Application of Self-Tuning Control System for Solution of Fault Tolerance Problem

Self-tuning control can provide desirable behaviour of a process even though the process parameters are unknown or may vary with time. Conventional self-tuning control requires that the speed of adaptation must be more rapid than that of the parameter changes. However, in practice, problems do arise when this is not the case. For example, when fault occurs in a process, the parameters may change very dramatically. A new approach based on simultaneous identification and adaptation of unknown parameters is suggested for compensation of rapidly changing parameters. High dynamic precision self-tuning control can be used for the solution of a fault tolerance problem in complex and multivariable processes and systems. Index Terms Self-tuning control, identification, fault tolerance, Singular Value Decomposition. I. DETERMINATION OF A MATHEMATICAL MODEL OF A PROCESS A mathematical model of a process on a stationary regime can be found from the sequence of Markov parameters using the classical Ho algorithm [1]. The Markov parameters can be obtained from input – output relationships or more directly as an impulse response of the system. It is well known that according to the theorem of Kronecker the rank of the Hankel matrix constructed from the Markov parameters is equal to the order of the system from which the parameters are obtained. Therefore, by consistently increasing the dimension of the Hankel matrix  until rank r  = rank 1  r the order of the system can be obtained as equal to r . However, in practical implementation, this rank – order relationship may not give accurate results due to several factors: sensitivity of the numerical rank calculation and bias of the rank if information about the process is corrupted by noise. This problem can be avoided using singular value decomposition (SVD) of the Hankel matrix: