# An Observer-Based Active Fault Tolerant Controller for Vehicle Suspension System
## 1 Introduction  
Over the past decades, vehicle suspension design has become an important research topic due to their attribution to improving ride comfort and handling stability of the vehicle body. Generally, the suspension system can be categorized into three types as passive suspension, semi-active suspension, and active suspension systems [1; 2]. Passive suspensions comprise springs and dampers installed between the vehicle body and the wheel axle, which can achieve good ride comfort or good road holding since these two criteria conflict with each other. Semi-active suspensions can offer better improvement by adjusting their variable damping coefficients and just needs lower power consumption. It should be noted that electrorheological and magnetorheological fluid dampers are usually preferred in semi-active suspension systems. In the active suspension system, an additional actuator (linear motor, hydraulic cylinder, etc.) is installed to suppress its vibrations caused by the road irregularities. As compared with the passive suspension, the semi-active and active suspension are more easily combined with the advanced control algorithms such as \(H_{\infty}\) control [3; 4], sliding-mode control [5], adaptive backstepping control [6; 7], T-S fuzzy control [8; 9], and nonlinear control [10; 11], wherein a good trade-off between the two conflicting suspension performances as ride quality and handling stability can be made. However, these control schemes are all based on the assumption that all of the components of vehicle suspension system work under the non-fault model, which is inconsistent with the actual application scenario [12; 13] in some ways. With the growing demand for safety, reliability, and maintainability in the vehicle suspension system, it is necessary to develop a comprehensive fault-tolerant control (FTC) scheme to maintain a desirable system performance whether there occurs a fault in active suspension system or not. It is well demonstrated in the previous studies [14; 15] that FTC possesses the ability to accommodate failures automatically and then maintains a stability and sufficient level of system performance. In general, there are two types of fault-tolerant control approaches named as thepassive and active ones. It should be noted that these two fault-tolerant control methods usually employ different design methodologies for the same control plants and will result in some unique properties. On the one side, for the development of the passive FTC scheme, a robust controller is often designed to deal with all the underlying faults. For instance, the authors in [16] proposed a sliding mode fault-tolerant control scheme for a nonlinear system guaranteeing the asymptotic stability of the control system under faults, yet it still possessed disadvantages like large chattering, which imposes some restrictions in its practical applications. In addition to this, a robust \(H_{\infty}\) fault tolerant controller was developed to maintain the stability and constraint performance of an active suspension system with the bounded actuator faults [17]. Moreover, some related research can also be found in [18; 19]. Specifically, an adaptive fault tolerant controller is proposed in [20] for an active suspension system with unknown actuator faults, which ensures the boundedness of the vertical and pitch angle displacements. It was noted that the aforementioned passive FTC approaches were only reliable for the specific system faults encountered in the system operation, wherein the designed FTC may not possess a better control performance under all kinds of faults. On the other hand, when designing active FTC schemes, it is usually aimed at ensuring the system stability with an acceptable constraint performance by reconfiguring the on-line controller with the fault detection and diagnosis (FDD) system, which can estimate and compensate for the system fault and has been used in many areas [21; 22; 23; 24; 25; 26; 27].