A novel approach to dynamic modelling of polymer extrusion for improved process control

Abstract

Polymer extrusion is a complex process and the availability of good dynamic models is key for improved system operation. Previous modelling attempts have failed adequately to capture the non-linearities of the process or prove too complex for control applications. This work presents a novel approach to the problem by the modelling of extrusion viscosity and pressure, adopting a grey box modelling technique that combines mechanistic knowledge with empirical data using a genetic algorithm approach. The models are shown to outperform those of a much higher order generated by a conventional black box technique while providing insight into the underlying processes at work within the extruder.

Dynamic gray‐box modeling for on‐line monitoring of polymer extrusion viscosity

“…It is the signal excited by a Gaussian sequence and the period of input change was also defined by a Gaussian sequence where the mean and standard deviation (r) were defined based on the measured pressure and viscosity response time to step changes in the inputs. Thus a wide operating range, including both the low frequency and high frequency spectra, was covered in the sequences while consecutive input changes were within practical operating limits [2]. The defined input sequence parameters are given in Table 2.…”

“…To determine the ''term pool'' for viscosity model, a complex term approximating to an Arrhenius-type relationship may be appropriate. But as this involves a difficult problem of tuning several parameters, the ''term pool'' with power law terms, N k1 T k2 3 (k 1 , k 2 is a constant) [2] is selected. For a continuous nonlinear function a general power law element could potentially fit the relationship accurately if enough terms are included.…”

“…Real-time monitoring of the quality of the extrudate material during the extrusion process is therefore desirable to achieve reduced set-up times and improved operation of the extrusion system. In comparison with melt temperature and pressure, melt viscosity is largely recognized as one of the most relevant indicators of melt quality as it is directly related to the esthetic/dimensional properties of the melt and the molecular orientation relating to the functional properties of a polymeric extrudate [1,2]. However, online viscosity measurement to a required standard has proved difficult to achieve due to the highly nonlinear and significant time delay behaviors of the process.…”

“…To tackle this problem, a soft sensor with a feedback structure was proposed in previous work [2,7]. The soft sensor structure is based on that of a state observer [8] where an open-loop estimator (viscosity model) is combined with a feedback correction mechanism performed by a pressure model.…”

“…The novel feedback structure enables the online adaptability of the viscosity model in response to modeling errors and disturbances, hence producing a reliable viscosity estimate. Both pressure and viscosity models were developed using gray-box modeling with GA [2,7]. Potential to relate model parameters on different grades of the same polymer (low density polyethylene) has been demonstrated.…”