Control of Nonlinear Systems with Input Delay

An algorithm for control of nonlinear systems with sector nonlinearity and a constant known time-delay in the control channel is proposed. To design the control law, a predictor of the controlled variable by the time-delay value is used. Unlike the predictor of O. Smith, the predictor under consideration can be applied to unstable systems, and differently from the predictor of A. Manitius and A. Olbrot, the proposed predictor does not contain an integral component, which requires accurate implementation to predict the regulated signal. Next, based on the proposed predictors, subpredictors are built, which are a sequential connection of a series of similar predictors, but with a shorter time-delay. As a result, the use of a subpredictor allows one to control plants with a larger time-delay, which is reflected in the closed-loop system, where the time-delay is as many times less than the original one as the number of predictors used in the prediction scheme of the controlled variable. Using the method of Lyapunov-Krasovsky functionals and the S-procedure, sufficient conditions for the stability of the closed-loop system are obtained in the form of solvability of linear matrix inequalities. The asymptotic convergence to zero of the state vector and the uniformly boundedness of all signals in the closed-loop system are proven. It is shown that the resulting linear matrix inequalities depend on the parameters of the plant, sector boundaries for nonlinearity and time-delay, which makes it possible to calculate their upper values when the closed-loop system remains stable. These problems may be relevant when calculating the upper value of the sector of the nonlinearity under consideration or the upper value of the time-delay during remote control. The results of computer modeling are presented, which illustrate the efficiency of the proposed approaches and demonstrate an increase in the possible time-delay in the system when using a subpredictor scheme. The example shows that when using a serial connection of two subpredictors instead of one, the maximum time-delay in the control channel can be doubled. Moreover, in contrast to the predictor of A. Manitius and A. Olbrot, the subpredictor scheme is simple due to the lack of implementation of the integral component.