Suboptimal and optimal extended horizon predictive control of the Hammerstein model

Predictive control algorithms have been worked out mainly to control linear plants. There is a great demand to apply different control ideas for nonlinear systems. Using predictive control algorithms for nonlinear systems is a promising technique. Extended horizon predictive control algorithms are given here for the nonlinear simple Hammerstein model as for this model the control algorithm can be derived easily as a straightforward extension of the linear case. A quadratic cost function is minimized, which considers the quadratic deviation of the reference signal and the output signal predicted in a future point beyond the dead time and also punishes big control signal increments. For prediction of the output signal on the basis of the information of the input and output signal available up to the actual time point a predictive model is needed. Predictive transformation of the Hammerstein model is given. Incremental model is advantageous since the cost function contains the control increment and not the control signal itself. Incremental transformation of the predictive Hammerstein model is described. Suboptimal and optimal extended horizon control algorithms are discussed with different assumptions for the control signal during the control horizon. The effect of the different strategies and the effect of the tuning parameters is investigated through simulation examples.