PARAMETERIZATION OF A TRACTIVE FORCE CONTROLLER

Abstract

Method and parameterization unit for parameterization of a tractive force controller of a controlled roller of a web-processing machine, the tractive force controller controlling a speed of the controlled roller in order to transport a material on the web-processing machine from the controlled roller to a further roller or from a further roller to the controlled roller at a line speed and while being subjected to the tractive force. The method includes, during a standstill test at a line speed of zero, increasing the tractive force to an identification tractive force, preferably 90% of a predetermined standstill tractive force operating point, to determine standstill system parameters of the tractive force system, to calculate standstill controller parameters of the tractive force controller from the standstill system parameters of the tractive force system, preferably by a frequency characteristic method, and to parameterize the tractive force controller using the standstill controller parameters.

Claims

1. A method for parameterization of a tractive force controller of a controlled roller of a web-processing machine, the tractive force controller controlling a speed of the controlled roller in order to transport a material on the web-processing machine from the controlled roller to a further roller or from a further roller to the controlled roller at a line speed and while being subjected to the tractive force, comprising: during a standstill test at a line speed of zero, increasing the tractive force to an identification tractive force, preferably 90% of a predetermined standstill tractive force operating point, to determine standstill system parameters of the tractive force system, to calculate standstill controller parameters of the tractive force controller from the standstill system parameters of the tractive force system, preferably by a frequency characteristic method, and to parameterize the tractive force controller using the standstill controller parameters.

2. The method according to claim 1, wherein the standstill system parameters of the tractive force system are determined by a preferably recursive least square method.

3. The method according to claim 1, wherein the standstill controller parameters are calculated by a frequency characteristic method.

4. The method according to claim 1, wherein a modulus of elasticity of the material is determined from the standstill system parameters of the tractive force system.

5. The method according to claim 1, wherein the tractive force is increased to a tensile tractive force, preferably 10% of the standstill tractive force operating point, before the increase to the identification tractive force.

6. The method according to claim 1, further comprising increasing the tractive force to the standstill operating tractive force, and after the tractive force operating point is reached, applying a jump in tractive force to the tractive force in order to determine the quality of the standstill controller parameters using a first standstill quality step response.

7. The method according to claim 1, wherein, after the standstill test, the method further comprises carrying out a creep test, wherein a first operating line speed and a tractive force at the level of a first tractive force operating point is provided, and a jump in tractive force is applied to the tractive force, to determine a creep step response and to identify fine system parameters based on the creep step response of the tractive force system, wherein fine controller parameters are calculated from the creep step response and the creep system parameters, and wherein the tractive force controller is parameterized using the fine controller parameters.

8. The method according to claim 7, wherein the fine system parameters of the tractive force system are identified by a preferably recursive least square method.

9. The method according to claim 7, wherein the fine controller parameters are determined by a frequency characteristic method.

10. The method according to claim 7, wherein at least one of a modulus of elasticity or a length of the medium is calculated from the fine system parameters for the first operating line speed.

11. The method according to claim 7, wherein a jump in tractive force is applied to the tractive force in order to determine the quality of the fine controller parameters for the first operating line speed using a creep quality step response, preferably by the best fit method.

12. The method according to claim 1, further comprising storing the standstill controller parameters, wherein extrapolation speed controller parameters for a number of extrapolation line speeds are extrapolated from the standstill controller parameters, and wherein during operation of the web-processing machine at a line speed within the range of one of the extrapolation line speeds, the associated extrapolation speed controller parameters for parameterizing the tractive force controller are called up.

13. The method according to claim 7, further comprising storing the fine controller parameters for the first operating line speed, wherein, during operation of the web-processing machine at a line speed within a range of the first operating line speed, the fine controller parameters for parameterizing the tractive force controller are called up.

14. The method according to claim 7, further comprising carrying out a speed test after the creep test, wherein a second operating line speed and a tractive force at the level of a second tractive force operating point being provided, and wherein a jump in tractive force is applied to the tractive force, to determine a speed test step response and identify further fine system parameters of the tractive force system, wherein the further fine controller parameters are calculated from the speed test step response and the further fine system parameters, and wherein the tractive force controller is parameterized using the further fine controller parameters.

15. The method according to claim 14, further comprising storing the further fine controller parameters for the second operating line speed, wherein, during operation of the web-processing machine at a line speed within the range of the second operating line speed, other fine controller parameters for parameterizing the tractive force controller are called up and the tractive force controller is parameterized using the further fine controller parameters.

16. The method according to claim 14, wherein additional fine controller parameters for additional operating line speeds are determined from the fine controller parameters and the further fine controller parameters, and wherein the tractive force controller is parameterized using the additional fine controller parameters.

17. The method according to claim 16, further comprising storing the additional fine controller parameters for the additional operating line speeds, wherein during operation of the web-processing machine at a line speed within the range of the respective additional operating line speed with the associated fine controller parameters, the associated additional fine controller parameters are called up to parameterize the tractive force controller and the tractive force controller is parameterized using the associated additional fine controller parameters.

18. A method of using a tractive force controller parameterized according to a method according to claim 1 for controlling a tractive force of a material in a web-processing machine, comprising: while being subjected to the tractive force, transporting the material from a controlled roller to a further roller or from a further roller to a controlled roller at a line speed.

19. A parameterization unit for parameterization of a tractive force controller of a controlled roller of a web-processing machine on which a material is transported from the controlled roller to a further roller or from a further roller to a controlled roller at a line speed, subjected to a tractive force, the tractive force being controllable via a speed of the controlled roller by the tractive force controller, comprising: during a standstill test at a line speed of zero, parameterization unit is configured to increase the tractive force to an identification tractive force, preferably 90% of a predetermined standstill tractive force operating point, to determine the standstill system parameters of the tractive force system and to calculate standstill controller parameters of the tractive force controller from the standstill system parameters of the tractive force system, preferably by a frequency characteristic method, and to parameterize the tractive force controller with the standstill controller parameters.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The present invention will be explained below in greater detail with reference to FIGS. 1 to 5, which show exemplary advantageous embodiments of the invention in a schematic and non-limiting manner. In the drawings,

[0036] FIG. 1 shows a general web-processing machine;

[0037] FIG. 2 shows zones of a web-processing machine;

[0038] FIG. 3 shows an adjustment of a tractive force at a standstill;

[0039] FIG. 4 shows a standstill test; and

[0040] FIG. 5 shows a crawl test or a speed test.

DETAILED DESCRIPTION

[0041] The particulars shown herein are by way of example and for purposes of illustrative discussion of the embodiments of the present invention only and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the present invention. In this regard, no attempt is made to show structural details of the present invention in more detail than is necessary for the fundamental understanding of the present invention, the description taken with the drawings making apparent to those skilled in the art how the several forms of the present invention may be embodied in practice.

[0042] FIG. 1 shows a web-processing machine 1 for continuous processes. A winder 2 is provided as a controlled roller, which winder is designed to wind a material 3 onto a winder core 20 or to unwind said material from the winder core 20, depending on whether the winder is at the beginning or end of the web-processing machine 1. As a result, it is always assumed that the material 3 is unwound from the winder core 20, but it is also always possible to wind the material 3 onto the winder core 20 in an analogous manner. The wound material 3 is pretensioned on the winder 2 and thus has a basic elongation ϵ.sub.0.

[0043] Furthermore, a traction roller 6 is provided that has a pressure roller 60 to transport the material between the traction roller 6 and the pressure roller 60 without slipping. The pressure roller 60 is not actively driven and is pressed against the traction roller 60. As a result of the coupling via the material 3, a change in the rotational speed of the winder 2 also has an effect on the traction roller 6. The traction roller 6 itself is driven at a traction roller speed v6, has no superimposed tractive force controller and thus represents the master. A line speed v of the material 3 is set by the traction roller speed v6. The line speed v is thus controlled by the circumferential speed of the traction roller 6, line speeds v of more than 1000 m/min being possible. The line speed v preferably has a trapezoidal profile, i.e. a linear increase from zero to the operating line speed v.sub.1, v.sub.2 at the beginning of the production process. The line speed v is kept constant at the desired operating line speed v.sub.1, v.sub.2 during the production process and is reduced linearly to zero again at the end of the production process.

[0044] The winder 2 has a winder speed v9′, which is composed on the one hand of a set winder speed v9 and a correction speed Δv9. The circumferential speed of the winder 2 is kept constant such that the set winder speed v9 varies depending on the diameter of the winder 2. The correction speed Δv9 is specified by a tractive force controller 9 in order to control the winder speed v9′. The winder 2 is thus the actuator for controlling the tractive force F in the material 3. The actual tractive force F.sub.actual is measured as a process variable using a measuring unit 5, for example a load cell, and fed back to the tractive force controller 9. The tractive force controller 9 calculates the correction speed Δv9 from the actual tractive force F.sub.actual and the set tractive force F.sub.set. Both the traction roller speed v6 and the set winder speed v9 are specified by the tractive force controller 9 only by way of example and can also be specified by a further component.

[0045] Because the winder 2 and the traction roller 6 are each connected in a contact region with the material 3 in a non-positive and slip-free manner, the line speed v can be equated approximately with the circumferential speed of the traction roller 6 and the winder 2. However, depending on the tractive force F that occurs, the circumferential speed of the winder 2 deviates minimally from the line speed v. Because the material 3 is unwound from the winder 2, it is advantageous if a change in the winder diameter is taken into account when determining the relationship between the circumferential speed of the winder 2 and the line speed v. For this purpose, the winder diameter can be measured or estimated.

[0046] If, on the other hand, a web-processing machine 1 has a dancer control, instead of the actual tractive force F.sub.actual, a dancer position is provided as a process variable to be returned. If a web-processing machine 1 has tractive force management instead of a tractive force controller 9, no return of process variables is provided at all.

[0047] There are also optional deflection rollers 4 provided in FIG. 1, which serve to guide the material 3, but are not driven themselves. The mass moment of inertia of the deflection rollers 4 is low and can often be neglected. However, during acceleration and braking processes, it may well be necessary to take into account the mass moment of inertia of the deflection rollers 4 and to generate a smooth line speed profile in order to minimize negative inertia effects.

[0048] A web-processing machine 1 usually consists of a plurality of sections, also called zones. In a web-processing machine 1, the term zone denotes a region between two driven rollers, between which the material 3 is clamped in a slip-free manner. The condition of the material 3 within a zone is influenced by the two driven rollers, which delimit the respective zone. In a zone, one roller serves as the master and one roller as the slave. It is often the case that at least three zones are planned in a web-processing machine 1: An entry zone A, a process zone B and an exit zone C, as indicated in FIG. 2. In the entry zone A, the material 3 is unwound from the winder 2 in that the corresponding tractive force F.sub.actual is controlled by the tractive force controller 9 in that said tractive force controller prescribes a winder speed v.sub.9′ for the winder 2. Web movement control is preferably provided in the entry zone A, which web movement control corrects a lateral offset of the material 3. A material buffer can also be present in order to store material. These are constructions having deflection rollers that increase the distance from one another and thus can accommodate more material 3. This is particularly useful in the winding and unwinding region when a roll change is to be carried out without stopping the machine. During the roll change, the material is removed from the buffer; the web-processing machine does not have to be stopped during this time. A machining process (e.g. printing, packaging, coating, punching . . . ) takes place in process zone B, which is why the highest demands on the accuracy of the tractive force F are made in process zone B. In the exit zone C, the material 3 is removed and/or wound up on a winding-up device 7, as shown in FIG. 2. As in the entry zone A, web movement control and/or a material buffer can be provided in the exit zone C. After removal, the material 3 can be transferred to a further, for example discontinuous, process.

[0049] Because all rollers with which the material 3 is in non-positive contact (i.e. the winder 2, the traction roller 6, the further traction roller 6′ and the winding-up device 7 in FIG. 2) are coupled by the material 3, the material properties of the material 3 can have a substantial influence on this coupling and thus on the design of the tractive force controller 9.

[0050] The line speed v is thus determined in a zone (entry zone A, process zone B, exit zone C) by a master, e.g. by the traction roller 6 in entry zone A. The entry zone A is subsequently considered. However, the calculation of the controller parameters is fundamentally also possible for tractive force controllers 9 in process zones B or exit zones C in an analogous manner—provided a master and a slave are provided.

[0051] At a standstill, i.e. at a line speed v of zero, the elongation of the material 3 can be determined via the position of the winder 2. The material 3 located between the winder 2 and the traction roller 6 has a basic length L0. Thus, the tractive force F in the entry zone A corresponds to the basic tractive force F.sub.0 with which the material 3 was wound onto the winder 2. If, as shown in FIG. 3, the position of the winder 2 is changed by an adjustment angle Δφ, the result is a change in length of the material 3 by the length difference ΔL, which results in a tractive force difference ΔF. For the tractive force F, the sum of the basic tractive force F0 and the tractive force difference ΔF is: F=F0+ΔF.

[0052] In order to change the tractive force F during operation, i.e. at a line speed v greater than zero, a corresponding correction speed Δv9 is, as mentioned, applied to the set winder speed v9 from which the winder speed v9′ of the winder 2 results. At a constant correction speed Δv9, a constant change in tractive force ΔF occurs after a certain period, the magnitude of which is strongly dependent on the line speed v that occurs. As a master, the traction roller 6 therefore specifies a line speed v, and the winder speed v9′ and thus the angular speed w of the winder 2 are changed via the correction speed Δv9 in such a way that the desired tractive force F.sub.actual is generated in the material 3. The winder 2 thus works, so to speak, against the traction roller 6 and thus generates the tractive force F in the material 3.

[0053] The angular speed ω of the winder 2 also changes at a constant line speed v as a function of the changed radius r of the winder 2 with ω=v/r. To ensure that the circumferential speed of the winder 2 corresponds to the line speed v of the system, the angular speed co or the correction speed Δv9 must thus always be adapted to the current radius r.

[0054] The tractive force controller 9 can, for example, correspond to a PI controller, other types of controllers, for example PID controllers, state regulators, etc. also being possible.

[0055] Controller parameters R.sub.F,v1, R.sub.F,v2, R.sub.F,vx of the tractive force controller 9 can be determined for various operating line speeds v.sub.1, v.sub.2, v.sub.x.

[0056] The material 3 can be in different forms (web, wire, etc.) and can consist of paper, fabric, plastics, metal, etc., for example. The material 3 can be viewed as a three-dimensional body. The material 3 has a length L that is initially at least roughly known and can subsequently be determined precisely. Furthermore, the material 3 has a modulus of elasticity E, which is usually not known. In addition, the material has a cross-section A, which is preferably known as precisely as possible in order to calculate the modulus of elasticity E from the line parameters (which represent the product of the cross-section and the modulus of elasticity E), e.g. from the fine line parameters—see below.

[0057] If the material 3 is subjected to a tractive force F in the longitudinal direction, a tractive stress σ=F/A arises depending on the cross-sectional area A of the material. Assuming that the cross-sectional area A does not change significantly due to the tractive force F acting from the outside, the tractive stress σ is directly proportional to the tractive force F. The tractive force F acting from the outside also generates an elongation ϵ of the material 3. For the design of the tractive force controller 9, only one region having a linear-elastic relationship of the tractive stress σ and the elongation ϵ is considered. This means that, in this region, the elongation ϵ increases linearly with the tractive stress σ, the gradient being described by the modulus of elasticity E. If the tractive stress σ is reduced again, the material 3 assumes the original length L again. The tractive stress in material 3 can be described with Hooke's law σ=E*ϵ. Since the tractive stress σ is assumed to be directly proportional to the tractive force F, it can also be assumed that the tractive force F is directly proportional to the elongation ϵ. The elongation ϵ describes the relation between the change in length ΔL resulting from the application of the tractive force F and the initial length L0. The relationship between the elongation ϵ and the tractive force F results as F=E*A*ϵ.

[0058] To determine the standstill controller parameters R.sub.F,o, a standstill test T.sub.0 having a line speed v of zero is carried out, an exemplary course of the tractive force F as well as the set winder speed v.sub.9 being shown in FIG. 4. The implementation of the standstill test T.sub.0 to determine the standstill controller parameters R.sub.F,o can be done on a parameterization unit 90, which can be an integral part of the tractive force controller 9.

