Abstract:
A method and apparatus are set forth for controlling and actuator in a moving web manufacturing process. The method includes: (1) measuring a plurality of actuator profiles and in response generating nominal response models thereof; (2) generating a multivariable profile prediction based on the nominal response models; (3) generating a multivariable control target based at least one of the actuator profile; and (4) adjusting control of the actuator by minimizing error between the multivariable control target and the multivariable profile prediction.

Description:
FIELD 
     The present specification relates to the manufacture of rolls, and more particularly to a method and apparatus for controlling reel building and roll runnability in moving web manufacturing. 
     BACKGROUND 
     Paper products are normally shipped in rolls from a paper mill to a converting or printing facility. Rolls made from different paper machines or made at different times or locations of the machine may have different reel building and roll runnability characteristics, where “runnability” is an indication of how well the roll pulls through the paper-making, converting, and printing processes, as well as the flatness and uniformity of the resulting web of paper. 
     Online paper finishing with multi-nip calenders is well known for building reels of super-calendered (SC) or light-weight coated (LWC) paper. High quality printing papers that are calendered online are thin, very dense and therefore resistant to additional compression. With these paper properties, it has-been found that traditional methods of cross direction (CD) reel build control using contacting calliper (thickness) sensors have been difficult to optimize. In order to precisely build an SC reel with good runnability, it is known in the art to monitor and control multiple properties during the manufacturing process, such as dry weight, moisture, and caliper (thickness). More particularly, these (and other) sheet properties may be controlled in a sheet-making machine in order for the sheet properties to match, as closely as possible, predefined target or desired values. 
     The control of sheet properties is accomplished through the use of various actuators, such as machine direction (MD) actuators that control the cross direction average of a sheet property, and cross direction (CD) actuators that affect both the average of a sheet property and the cross direction shape of the sheet property. In general, the cross direction (CD) is typically perpendicular to the machine direction (MD). Overall control of sheet properties presents a problem of very large scale, with multiple inputs and outputs (e.g. several hundred CD actuators may be required to control one or more paper quality profile(s) consisting of typically 500-1200 measurement points each corresponding to 5-10 mm resolution across the web). To that end, multivariable control processes have been developed for cross-direction paper quality control, as set forth, for example, in US Patent Publication 2008/0017341 (Maenpaa et al); Calvin Fu, Jarmo Ollanketo and Jukka Makinen, “ Multivariable CD Control and Tools for Control Performance Improvement ”, published at the Control Systems 2006 Conference, Jun. 6-8, 2006, Tampere, Finladd, pp. 215-220; and Seyhan Nuyan, Calvin Fu and Steven Bale, “CD Response Detection for Control”, presented in 1998 at the TAPPI PCE&amp;I Conference, Vancouver, BC, Mar. 16-29, 1998, pp. 95-105 (hereinafter “Nuyan et al”). 
     There remains a significant challenge in determining which of a multitude of paper quality profiles (e.g. reel diameter, hardness; pre-wound or wound-in tension, moisture, caliper (thickness), etc.) should be selected as control variables in a multivariable CD (MVCD) control process to address different problems (e.g. degraded roll runnability due to air entrapment versus mass variations in the web). The challenge in selecting appropriate control variables or profiles is particularly acute with highly finished grades (i.e. highly calendered) which, as discussed above, are very thin, very dense, and are characterized by very low compressibility. For example, when highly calendered papers are wound in a reel, air accumulation between layers becomes a significant factor resulting in undesired reel diameter profile shape and abnormal reel building even if the caliper profile is flat or shaped to a desired target. Therefore, using only the caliper profile for CD control is not sufficient. On the other hand, simple reel diameter control also is not an adequate solution to reel building/roll runnability problems because reel diameter measurements alone do not distinguish between irregularities caused by air entrapment and mass (caliper). Moreover, conventional solutions to these two problems are mutually exclusive; i.e. correcting problems due to air-entrapment requires an opposite control action to the action required to correct problems caused by uneven caliper (mass). 
     As indicated above, hardness of the reel may also provide an indicator of the reel-build process. Reel hardness is traditionally measured as the amplitude of a pulse produced by a force button on a rotating wheel that contacts the paper web. The amplitude is correlated with the force or hardness of the reel, which may therefore be considered to represent a composite measurement that better describes the reel building process than caliper does. Nonetheless, hardness measurement alone also fails to provide sufficient information for adequately controlling the reel building process, for the reasons set forth above in connection with reel diameter and caliper. 
     Indeed, other complex interrelations may also exist between various factors that give rise to a particular problem (e.g. the effect of forces resulting from local tension variability (LTV) on air dynamics, correlations between local hardness and LTV, or correlations between tension and moisture profiles and hardness measurement). 
     SUMMARY 
     According to one aspect of this specification, a method is set forth for controlling at least one actuator in a moving web manufacturing process, comprising determining a plurality of cross-directional property profiles and generating nominal response models thereof; generating a multivariable profile prediction based on the nominal response models; generating a multivariable control target based on the plurality of cross-directional property profiles; and adjusting control of the at least one actuator by minimizing error between the multivariable control target and multivariable profile prediction. 
     According to another aspect of this specification, a method is set forth for controlling at least one actuator in a moving web manufacturing process, comprising one of either measuring or calculating a single cross-directional property profile and in response, generating a nominal response model thereof; generating a single-variable profile prediction based on the nominal response model; generating a single-variable control target based on the cross-directional property profile; and adjusting control of the at least one actuator by minimizing error between the single-variable control target and single-variable profile prediction. 
     According to a further aspect of this specification, a cross-directional control system is set forth characterized in that current response profiles are generated for at least one of a specific process and specific reel conditions based on a selection of cross-directional profiles from the group consisting of reel diameter, caliper, hardness, moisture, tension, and weight. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments will be better understood with reference to the following Figures in which like numerals denote like parts and in which: 
         FIG. 1  is a schematic representation of a diagram of reel building arrangement incorporating a method and apparatus for controlling at least one actuator affecting reel runnability; 
         FIG. 2  is a schematic representation of a multivariable CD (MVCD) control system in the arrangement of  FIG. 1 ; 
         FIG. 3  is a simplified flowchart showing a method of controlling at least one actuator in the system of  FIG. 1 ; 
         FIG. 4  is a schematic representation of multivariable control; target block in the arrangement of  FIG. 1 ; and 
         FIG. 5 , comprising  FIGS. 5A and 5B , are graphs showing exemplary control weightings for use in the multivariable control target block of  FIG. 4 . 
     
    
    
     DETAILED DESCRIPTION 
     Turning to  FIG. 1 , a multi-nip calender  10  is shown comprising six rolls  11 ,  12 ,  13 ,  14 ,  15  and  16  and five nips  1 ,  2 ,  3 ,  4  and  5 . A web W runs around a guide roll  6 , into the topmost nip  1  of the calender, which is disposed between the topmost rolls  11  and  12  of the calender. The upper roll  11  may, for example, be advantageously covered with a resilient surface, such as polymer, while the lower roll  12  may be a smooth-surface press roll, such as a metal roll. 
     An induction heating system  21  generates magnetic flux that creates eddy currents for heating the surface of the calender roll  12  to a high surface temperature, thereby providing local non-contact heating of the metal roll  12  for better gloss, increased nip load and improved caliper and hardness. 
     From the topmost nip  1 , the web W runs over a turning roll  7  into the second calendaring nip  2 , which is formed between the heated smooth-surface press roll  12  and a roll  13  covered with a resilient cover, such as a polymer roll. 
     The web W then passes from the second nip  2  around the roll  13  and thence to a third nip  3 . The web W runs from the third nip  3  over a turning roll  7  into the fourth calendaring nip  4 , which is formed, like the first nip  1 , advantageously between a smooth-surface press roll  15 , such as a metal roll, which is the lower roll of the fourth nip  4 , and a roll  14  covered with a resilient cover, such as a polymer roll, which is the upper roll of the fourth nip  4 . 
     From the fourth nip  4  the web W runs again over a turning roll  7  into the fifth calendaring nip  5 , which is formed, like the second calendaring nip  2 , advantageously between a smooth-surface press roll  15 , such as a metal roll, which is the upper roll of the fifth nip  5 , and a roll  16  covered with a resilient cover, such as a polymer roll, which is the lower roll of the fifth nip  5 . 
     According to an exemplary embodiment, any one or more of the rolls  11 - 16  may be zone-controlled rolls for providing profiling capabilities (i.e. multiple zone-controlled adjustment of diameter by small amounts (typically 0.5-1.0 mm) in cross direction), as is known in the art. 
     After the fifth nip  5 , the web W is arranged to run through a thickness (caliper) measuring unit  8  and thence around a last turning roll  7  on to a reel-up/winder or spool  9 . A reel diameter and hardness measuring unit  25  includes a measurement wheel  27  connected via an arm  29  to a pedestal or base. Unit  25  measures hardness measurement according to conventional methodology known in the art as the Backtender&#39;s Friend; for sensing cross-direction reel hardness via a piezo-electric crystal embedded in the rotating wheel  27 . However, in addition to the conventional piezo-electric crystal, measurement unit  25  also includes a second piezo-electric crystal that measures the contact pressure applied by the measurement wheel  27  against the building paper reel on the spool  9 . The measurement of hardness can therefore be taken independently of applied pressure as the reel it building. This is accomplished using a mathematical formula that includes reel diameter. As the reel builds, the angular position of the loading arm  29  changes. The loading arm  29  is therefore equipped with a rotation transducer to indicate the angular position of the wheel  27  and the diameter of the building reel as the sensor traverses from edge to edge of the web W. 
     A multivariable CD (MVCD) control system  31  is arranged in connection with the multi-nip calender  10  for controlling reel building and, roll runnability as the web W winds on to spool  9 , via a control feedback loop between actuators, such as the induction heater  21  (and/or zone-controlled rolls), and measurement units, such as units  8  and  25 . The results of measurements from units  8  and  25  are processed by the MVCD control system  31  for providing control action outputs for controlling actuators  21 , etc. The non-limiting embodiment shows only a single actuator (induction heater)  21  being controlled by the MVCD control system  31 , although in practice numerous actuators may be controlled. Similarly, the embodiment of  FIG. 1  shows only two profile measurement units  8  and  25  whereas additional measurement units may be included (e.g. moisture detection, local tension variability (LTV), etc.) 
     Before further describing the non-limiting exemplary embodiment of MVCD control system  31  in  FIG. 1 , a brief description of multivariable CD control will be provided. 
     A single variable CD process model typically includes: CD actuator to measurement profile mapping, CD actuator response shape and time domain dynamics. Mapping relates the position of actuators to the position of databoxes in the measurement profile, where a “databox” is an array element in the measurement profile representing a specific measurement value at a particular CD position. The CD actuator response shape represents the change in measurement profile when only a single actuator is moved while other actuators are maintained at their “pre-bump” state. The response shape so determined is the static transfer function in space. CD actuator time domain dynamics refers to the machine direction (MD) development of the response in time. It is generally assumed to be linear, as well as time and space invariant. 
     A simple first order time domain model consists of time delay, response gain and time constant. This model can be expressed using the concept of a response matrix in the following format: ΔP i (t)=R i ·ΔU i (t), wherein ΔP i (t) is an n-element vector representing an n cell measurement profile error from its target, ΔU i (t) is an m-element vector representing an m cell CD actuator control action, and R i =G i (q −1 )·A i  represents a CD model, where the polynomial G i (q −1 ) is the dynamic part of the model. For the first order model, the dynamic part contains time delay and time constant information. The n by m response matrix. A i  is composed using the CD process mapping and CD actuator response shape and gain. 
     For multivariable CD control, models from several CD actuators to a number of paper quality profiles need to be considered. The following model can therefore be used for a multivariable CD process with M actuators and N profiles, which is essentially a dimension expansion of conventional single-variable CD control: 
     
       
         
           
             
               
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     In the foregoing equation, ΔU is a one-dimensional vector representing M CD actuator control actions; ΔP is a one-dimensional vector representing N measurement profile errors. Different actuator and measurement profiles can have different resolutions. Each element of the response matrix R contains a CD model associated with the corresponding actuator and measurement profile, which includes the time domain, CD actuator response and mapping. 
     With reference to  FIGS. 1-3 , upon collection of CD actuator excitation and profile responses via the profile measurement block  33  (step  55  in  FIG. 3 ), a modeling algorithm  35  generates CD nominal response models (step  57 ) via dynamic mapping block  37  and response generation block  39 , set forth in&#39;greater detail in Nuyan et al, referred to above. 
     The determination CD property profile at step  55  may be via measurement, calculation (or both), and the CD property profiles may include density (calculated from measurements of weight and thickness), stiffness (calculated from measurements of diameter and hardness), caliper profile, reel hardness profile, reel diameter profile, a composite of reel hardness profile and reel diameter profile, as discussed in greater detail below, or other. 
     A profile validation block  41  excludes any abnormal profiles that may cause extreme control actions. 
