Additive fault tolerant control of nonlinear singularly perturbed systems against actuator fault

Abstract

This paper presents the design of an additive fault tolerant control for nonlinear time-invariant singularly perturbed systems against actuator faults based on Lyapunov redesign principle. The overall system is reduced into subsystems with fast and slow dynamic behavior using singular perturbation method. The time scale reduction is carried out when the singular perturbation parameter is set to zero, thus avoiding the numerical stiffness due to the interaction of two different dynamics. The fault tolerant controller is computed in two steps. First, a nominal composite controller is designed using the reduced subsystems. Secondly, an additive part is combined with the basic controller to overcome the fault effect. The derived ε -independent controller guarantees asymptotic stability despite the presence of actuator faults. The Lyapunov stability theory is used to prove the stability provided the singular perturbation parameter is sufficiently small. The theoretical results are simulated using a numerical application.K e y w o r d s: nonlinear time-invariant singularly perturbed systems, singular perturbation method, additive fault tolerant control, actuator defect, Lyapunov theory

Reconfigurable control of flexible joint robot with actuator fault and uncertainty

“…To show how this can be achieved, we construct a weighted sum of the Lyapunov functions. Define this function as [5]…”

“…The two time scales include a fast time scale (FTS) and a slow time scale (STS). The singular perturbation technique (SPT) is widely applied in the system which can be divided into a fast subsystem and a slow subsystem [5]. Thanks to the advantage of model reduction, this technique is capable of decomposing a higher order system into two systems of lower order [6][7][8].…”

“…There exists a known positive constant D(x, y) > F (x, y) , D(x, y) > ∆ 1 (q,q) and D(x, y) > ∆ 2 (q,q) for all t ≥ 0 . Thus, the fault tolerant control designed to stabilize the faulty system (20) is presented as[5] …”

A Synchronous Sampling Based Harmonic Analysis Strategy for Marine Current Turbine Monitoring System under Strong Interference Conditions

“…Regarding current-based detection methods, fault causes can be divided into two types: additive and multiplicative faults. Additive faults refer to the superposition of a pulse signal, a constant signal or a random small signal on the original normal signal [5], while multiplicative faults refer to signals with a certain frequency superimposed on the original normal signal [6]. For additive fault detection, time-domain statistical analysis can be used.…”

Neural Network-Based Adaptive Tracking Control for a Class of Nonlinear Singularly Perturbed Systems

“…The many industrial systems, such as power systems, motor control systems, electronic circuit systems, robotics systems, have ''slow'' and ''fast'' dynamics due to the presence of some small parameters such as capacitances, resistances, inductances, moments of inertia, and so on [1]- [5]. It gives rise to significant difficulties in analyzing and designing the system because the small parameters can lead to high dimensionality and ill-conditioned numerical issues.…”