[0059] During the standstill test T.sub.0, the traction roller speed v.sub.6 is zero. When the standstill test T.sub.0 is carried out, the material 3 is stretched by a negative set winder speed v.sub.9=v.sub.0. This means that the set winder speed v.sub.9=v.sub.0 acts against the direction of rotation of the winder 2, which is present in a production operation. Because the traction roller 6 does not move or moves only negligibly, a counter-torque is built up, but the line speed v remains zero during the standstill test T.sub.0. In a first portion T.sub.01 of the standstill test T.sub.0, the winder 2 is operated at the negative set winder speed v.sub.9=v.sub.0 until the tractive force F reaches a tensile tractive force F.sub.w1, preferably 10% of the tractive force operating point F.sub.op. Once the tractive force F has reached the tensile tractive force F.sub.w1, a set winder speed v.sub.9 of zero is again specified in an initialization phase Toa in order to keep the tractive force F constant at the tensile tractive force F.sub.w1.

[0060] Subsequently, during an identification phase T.sub.03, the tractive force F is increased to an identification tractive force F.sub.w2, preferably 90% of the standstill tractive force operating point F.sub.op, in that the negative set winder speed v9=v0 is again specified for the winder 2. In the identification phase T.sub.03, the standstill controller parameters R.sub.F,o are determined from the standstill system parameters of the tractive force system G.sub.F,0, which is preferably done by a frequency characteristic method.

[0061] The tractive force controller 9 can be parameterized using the standstill controller parameters R.sub.F,o, whereupon the tractive force F is increased to the standstill tractive force operating point F.sub.op. A jump ΔF can then be applied to the tractive force F in order to determine the quality of the standstill controller parameters R.sub.F,o using a first standstill quality step response g0, for example by a recursive best fit method.

[0062] If standstill controller parameters R.sub.F,o are of sufficient quality, a creep test T1 can be carried out in order to determine fine controller parameters R.sub.F,v1 for a first operating line speed v.sub.1, the tractive force F and the constant first line speed v.sub.1 being shown in FIG. 5. The implementation of the creep tests T1 to determine the fine controller parameters R.sub.F,v1 can also take place on the parameterization unit 90, but also on a separately designed fine parameterization unit.

[0063] During the creep test T.sub.1, the material 3 is moved at a first operating line speed v.sub.1. The tractive force controller 9 is parameterized using the standstill controller parameters R.sub.F,o determined during the standstill test T.sub.0. During the creep test T.sub.1, a first tractive force operating point F.sub.op1, which can correspond to the standstill tractive force operating point F.sub.op of the standstill test T.sub.0, is specified for the tractive force F. The tractive force controller 9 controls the set winder speed v9 of the winder 2 in order to regulate the tractive force F to the first tractive force operating point F.sub.op1.

[0064] Identification in the case of a closed control loop has the advantage that unknown disturbances can be compensated for by the tractive force controller 9. However, it must also be taken into account that the controlled system is excited only by the correction speed Δv.sub.9 supplied by the tractive force controller 9. A jump in tractive force ΔF is therefore applied to the tractive force F, which corresponds to a sudden change in the tractive force operating point F.sub.op1 in order to ensure sufficient excitation of the controlled system. An identification phase T.sub.11 starts again with the jump in tractive force ΔF. The fine system parameters G.sub.F,v1 of the tractive force system for the first operating line speed v.sub.1 are identified from a creep step response h1 by the (recursive) least squares method. Because the control loop is closed, the tractive force F ideally reaches the tractive force operating point F.sub.op1 after the rise time t.sub.r. Because the rise time t.sub.r was specified for the standstill controller, the tractive force controller 9 parameterized according to the standstill controller parameters R.sub.F,o does not necessarily have to be able to meet the rise time t.sub.r time in the creep test.

[0065] The fine controller parameters R.sub.F,v1 for the first operating line speed v.sub.1 are determined for the first operating line speed v.sub.1 from the obtained first step response h1 and the determined fine track parameters G.sub.F,v1 of the tractive force system. The modulus of elasticity E and/or the length L of the material 3 for the first operating line speed v.sub.1 can be determined from the fine line parameters G.sub.F,v1.

