Modeling and control of various styles of paper machine headboxes

Abstract

In this thesis non-linear mathematical models of a typical paper machine approach system with three different styles of headboxes are presented. The non-linear models include the dynamics of the fan pump, DC motor, pressure screen, attenuator, headbox and piping sections. Headbox models of a hydraulic and two air-cushioned headboxes (traditional and internal weir) are covered. The models were developed from first principles. Total head at the headbox slice is controlled by manipulation of the applied armature voltage of the variable speed DC motor. Stock level in the air-cushioned headboxes is controlled by manipulation of the air pad bleed valve. Simple analog Proportional-Integral (PI) controllers were selected to track without offset the desired level and total head set-points. The downhill simplex method developed by Nelder and Mead was used for controller fine-tuning. The performance criterion was the integrated absolute error (IAE) with weighting factors for both pressure and level loops. Frequency responses for each model were generated using a commercially available software program called EASY5™. Step and frequency response plots were generated at operating points of 60, 75 and 90 kPa to evaluate the non-linear behaviour of each headbox model. The step response plots highlighted the strong interaction that exists between level and pressure loops of the air-cushioned headboxes. With the PI gains used the transient responses of the pressure loop of all headboxes were underdamped. The open-loop frequency responses in all models illustrated the non-linearity of the centrifugal fan pump. In addition the effect of the fan pump on the stock level and total head was found to be strong. The effect of the bleed valve on the stock level was also determined to be strong. With the traditional headbox the effect of the bleed valve on the total head was found to be weak whereas with the weir headbox at low frequencies it was found to be strong. One-way decoupling was proposed to improve the control performance of the aircushioned headbox level loop. For simplicity a lead / lag compensator was selected to approximate the ideal decoupling frequency response determined directly from the open-loop frequency responses. A significant reduction in stock level deviations before and after the addition of one-way decoupling in both the time and frequency domain was observed thereby proving its usefulness when combined with the feedback PI controllers.