     A profile prediction or CD control simulation block  43  operates in connection with the core multivariable optimization block  45  and a target profile generation block  47  to process the measured cross-directional property profiles (e.g. hardness, reel diameter, calliper, etc.), calculate future profile error (step  59  in  FIG. 3 ) and control targets (step  61  in  FIG. 3 ), and perform multivariable control optimization (step  63 ) using the generated nominal profile models for generating control outputs (e.g. to zone-controlled rolls, induction heating system  21 , etc.) of the calender stack  10  via CD actuator handler  49  (step  65  of  FIG. 3 ). 
     More particularly, as shown in  FIG. 2 , a multivariable process model  51  is generated by the modelling block  35 , response generation block  39  and dynamic mapping block  37 . The model  51  is illustrated as a two-dimensional matrix representing a 3×3 CD process where the respective rows represents different profiles (e.g., hardness, calliper, etc.) and the columns represent different actuators in the multi-nip calender  10 . The highlighted box (G 23 (q −1 )) shows the CD response (z-axis) for a single actuator, where the x-axis represents the CD direction and the y-axis represents the MD direction. 
     In relation to the process model discussed above, ΔP(t)=[G(q −1 )F(A)]ΔU(t), the predicted error ΔP(t) calculated by profile prediction block  43  is indicated by e(i) in  FIG. 2 , the calender stack control output (out) of multivariable optimization block  45  is represented by successive control actions ΔU(t), and the model transfer function  51 , G(q −1 )F(A), is output from modeling algorithm  35 , dynamic mapping block  37  and response generation block  39 . Optimization of the controlled action is effected by minimizing the error e(i) between the target profile (sp) output from target profile generation block  47  and the predicted CV (me pr ), within predefined actuator constraints for a prediction time period between hmin and hmax, where hmin is the minimum prediction horizon and hmax is the maximum prediction horizon. 
     According to an exemplary embodiment, weightings may be applied by the target profile generation block  47  to different profiles, as shown in  FIGS. 4 and 5 . Thus, different weightings may be applied to respective ones of a first plurality of profiles input to optimization block  45  based on a further property or a measure of dispersion of a further property. 
     According to another exemplary embodiment, two or more of the profiles may be combined to create a composite profile for application to the optimization block  45 . Moreover, it is contemplated that the dynamic weighting of cross-directional property profiles may be controlled by a further property or a measure of dispersion of a further property. For example, in a highly calendered application it may be desirable to create a composite profile from the reel hardness and reel diameter profiles and provide dynamic weightings to the caliper profile (Weighting  1 ) and composite profile (Weighting  2 ) based on the average reel diameter. This is because the diameter of the building reel will affect the influence of respective profiles on the desired control action. Specifically, at the start of the reel building process (when the reel diameter is small), it is desirable that the caliper profile have a higher weighting than the composite whereas at large reel diameters the combined reel hardness and reel diameter profiles should be emphasized in the optimization process, as shown in  FIGS. 5A and 5B , wherein f(R) is the varying weighting as a function of reel diameter and f(σ) is the varying weighting as a function of one of either base sheet moisture or weight variability. 
     The cross-directional property profile(s) may be selected based on a function of one of either a specific process or specific reel condition, such as a measured reel property (caliper, reel diameter, reel hardness, etc.) The specific process comprises the specific reel condition plus a function of a base sheet property, such as weight profile, tension profile and moisture profile. The selection function may, for example, be a measure of dispersion of a further property or may be a function such as average reel diameter. Where the function is a measure of dispersion, that measure may, for example, be one of variance, standard deviation (σ), multiples of standard deviations, coefficients of variation, etc. 
     Specific embodiments have been shown and described herein. However, modifications and variations may occur to those skilled in the art. For example, although the exemplary embodiment of  FIG. 1  refers to measuring caliper, reel diameter and reel hardness, other measured cross-directional property profiles are possible, such as tension (pre-wound tension or wound-in tension). Also, although the exemplary embodiment of  FIG. 4  shows two cross-directional property profiles, it is entirely possible that three or more profiles may be combined. Furthermore, although the two cross-directional property profiles shown in  FIG. 4  are caliper profile and a composite of reel hardness profile and reel diameter profile, it is contemplated that the two cross-directional property profiles may be caliper profile and only one of reel hardness profile and reel diameter profile. In addition, whereas the dynamic weighting of cross-directional property profiles is discussed above as being controlled by average reel diameter, it is contemplated that the controlling further property may be a function of weight or tension. Moreover, although the described embodiments set forth a multivariable optimization process, it is contemplated that a single variable solution may be provided using only one controlled variable and means of target generation and/or response generation. 
     All such modifications and variations are believed to be within the sphere and scope of the present embodiment.