[0066] A second jump in tractive force ΔF can be applied to the tractive force F in order to determine the quality of the fine controller parameters R.sub.F,v1 for the first operating line speed v.sub.1 using a creep quality step response h2, which can be done by the recursive best fit method.

[0067] Analogously to the creep test T.sub.1, a speed test T.sub.2 can also be carried out, which corresponds to a creep test T.sub.1 at a higher line speed v.sub.2, preferably at a maximum line speed. The tractive force controller 9 is parameterized using the fine controller parameters R.sub.F,v1 determined as part of the creep test T.sub.1 in order to determine further fine controller parameters G.sub.F,v2 for the second operating line speed v.sub.2. The speed test T.sub.2 can take place during the creep test T.sub.1 by providing a second operating line speed v.sub.2 and a tractive force F at the level of a second tractive force operating point F.sub.op2, which corresponds, for example, to the first tractive force operating point F.sub.op1. A jump in tractive force ΔF is applied to the tractive force F, a speed test step response h2 is determined and the further fine system parameters G.sub.F,v2 of the tractive force system are identified from the speed test step response h2. Further fine controller parameters R.sub.F,v2 are determined from the speed test step response h2 and the further fine system parameters G.sub.F,v2. The quality of the fine controller parameters can also be checked by applying a jump in tractive force ΔF to the tractive force F.

[0068] The implementation of the speed tests T.sub.2 to determine the further fine controller parameters G.sub.F,v2 can also take place on the parameterization unit 90, but also on a further fine parameterization unit that is designed separately.

[0069] If no controller parameters were determined between the first operating line speed v.sub.1 and the second (preferably maximum) operating line speed v.sub.2, additional controller parameters R.sub.F,vx for additional operating line speeds v.sub.x can also be determined offline, i.e. without further test procedures. This can be done by performing a coefficient comparison as part of a frequency characteristic method, or by interpolation between the fine controller parameters R.sub.F,v1 and the further fine controller parameters R.sub.F,v2 along a function.

[0070] The additional controller parameters R.sub.F,vx determined for the additional line speeds v.sub.x (as well as the fine controller parameters R.sub.F,v1 for the first operating line speed v.sub.1 and/or the further fine controller parameters R.sub.F,v2 for the second operating line speed v.sub.2) can be stored as a parameter set for the tractive force controller 9 and called up during operation if required.

[0071] The parameterization unit 90 and/or the fine parameterization unit and/or the further fine parameterization unit can comprise microprocessor-based hardware, for example a computer or digital signal processor (DSP), on which appropriate software for performing the respective function is executed. The parameterization unit 90 and/or the fine parameterization unit and/or the further fine parameterization unit can also comprise an integrated circuit, for example an application-specific integrated circuit (ASIC) or a field programmable gate array (FPGA), also with a microprocessor. The parameterization unit 90 and/or the fine parameterization unit and/or the further fine parameterization unit can also comprise an analog circuit or an analog computer. Mixed forms are conceivable as well. It is also possible for different functions to be implemented on the same hardware.

[0072] An identification of system parameters of a tractive force system G(s) is shown below by way of example. The standstill system parameters of the tractive force system G.sub.F,0(s) are determined and used to determine the standstill controller parameters R.sub.F,0 (standstill test T.sub.0). Furthermore, the fine system parameters of the tractive force system G.sub.F,v1 (s) are determined and used to determine the fine controller parameters R.sub.F,v1 of a tractive force controller 9 (creep test T.sub.1). The system parameters are identified first by a standstill test T.sub.0, i.e. at a line speed v of zero, and then by a creep test T.sub.1, i.e. at a line speed v not equal to 0.

[0073] The material 3 has a basic elongation ϵ.sub.0, the basic elongation ϵ.sub.0 in the case of lightly wound material 3 also being zero or at least negligible.

