Design of Linear Matrix Inequality-Based Adaptive Barrier Global Sliding Mode Fault Tolerant Control for Uncertain Systems with Faulty Actuators

Abstract

This paper proposes a linear matrix inequality (LMI)-based adaptive barrier global sliding mode control (ABGSMC) for uncertain systems with faulty actuators. The proposed approach is derived using a novel global nonlinear sliding surface to guarantee the global dynamic property and to ensure system stability and the occurrence of sliding in the presence of actuator faults. The optimal coefficients of the sliding surface are determined using the LMI method. The system’s asymptotic stability is proven using Lyapunov theory. Additionally, an adaptive barrier function is considered to ensure the convergence of the output variables to a predefined locality of zero in a limited time, even where external disturbances and actuator faults are present. In order to decrease the steepness of the control action and mitigate the chattering phenomenon, the hyperbolic tangent function is employed instead of the signum function in the sliding mode control. The proposed method is validated using a simulation study of the Genesio’s chaotic system.

Fault Detection of WECSs Based on Improved SVO and Fourier Transformation

“…The selection process of one vertexes set j v is as follows. Firstly, a random state is selected from one simulation result of the system (10). Secondly, an extreme value is randomly selected from the simulation curve of the selected state and the corresponding simulation moment is recorded.…”

“…Fekih et al used the adaptive barrier function to reduce the impact of system noise and actuator faults. Based on this, they designed the Linear Matrix Inequalitybased adaptive barrier global sliding mode fault tolerant control for actuator faults in uncertain systems in [10], and adaptive barrier fast terminal sliding mode actuator faulttolerant control approach for quadrotor UAVs in [11], both with good performance. Some studies designed observerbased fault detection strategies for the original model.…”

Adaptive Barrier Fast Terminal Sliding Mode Actuator Fault Tolerant Control Approach for Quadrotor UAVs

“…In [45], an adaptive type-2 fuzzy backstepping fault tolerant controller was proposed to remove the effects of the parameter uncertainties, external disturbances, and actuator faults. In [46], an LMI-based adaptive barrier global sliding mode control approach was used to reduce the parametric uncertainties, external disturbances, and actuator faults. In [47], two proportional-derivative (PD) controllers and an adaptive fuzzy TSMC was proposed to stabilize a quadrotor.…”

Finite‐time robust performance improvement for non‐linear systems in the presence of input non‐linearity and external disturbance

“…In dynamical systems, actuators are usually subjected to hard non-linearities such as dead-zone (or dead-band), backlash, saturation, hysteresis, quantization, and others. Such a character would have significant effects on the system's stability and performance [1][2][3]. Nowadays, several control strategies have would be straightaway tricks for the hard non-linearity in the linear time-invariant (LTI) systems [9].…”

“…In dynamical systems, actuators are usually subjected to hard non‐linearities such as dead‐zone (or dead‐band), backlash, saturation, hysteresis, quantization, and others. Such a character would have significant effects on the system's stability and performance [1–3]. Nowadays, several control strategies have been developed to handle input nonlinearity [4], with methods such as the anti‐windup scheme [5], composite nonlinear feedback [6], and constructing the augmented system [7] being the most important.…”