Robust Control of the Objects with Distributed Delay on a State Vector and Input

Abstract

The article is devoted to studying of the object, the mathematical model of which is the vector equation with a distributed delay on a state vector and input signal. It is assumed that the parameters of the mathematical model are unknown, and the limited disturbance influencing the object is unmeasured. The problem of tracing of a reference signal is formulated. In order to ensure qualitative tracking of the reference signal, it is necessary to compensate for the influence of the unmeasured disturbance on the output variable. For solving of this problem the method of the internal model is used. This method proved itself in designing of the robust controls for the discrete systems. In this paper it is used for the continuous systems. The problem of the robust control of the objects with the distributed delay on the state vector and input is being solved. It is assumed that the parameters of the mathematical model of an object are unknown, and only the output variables are available for measurement. As the target conditions the accuracy of tracking of the reference signal is accepted. The control algorithm was obtained allowing to compensate for the aprioristic uncertainty and to reduce essentially the influence of the unmeasured bounded external limited disturbance. The equations of the closed system are a singular system of equations. It was proved, that the received control algorithm ensured implementation of the target conditions. The numerical examples and the results of the computer simulation, which have demonstrated the efficiency of the received algorithm of tracking, are presented.