[00001]$E=2.Math.{10}^7\frac{N}{m^2}$

is assumed as the modulus of elasticity, L=4.5 m as the length, A=2.8.Math.10.sup.−5 m as the cross-section and ϵ.sub.0=0,1786 as the basic elongation. The identification of the standstill system parameters of the tractive force system G.sub.F,v0(s) is initially carried out in an uncontrolled manner in the open control loop and then in the closed control loop.

[0074] The general transfer function of the tractive force system G(s) is described by

[00002]$G\left(s\right)=\frac{\mathrm{AE}\left(1+{ϵ}_0\right)}{\mathrm{sL}+v}\mathrm{or}G\left(s\right)=\frac{b_0}{a_{1}s+1}$

with the coefficients

[00003]$b_0=\frac{\mathrm{AE}\left(1+{ϵ}_0\right)}{v}\mathrm{and}{a}_1=\frac{L}{v}.$

[0075] At line speeds v greater than 0, two standstill system parameters of the tractive force system G.sub.F,v(s) can be estimated, whereby the length L and the modulus of elasticity E can be determined.

[0076] For the standstill, i.e. a line speed v=0, the tractive force system

[00004]$G_{F,0}\left(s\right)=K_S\frac{1}{s}\mathrm{with}{K}_S=\frac{\mathrm{AE}\left(1+{ϵ}_0\right)}{L}\mathrm{applies}.$

[0077] At a standstill, there is therefore only one coefficient K.sub.S, which is why only one system parameter can be estimated here. The modulus of elasticity E can only be determined from this standstill system parameter if the length L of the material 3 is known.

[0078] A standstill test T.sub.0 is now carried out with an open control loop, it being assumed that the material 3 in the web-processing machine 1 has a line speed v of 0 m/min. As shown in FIG. 4, a jump to the set winder speed v.sub.9 of winder 2 is applied. A step response is also determined, i.e., tractive force F is observed to see how it behaves.

[0079] The standstill system parameters of the tractive force system G.sub.F,0(s) in the form of the coefficient K.sub.S are determined from the step response by the (recursive) least squares method. Thus, in this example, the result is the coefficient with K.sub.S=144.66. With a known length L=4.5 m, the result for the modulus of elasticity is

[00005]$E=\frac{K_{S}L}{A\left(1+{ϵ}_0\right)}=1.97.Math.{10}^7\frac{N}{m^2}.$

[0080] Because all the required standstill system parameters of the tractive force system G.sub.F,0(s) are now known, the standstill controller parameters R.sub.F,v0 can be determined and the controller can thus be designed.

[0081] The controller ultimately has the form

[00006]$R_F\left(s\right)=v_R\left(\frac{{\mathrm{sT}}_R+1}{s}\right)$

and is designed with the specifications ω.sub.ct.sub.r≈1.5 and Ø[°]+ü[%]≈70, where ω.sub.c is the crossover frequency of the open loop, t.sub.r is the rise time of the step response of the closed loop, Ø describes the phase reserve and ü describes the overshoot of the step response of the closed circuit.

[0082] The frequency characteristic method is now used. For this purpose, a desired rise time t.sub.r is specified, for example 0.17 s. This therefore results in a crossover frequency

[00007]${\omega }_c=\frac{1.5}{t_r}=8.823\mathrm{Hz}.$

With an overshoot ü of ü=10%, the phase reserve is Ø[°]=70−ü[%]=60°. The argument of the transfer function at the crossover frequency ω.sub.c is calculated with

[00008]$G\left(j\omega \right)=\frac{K_S}{j\omega }$$\mathrm{and}$$\arg \left(G\left(j\omega \right)\right)=-90°.$

[0083] The time constant T.sub.R is further calculated with

[00009]$T_R=\frac{1}{{\omega }_c}\tan (-90+\varnothing -\arg \left(G\left({j\omega }_c\right)\right)=0.1963.$

The time constant T.sub.R was thus determined as the first controller parameter R.sub.F,v0.

[0084] The system at the crossover frequency is equal to:

[00010]$.Math.G\left({j\omega }_c\right).Math.=\frac{.Math.K_S.Math.}{.Math.{j\omega }_c.Math.}=16.40$

[0085] This results in the amplification

[00011]$V_R=\frac{{\omega }_c}{.Math.G\left({j\omega }_c\right).Math.\sqrt{1+{\left(T_R{\omega }_c\right)}^2}}=0.2690$

for tractive force controller 9.

