Second-order element, process modeling

Table 12.1 presents the PID controller tuning relations for the parallel form that were derived by Chien and Fruehauf (1990) for common types of process models. The IMC filter / was selected according to Eq. 12-21 with r = 1 for first-order and second-order models. For models with integrating elements, the following expression was employed ... 

Chin and Shyu (1988) have predicted die swell of polymers based on the assumption that polymeric fluids obey Criminate-Ericksen-Filbty (CEF) equation. They obtained an equation for die swell that depends on the processing conditions and thus helps to choose such for the required die swell. Similarly, Mitsoulis (1999) used the streamline finite element method to compute the die swell using different slot cross-sections such as circular, square, and cross-shaped sections. The fluid models used were Newtonian, viscoplastic (Bingham), and second order fluid. In addition to the finite element methods, the finite volume method has also produced very good results (Xue et al, 1995). 

A first-order model is assumed, so na and nb are both set equal to 1. The command th = arx[z,[na nb nk]) calculates the values of b = 0.00 16 and a = -0.953. The variance is given in the th matrix of results in the (1, 1) element (0.0022). Choosing values of nk greater or less than 8 gives larger variances. The time constant and steady-state gain can be calculated from the a and b values To = 113 seconds and Kp = —0.0779°C/%. These results are similar to those found by fitting a first-order model to step test data from the process. 

---