IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 2, APRIL2015 675 Vibration Isolation for Active Suspensions With Performance Constraints and Actuator Saturation Weichao Sun, Student Member, IEEE, Huijun Gao, Fellow, IEEE, and Okyay Kaynak, Fellow, IEEE Abstract—This paper investigates the problem of vibration iso- lation for vehicle active suspension systems, where parameter un- certainties, external disturbances, actuator saturation, and per- formance constraints are considered in an unified framework. A constrained adaptive robust control technology is developed to not only stabilize the attitude of vehicle in the context of parameter un- certainties and external disturbances, but also cover the problems of actuator saturation and performance constraints. Furthermore, the performance analysis of the closed-loop systems is given, by means of rigorous mathematical derivations. Extensive compara- tive experimental results are obtained to illustrate the effectiveness of the proposed control law. Index Terms—Active suspension system, actuator saturation, adaptive control, performance constraints, robust control. I. INTRODUCTION V EHICLE suspension systems are of importance for con- tributing to the car’s handling and keeping vehicle occu- pants comfortable and reasonably well isolated from road noise, bumps, and vibrations, etc. [1]–[10]. Since an appropriate con- trol strategy for active suspension systems can enhance the ride comfort and vehicle handling and stability, this research area has remained attractive for many years [11]–[14]. Active sus- pension systems, apart from their basic task of carrying car body, are able to isolate the body as far as possible from road-induced chock and vibrations, provide comfort for passengers, and to maximize tire–road contact for enhanced vehicle handling and stability. Since the actuators pull down or push up together with the suspension motions, the limitations arising from this character should be taken into account, that is, while increasing the ride comfort, the suspension working space must be preserved. In Manuscript received December 18, 2013; revised March 11, 2014; accepted April 3, 2014. Date of publication May 20, 2014; date of current version October 24, 2014. Recommended by Technical Editor Y. Li. This work was supported in part by the National Natural Science Foundation of China under Grant 61333012 and Grant 61203035, in part by the Key Laboratory of Integrated Automation for the Process Industry, Northeast University, and in part by the Fundamental Research Funds for the Central Universities, China. W. Sun is with the State Key Laboratory of Robotics and System (HIT), Harbin Institute of Technology, Harbin 150080 China (e-mail: w.sun@hit.edu.cn). H. Gao is with the State Key Laboratory of Robotics and System (HIT), Harbin Institute of Technology, Harbin 150080, China, and also with King Abdulaziz University (KAU), Jeddah, Saudi Arabia (e-mail: hjgao@hit.edu.cn). O. Kaynak is with the Electrical and Electronic Engineering Depart- ment, Bogazici University, Bebek 80815, Istanbul, Turkey, and also with Harbin Institute of Technology, Harbin 150080, China (e-mail: okyay.kaynak@ boun.edu.tr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMECH.2014.2319355 order to guarantee the car safety, the uninterrupted contact of wheels to road should be ensured, namely, the dynamic tire deflection should be small. However, the aforementioned de- sign requirements are highly conflicting. For example, enhanc- ing ride comfort calls for larger suspension stroke and smaller damping of wheel-hop mode and hence leads to a degradation in vehicle handling and stability [15]. Many active suspension control approaches are proposed to manage the tradeoff be- tween conflicting requirements, and a large number of different arrangements has been investigated. In robust control, H ∞ and H 2 or the combination of both gives very satisfactory results, except for the fact that these studies are based on a linear model, while at high frequencies, some unmodeled nonlinearities will rise up [16]. Regarding nonlinear control strategies, a sliding mode controller is used by [17], [18] and gives good closed- loop results. Another nonlinear controller that can be used is based on the backstepping technology as in [19], and the con- troller gives very good results, but performance requirements such as road holding and actuator saturation are not considered in the controller design. Another problem to be noted is actuator saturation. Ac- tuator saturation appears frequently in engineering systems, which is also a source of performance degradation and the closed-loop system instability [20]–[25]. Therefore, the anal- ysis and synthesis of control systems with actuator saturation have been a highlighted research topic in the industry, especially for vehicle suspension systems, where performance constraints and inevitable uncertainties are involved in saturation prob- lem, which will bring considerable difficulties in the process of controller design. In conclusion, it seems to be a meaningful work to develop a novel control law for nonlinear uncertain ac- tive suspensions, considering necessary performance constraints and possible actuator saturation, which motivates our present study. Compared with the existing results, most of which just con- sider partial performances, this paper proposes a constrained adaptive robust control strategy for vehicle active suspension systems to improve the ride comfort in the presence of parame- ter uncertainties and external disturbances, where performance constraints and actuator saturation are considered simultane- ously. Inspired by [24], [26]–[28], this paper converts the mul- tiobjective control of active suspensions into a constrained and saturated tracking problem, such that the closed-loop suspen- sion systems are able to stabilize the vertical motion of vehicle in the context of the system with parameter uncertainties and ex- ternal disturbances on one hand, and on the other, the actuator 1083-4435 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.