Robust H∞ Proportional-Integral Observer for Fault Diagnosis: Application to Vehicle Suspension

A Hybrid Fault-Tolerant Control for Nonlinear Active Suspension Systems Subjected to Actuator Faults and Road Disturbances

“…where u f is the desirable control force of the proposed faulttolerant controller, u n � Kx f is nominal state-feedback controller, u c � − Mf is H ∞ observer-based compensation controller, K is the gain matrix of nominal state-feedback controller, f is the actuator fault estimation achieved by the designed robust H ∞ observer in (10), and M is a known matrix with appropriate dimension. Substituting (30) into (6) results in (31) as…”

“…For ∀w ∈ L 2 [0, +∞), one can get J z < 0 from _ V 2 < 0, that is, ‖z‖ < c‖w‖ (see (41) and (42)). Furthermore, system (31) has H ∞ performance β if and only if the controlled system is asymptotically stable and the inequality ‖z‖ < c‖w‖ holds for ∀w ∈ L 2 [0, +∞) under χ 2 < 0 conditions. e proof is completed.…”

“…□ Theorem 4. For given positive scalars c and λ 2 , the closedloop system (31) is asymptotically stable and has a prescribed H ∞ disturbance attenuation level c > 0, if there exist symmetric positive definite matrix Q, R with appropriate dimension and the gain matrix K such that the following inequality holds:…”

“…In addition, an adaptive fault-tolerant compensation controller was proposed in [30] to enhance the output performance for a kind of vehicle suspension system, wherein the failure model was described by a scalar Markovian type function. A robust H ∞ proportional-integral observer-based fault diagnosis method for the vehicle suspension system was addressed in [31], wherein the constant gain fault was diagnosed by an observer. However, these fault-tolerant control designs did not take the suspension's nonlinearities as well as the actuator faults into account when designing the corresponding controllers; moreover, the fault estimation accuracy has to be considered and enhanced if one wants to develop an effective fault-tolerant controller.…”

“…In the context of the above discussions, this paper proposes a hybrid fault-tolerant control design for nonlinear active suspension subjected to the actuator faults and road disturbances. Herein, compared with the most related faulttolerant control methods in [16,19,21,31,32], we make several steps forward. First, an augmented closed-loop system model is established for the nonlinear active suspension system with the actuator faults and road disturbances, which were rarely present in the previous papers.…”