True total extrusion process control

Concentrating on the control of the extrusion process, it is clear from the literature [54-68] that true total extrusion process control is quite complicated and has not been fully achieved in practice. Under true total process control, the process is considered a multivariable system and the interaction between the variables is known and fully taken into account in the control scheme. One can therefore assume that many commercial microprocessor-based controllers that control melt temperature, pressure, and extrudate dimensions are most likely built with more or less independent control loops, each controlling only one variable. These controllers more or less consolidate multiple discrete controllers into one convenient package without major changes to the individual control characteristics. This may reduce cost but does not necessarily improve overall control performance. 

The first requirement in the development of a true extrusion process control is a dynamic process model. The goodness of the process control will depend very strongly on the accuracy of the process model. However, obtaining a good dynamic process model is quite complicated in practice. The dynamic process model can, in principle, be derived from extrusion theory, and various attempts in that direction have indeed been made [50-54]. As will be discussed in Chapter 7, extrusion theory to date has not been developed to a point that the entire process can be predicted 

Most work on the development of dynamic process models has been empirical this work is usually referred to as process identification. As mentioned earlier, two classes of empirical identification techniques are available one uses deterministic (step, pulse, etc.) functions, the other stochastic (random) identification functions. With either technique, the process is perturbed and the resulting variations of the response are measured. The relationship between the perturbing variable and the response is expressed as a transfer function. This function is the process model. Empirical identification of process models by the deterministic method has been reported by various workers [55-58]. A drawback of this method is the difficulty in obtaining a measurable response while restricting the process to a linear response (small perturbation). If the perturbation is large, the process response will be nonlinear and the representations of the process with a linear process model will be inaccurate. 

Stochastic identification techniques, in principle, provide a more reliable method of determining the process transfer function. Most workers have used the Box and Jenkins [59] time-series analysis techniques to develop dynamic models. An introduction to these methods is given by Davies [60]. In stochastic identification, a low amplitude sequence (usually a pseudorandom binary sequence, PRBS) is used to perturb the setting of the manipulated variable. The sequence generally has an implementation period smaller than the process response time. By evaiuating the auto- and cross-correlations of the input series and the corresponding output data, a quantitative model can be constructed. The parameters of the model can be determined by using a least squares analysis on the input and output sequences. Because this identification technique can handle many more parameters than simple first-order plus dead-time models, the process and its related noise can be modeled more accurately. 

Identification of the noise and its probable causes usually leads to the most effective method of removing these disturbances. 

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