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In this paper, the problem of fault estimation and fault-tolerant control for half-car active suspension system with simultaneous varying sprung and unsprung mass, actuator fault, and sensor fault is investigated. First, Takagi-Sugeno fuzzy approach is used to describe the uncertain half-car active suspension system with simultaneous actuator fault and sensor fault. Then, a novel augmented descriptor sliding mode observer is designed to estimate the state of system, actuator fault, and sensor fault with good precision. Based on the state and fault estimation, a fault-tolerant sliding mode control scheme is designed to stabilize the resulting fault half-car active suspension system. By utilizing Lyapunov stability theory, the existence condition for the proposed sliding mode observer and fault-tolerant sliding mode controller is provided in terms of linear matrix inequalities (LMIs). In addition, it is shown that the reachability of the developed sliding surface can be ensured under the design control law.Finally, simulation results for uncertain half-car active suspension systems are presented to demonstrate the effectiveness of the proposed design techniques. KEYWORDSfault estimation, fault-tolerant control, sliding mode control, T-S fuzzy system, uncertain half-car active suspension system *Nomenclature: , pitch angle; b 1 , distance between the front axle and the center of mass; b 2 , distance between the rear axle and the center of mass; cf and c r , stiffness of the passive elements of front wheel and rear wheel, respectively; I 2 , mass moment of inertia for the pitch motions; K 2f and K 2r , front and rear suspension spring stiffness, respectively; M 2 , car body mass; m 1f and m 1r , front and rear unsprung masses, respectively; u f (t) and u r (t), front actuator and rear actuator force inputs, respectively; Z 2 , car body displacement; Z 0f and Z 0r , road inputs related to the front and rear wheel, respectively; Z 1f and Z 1r , mass displacement of front and the rear unsprung, respectively; Z 2f and Z 2r , mass displacement of front and rear body, respectively.

A knee exoskeleton with an adaptive instantaneous rotation center and impact absorption is used for rehabilitation. Due to the human knee joint’s special physiological structure and motion characteristics, the exoskeleton mechanism needs to be designed for both static and dynamic aspects. Therefore, a novel knee exoskeleton mechanism was designed. To adapt to the rotation center of the knee joint, a mechanism with cross-configuration was designed according to the equivalent degree of freedom and the stiffness of the springs was calculated by its combination with gait motion, so that the average force of the human body was minimized. A dynamic model of the exoskeleton was established. To overcome the uncertainty in the parameters of the human and robotic limbs, an adaptive controller was designed and a Lyapunov stability analysis was conducted to verify the system. A simulation was conducted and experimental results show that the tracking error of the knee joint angle between the actual and desired trajectory was within the range of −1 to 1 degree and indicate the effectiveness of the controller.

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