Updating of a lumped model for an experimental web tension control system using a multivariable optimization method’

The modelling and the control of web handling systems have been studied for a long time; correct modelling is necessary in order to design a better control system or to identify the plant parameters experimentally. On the web dynamics itself, lumped parameters expressions may be used to designate a web section between two adjacent drive rolls, and there is the necessity of incorporating the property of viscoelasticity to the web. In this paper the lumped model of a new web tension experimental system is updated; the model is based on the conservation mass, torque balance and viscoelasticity (Voigt approach). The experimental system consists of four sections each of which is driven by a servomotor; the speed and tension feedback, by using encoders and tension sensors, drives simultaneously the four servomotors through a real time C programmed D/A board. Usually, as described in the literature, these kinds of models are developed in the Laplace domain and the block scheme gives a graphical interpretation of the interaction between different sections. The transformation of the block scheme in a differential equation system in the time domain is fully described in this paper; it is not a simple step and it requires the introduction of not null initial condition for the derivative of physical variables. Moreover, the problem of validation has been dealt with in detail in this paper, considering simultaneously 2 different combinations of input data in open loop and a multivariable optimization method in order to estimate a certain number of unknown parameters. The results will show the accuracy of this kind of lumped parameters model for the complex experimental systems and useful information for successively designing an efficient control strategy.