Stability Analysis of the Neural Network Based Fault Tolerant Control for the Boiler Unit

This paper deals with the stability analysis of the fault accommodation control system. When a fault is detected, the fault tolerant control tries to compensate the fault effect by adding to the standard control the auxiliary signal. This auxiliary control constitutes the additional control loop which can influence the stability of the entire control system. This paper focuses on the stability analysis of proposed control scheme based on the Lyapunov direct method. Nowadays everyone can observe very rapid and significant progress in the automation industry. Not only very sophisticated and complex systems are fully automated, but also the simple one. Unfortunately with the growing number of components of a production system the probability of system faults becomes higher and higher. This makes necessary to design a control system which automatically adapt the proper behaviour in the case of faults. In the previous works of the authors, a fault detection and accommodation methodology for the boiler unit was proposed [?]. The already elaborated methodology uses a robust state space model of the system and nonlinear state observer, both carried out by means of artificial neural networks. The designed fault tolerant control tries to compensate a fault effect by adding the auxiliary signal to the standard control generated using e.g. the classical PID controller. The auxiliary control constitutes the additional control loop which can influence the stability of the entire control system. Thus, in this paper the stability analysis of the proposed control scheme based on the Lyapunov direct method is presented. 1 Problem formulation Let consider a nonlinear dynamic system governed by the following state equation: x(k + 1) = g(x(k),u(k)) + f(x(k),u(k)), (1) where g(·) is a process working at the normal operating conditions, x(k) is the state vector, u(k) is the control and f(·) represents a fault affecting the process. 1 This work was supported in part by the Ministry of Science and Higher Education in Poland under the grant N N514 6784 40.