonlinear control; predictive control; optimal control differential flatness; model predictive control; automotive suspension; nonlinear control; predictive control; optimal control

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MDPI and ACS Style

Rodriguez-Guevara, D.; Favela-Contreras, A.; Beltran-Carbajal, F.; Sotelo, C.; Sotelo, D. A Differential Flatness-Based Model Predictive Control Strategy for a Nonlinear Quarter-Car Active Suspension System. Mathematics 2023, 11, 1067. https://doi.org/10.3390/math11041067

AMA Style

Rodriguez-Guevara D, Favela-Contreras A, Beltran-Carbajal F, Sotelo C, Sotelo D. A Differential Flatness-Based Model Predictive Control Strategy for a Nonlinear Quarter-Car Active Suspension System. Mathematics. 2023; 11(4):1067. https://doi.org/10.3390/math11041067

Chicago/Turabian Style

Rodriguez-Guevara, Daniel, Antonio Favela-Contreras, Francisco Beltran-Carbajal, Carlos Sotelo, and David Sotelo. 2023. "A Differential Flatness-Based Model Predictive Control Strategy for a Nonlinear Quarter-Car Active Suspension System" Mathematics 11, no. 4: 1067. https://doi.org/10.3390/math11041067

APA Style

Rodriguez-Guevara, D., Favela-Contreras, A., Beltran-Carbajal, F., Sotelo, C., & Sotelo, D. (2023). A Differential Flatness-Based Model Predictive Control Strategy for a Nonlinear Quarter-Car Active Suspension System. Mathematics, 11(4), 1067. https://doi.org/10.3390/math11041067

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