*Article* **An Adaptive Controller Design for Nonlinear Active Air Suspension Systems with Uncertainties**

**Jinhua Zhang , Yi Yang and Cheng Hu \***

School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China **\*** Correspondence: c\_hu@gzhu.edu.cn

**Abstract:** Active air spring suspensions can improve the vehicle ride comfort and meanwhile realize the vehicle height regulation, and therefore, they have been widely used and studied. However, to achieve better ride comfort and a satisfactory vehicle body height adjustment, the active air suspension controller becomes an indispensable and significant part of the system. Since the nonlinear suspension system possesses uncertainties, it is difficult to take into account both ride comfort and height regulation. This study innovatively proposes an adaptive control algorithm to specifically address the problem of vehicle height regulation and ride comfort for nonlinear active air suspension systems with uncertainties. The accurate tracking to reference vehicle body height curves is realized, and the ride comfort is also improved. Through simulations with two scenarios, it is illustrated that the active air suspension controller owns better control effectiveness than the PID controller. Compared with the PID controller, the designed controller can track the reference vehicle body height curves faster and more accurately. The result also verifies the priority of the designed controller.

**Keywords:** active air suspension; nonlinear systems; uncertainties; adaptive control; Lyapunov stability

**MSC:** 93-10

**Citation:** Zhang, J.; Yang, Y.; Hu, C. An Adaptive Controller Design for Nonlinear Active Air Suspension Systems with Uncertainties. *Mathematics* **2023**, *11*, 2626. https://doi.org/10.3390/ math11122626

Academic Editors: Camelia Petrescu and Valeriu David

Received: 22 April 2023 Revised: 6 June 2023 Accepted: 7 June 2023 Published: 8 June 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
