Active scanner control on paper machines

Highlights

• scanner path utilized as a manipulatable variable in paper machine cross-directional control.

• faster response to load disturbances.

• estimation of process noise and basis weight estimate uncertainty based on web-wide transmittance measurement.

• adaptive model between transmittance and basis weight.

ABSTRACT

The cross-directional (CD) basis weight control on paper machines is improved by optimizing the path of the scanning measurement. The optimal path results from an LQG problem and depends on how the uncertainty of the present estimate of the basis weight and the intensity of process noise vary in CD. These factors are assessed by how accurately the CD basis weight estimate predicts the measured optical transmittance with a linear adaptive model on synchronized basis weight and transmittance data. Simulations on optimized scanner path in disturbance scenarios are presented, and the practical implementation of scanner control is discussed.

Introduction

For example, paper, tissue, board and plastic films are manufactured as webs, which may be up to 10 m wide and run at speeds of up to 40 m/s. In papermaking, a distributing element, called headbox, transforms the material flow in a pipeline into a web first supported by a wire and then dried and reeled as a continuous sheet. For the uniformity of quality it is essential that the material is evenly distributed along the width of the web (hereafter: cross direction, CD) and in time (hereafter: machine direction, MD). The amount of material per area, basis weight, can be reliably measured based on transmittance of beta radiation [1]. However, beta transmittance cannot be cost-efficiently measured web wide, but only pointwise. The common practice is to measure basis weight with a device that scans regularly back and forth over the running web just before the reeler (e.g. [2]). The measurement signal is divided into an MD and CD component [[3], [4], [5]].

Basis weight is controlled in MD and in CD by adjusting the feed flowrate and/or consistency in time and across the headbox. In particular, the flowrate in CD can be adjusted by changing locally the slice opening of the headbox [[6], [7], [8], [9]], and the consistency can be adjusted by locally diluting the slice flow [9,10]. Such an action affects typically a region of 10-50 cm wide in CD, so that with actuator spacing of 5-20 cm, the effects are overlapping. The response of slice opening control has typically the “Mexican hat” shape in CD whereas dilution control response is approximately Gaussian [2,9]. The flowrate/consistency response is fast, of the order of a few seconds, and limited only by actuator mechanics with the dilution control being the faster one. On the other hand, CD variations are claimed to be very static, mostly characteristic to the production line [11].

The state-of-the-art basis weight control seeks for the best setting of actuators based on the CD variation estimate [12,13]. Three factors make CD control rather slow and limit severely its performance. Firstly, the delay from the actuators at the headbox to the scanning measurement at the reeler is rather long, of the order of one minute. Secondly, the filtering of the scanning measurement for having a good quality CD basis weight estimate requires several scanner crossings over the web and takes of the order of few minutes. Thirdly, the responses of the actuators are somewhat uncertain [14], in particular close to the web edges. Spatial misalignment of the response leads to oscillating control actions, and even rather small alignment error causes spatial instability, known as the “picketing” [2,15,16]. As a result, the changes in actuator settings must be made rather conservatively.

In practice CD control with accurate response models is an MPC on the actuator settings, efficient in reducing stable CD variation features specific to each product grade but rather slow in correcting intragrade variations. For a review on CD estimation and control, see [17]. The MD feedback control is able to compensate basis weight variations with time scale of a few minutes and longer [18,19].

This paper discusses how CD control can be improved by taking the scanner path as an additional actuation degree of freedom, and present a practical method to plan the scanner path. Roughly speaking, the measurement should be made where it matters most: where the basis weight estimate is poor and where a CD actuator can have an effect. The dynamic planning of the scanner path is an example of sensor management problem, which is defined in [20] as “[..] control of the degrees of freedom in an agile sensor system to satisfy operational constraints and achieve operational objectives.” Sensor management problems have been analyzed for example in the context of sensor networks with constraint communication resources [21], and for operable machine vision in robotics, e.g. [20,22,23]. Sensor management problems fall in the category of partially observable Markov decision processes (POMDP) [24] and can be classified according to the properties of state space, action space, measurement data space, sensing degrees of freedom, state observability, and the objective function [25]. The best-known case of POMDP problems relevant in sensor management is the linear-quadratic-Gaussian (LQG) control problem with operable sensor degrees of freedom. In a LQG problem the state space is Rⁿ, the action space is a product of R^m (process actions) and a discrete set (sensing actions), measurement data space is R^k, the motion of the sensor in the discrete set is deterministic, state is observable up to a Gaussian noise, and the objective function is quadratic in the sequence of future process actions. Unconstrained LQG is solvable in closed form, and the solution is separable [26]: the process control actions are determined by the most likely state and the sensing actions by the uncertainty of the state estimate. In linear-Gaussian systems, the latter depends only on which sensing actions have been taken, not on which data has been obtained, and thus the sequence of sensing actions is a regular policy that can be solved offline.

Earlier works considered the path of basis weight scanner as a manipulated variable in CD control [27,28]. The problem was formulated as an LQG with a discretized set of sensing subpaths, and the optimal scanner path as a response to temporal changes in CD process noise (co)variance was solved.

Basis weight control is an LQG problem, and if process noise covariance is uniform in CD, regular scanning is optimal. However, disturbances may cause the CD profile estimate to become suddenly uncertain or rapidly degrading at some regions in CD. In such situations, it may be beneficial to allocate the scanning sensor temporarily to this region. To detect such a situation, the uncertainty in basis weight estimate must be assessed with an independent measurement.

The main contribution in this paper is in that the quality of basis weight estimate and its degradation rate is estimated based on web-wide optical transmittance measuremen. Then the scanner path is controlled accordingly by applying the methods in [27,28]. For this purpose, the relationship between optical transmittance and basis weight is estimated adaptively. The quality of the CD basis weight estimate is assessed by how well the CD transmittance can be predicted. Simulations illustrate how the scanning path changes e.g. as a result of increased basis weight process noise at a CD region. The practical implementation of the proposed method is discussed and extensions to the automatic scanner path control proposed.

This paper is organized as follows. Section 2 reviews the web quality measurement systems on modern paper machines. Section 3 outlines the stages in paper machine CD control with active scanning. Section 4 first formulates the control as an LQG problem, and then specifies the scanner path optimization, given current basis weight estimate uncertainty and process noise variance in CD. Subsection 4.3 details the main contribution, the method for evaluating the basis weight estimate uncertainty and process noise variance by using transmittance measurement data so that scanner path can be planned for optimal control performance. Section 5 provides simulation results for scanner path control and CD control in disturbance scenarios. Section 6 discusses practical implementation of the proposed method, and other potential applications of synchronized basis weight and transmittance measurement in CD control, including joint basis weight estimation and maintaining high-quality CD actuator response models. Section 7 concludes the main results and their practical implications.