[0086] Thus, the time constant T.sub.R and the amplification V.sub.R were determined as standstill controller parameters R.sub.F,0 for the controller

[00012]$R_F\left(s\right)=v_R\left(\frac{{\mathrm{sT}}_R+1}{s}\right)$

and the tractive force controller 9 was parameterized using these standstill controller parameters R.sub.F,v0. The controller design for the standstill test T.sub.0 is thus completed.

[0087] The tractive force controller 9 parameterized by the standstill test T.sub.0 is now used to carry out a creep test T.sub.1 in a closed control loop, it being assumed, for example, that the material 3 in the web-processing machine 1 has a line speed v of 15 m/min. A jump in tractive force ΔF is subsequently applied to the tractive force F, as shown in FIG. 5.

[0088] The fine system parameters of the tractive force system G.sub.F,0(s) are determined from the jump in tractive force ΔF in the form of the coefficients a1 and b0 using the (recursive) least squares method, which result, for example, with α1=18.095 and b.sub.0=2691.1. Thus, the length L=a.sub.1 v=4.52 m and the modulus of elasticity is equal to

[00013]$E=\frac{b_{0}v}{A\left(1+{ϵ}_0\right)}=2.04.Math.{10}^7\frac{N}{m^2}.$

A comparison with the result determined above as part of the standstill test T.sub.0 for the modulus of elasticity of E=1.97*10.sup.7 N/m shows that the result of the standstill test was already sufficiently precise.

[0089] The determination of the fine controller parameters R.sub.F,v1 of the tractive force controller 6 for the creep test T.sub.1 takes place fundamentally analogously to the determination of the standstill controller parameters R.sub.F,0 for the standstill test T.sub.0.

[0090] For the determination of the standstill system parameters G.sub.F,0, however, the tractive force F is increased to an identification tractive force F.sub.w2, whereas a jump in tractive force ΔF is applied to determine the fine system parameters G.sub.F,v1.

[0091] The argument of the transfer function at the crossover frequency ω.sub.c is calculated with

[00014]$\arg \left(G\left({j\omega }_c\right)\right)=\arg \left(\frac{b_0}{a_1{j\omega }_c+1}\right)=-89.64°.$

The time constant T.sub.R is further calculated with

[00015]$T_R=\frac{1}{{\omega }_c}\tan (-90+\varnothing +\arg \left(G\left({j\omega }_c\right)\right)=0.1929.$

The time constant T.sub.R was thus determined as the controller parameter R.sub.F,v1.

[0092] The system at the crossover frequency is:

[00016]$.Math.G\left({j\omega }_c\right).Math.=\frac{.Math.b_0.Math.}{.Math.1+a_1{j\omega }_c.Math.}=16.86.$

This results in the amplification

[00017]$V_R=\frac{{\omega }_c}{.Math.G\left({j\omega }_c\right).Math.\sqrt{1+{\left(T_R{\omega }_c\right)}^2}}=0.2651$

for the tractive force controller 9.

[0093] Thus, the time constant T.sub.R and the amplification V.sub.R are determined as fine controller parameters R.sub.F,v1 for the controller

[00018]$R_F\left(s\right)=v_R\left(\frac{{\mathrm{sT}}_R+1}{s}\right).$

The controller design for the creep test is thus complete, whereby the tractive force controller 9 can be parameterized using the fine controller parameters R.sub.F,v1.

[0094] It is noted that the foregoing examples have been provided merely for the purpose of explanation and are in no way to be construed as limiting of the present invention. While the present invention has been described with reference to an exemplary embodiment, it is understood that the words which have been used herein are words of description and illustration, rather than words of limitation. Changes may be made, within the purview of the appended claims, as presently stated and as amended, without departing from the scope and spirit of the present invention in its aspects. Although the present invention has been described herein with reference to particular means, materials and embodiments, the present invention is not intended to be limited to the particulars disclosed herein; rather, the present invention extends to all functionally equivalent structures, methods and uses, such as are within the scope of the appended claims.