Design of adaptive fault‐tolerant controllers for perturbed nonlinear ODE‐PDE cascaded systems

• Published in: International journal of robust and nonlinear control 2024-01, Vol.34 (2), p.1077-1095
• Main Authors: Cheng, Chih‐Chiang, Lin, Yuan‐I, Wen, Chih‐Chin
• Format: Article
• Language: English
• Subjects: Actuators; Adaptive control; Adaptive systems; Dynamical systems; Effectiveness; fault tolerant control; Nonlinear differential equations; nonlinear systems; Partial differential equations; Perturbation; perturbation estimator; Robustness (mathematics); sliding mode control; Stability analysis; Upper bounds
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7019

An adaptive fault‐tolerant control (FTC) scheme is proposed in this article for a class of perturbed cascaded dynamic systems governed by nonlinear differential equation‐partial differential equation (ODE‐PDE) to solve regulation problems. The sliding surface is introduced first, then the controller which can handle actuator faults is designed. Adaptive and perturbation estimation mechanisms are employed in the proposed control scheme so that there is no need to know the upper bounds of perturbations as well as perturbation estimation error in advance. In addition, the adaptive mechanism embedded is capable of adapting the unknown upper bounds of time‐varying loss of effectiveness of the actuators. The stability analysis confirms that the proposed control strategy can drive both the states of ODE and PDE into zero within a finite time even if the actuator fault occurs. At last, a numerical example is given to verify the robustness and effectiveness of the proposed FTC scheme.