Spatio-Temporal Modeling for Wiener Distributed Parameter Systems

For Wiener distributed parameter systems (DPS), a spatio-temporal Wiener model (a linear DPS followed by a static nonlinearity) is constructed in this chapter. After the time/space separation, it can be represented by the traditional Wiener system with a set of spatial basis functions. To achieve a low-order model, the Karhunen-Loeve (KL) method is used for the time/space separation and dimension reduction. Finally, unknown parameters of the Wiener system are estimated with the least-squares estimation and the instrumental variables method to achieve consistent estimation under noisy measurements. The simulation on the catalytic rod and the experiment on snap curing oven are presented to illustrate the effectiveness of this modeling method.