Method for controlling a movement of a movably mounted body of a mechanical system

Abstract

A method for controlling movement of a movably mounted body (14) of a mechanical system (2, 56, 62). The mechanical system (2, 6, 62) includes a drive unit (4, 64), which is operated by a medium, and also a control valve (20, 22). The movably mounted body (14) is driven by the drive unit (4, 64). A drive movement of the drive unit (4, 64) is controlled with the aid of the control valve (20, 22). In order to avoid or reduce excitation of undesired vibrations in the mechanical system (2, 56, 62), it is proposed that the control valve (20, 22) be actuated using a control signal (u(t)) which comprises a first and also a further switching pulse (S.sub.1, S.sub.3) each having a prespecified pulse duration. The pulse duration of the first switching pulse (S.sub.1) is equal to the pulse duration of the further switching pulse (S.sub.3). A time difference (Δt.sub.1-3) between the start of the first pulse (S.sub.1) and the start of the further switching pulse (S.sub.3) is matched to a natural period duration of the mechanical system (2, 56, 62).

Claims

1. A method for controlling a movement of a movably mounted body of a mechanical system, wherein the mechanical system comprises a drive unit which is configured to be operated by a medium, and a control valve; the method comprising: driving the movably mounted body by the drive unit, controlling a drive movement of the drive unit using the control valve; actuating the control valve by a control signal u(t) which comprises a first switching pulse and a further switching pulse (S.sub.1, S.sub.3), with each pulse having a predefined pulse duration, the pulse duration of the first switching pulse (S.sub.1) being equal to the pulse duration of the further switching pulse (S.sub.3); and a time interval (Δt.sub.1-3) between the start of the first switching pulse (S.sub.1) and the start of the further switching pulse (S.sub.3), the time interval being adapted to an intrinsic period duration of the mechanical system.

2. A method according to claim 1, wherein the time interval (Δt.sub.1-3) between the start of the first switching pulse (S.sub.1) and the start of the further switching pulse (S.sub.3) is a linear function of the intrinsic period duration.

3. A method according to claim 2, wherein the time interval (Δt.sub.1-3) between the start of the first switching pulse (S.sub.1) and the start of the further switching pulse (S.sub.3) is at least half of the intrinsic period duration.

4. A method according to claim 1, further comprising if the control valve has a switching time which is longer than a sixth of the intrinsic period duration, the time interval (Δt.sub.1-3) between the start of the first switching pulse (S.sub.1) and the start of the further switching pulse (S.sub.3) is a function of the switching time.

5. A method according to claim 1, further comprising the pulse duration of the first switching pulse (S.sub.1) and the pulse duration of the further switching pulse (S.sub.3) are each a linear function of the intrinsic period duration.

6. A method according to claim 1, further comprising if the control valve has a switching time which is longer than a sixth of the intrinsic period duration, the pulse duration of the first switching pulse (S.sub.1) and the pulse duration of the further switching pulse (S.sub.3) are each a linear function of the switching time.

7. A method according to claim 1, further comprising the control signal u(t) has an additional switching pulse (S.sub.2) with a predefined pulse duration between the first and the further switching pulses (S.sub.1, S.sub.3).

8. A method according to claim 7, further comprising a time interval (Δt.sub.1-2) between the start of the first switching pulse (S.sub.1) and the start of the additional switching pulse (S.sub.2) is a linear function of the intrinsic period duration.

9. A method according to claim 7, further comprising separating the first switching pulse and the additional switching (S.sub.1, S.sub.2) pulses from one another by a first pause with a predefined pause duration, and the additional switching pulse and the further switching pulse (S.sub.2, S.sub.3) are separated from one another by a second pause with a second predefined pause duration, the pause duration of the first pause and the pause duration of the second pause each being a linear function of the intrinsic period duration.

10. A method according to claim 9, wherein the pause duration of the first pause is equal to the pause duration of the second pause.

11. A method according to claim 1, wherein the medium for operating the drive unit is a liquid.

12. A method according to claim 1, wherein the control valve is a digital valve.

13. A method according to claim 1, further comprising the movably mounted body is a pressure roller of a coiler, and the drive unit is a hydraulic cylinder.

14. A method according to claim 13, further comprising: during a winding operation of a metal strip for winding the metal strip onto a coiler drum, pressing the pressure roller against the metal strip then on the coiler with the aid of the drive unit; moving the pressure roller by the drive movement of the drive unit, during at least one phase of the winding operation for spacing the pressure roller apart from the metal strip when a strip beginning of the metal strip lies on the coiler drum to run through between the pressure roller and the coiler drum.

15. A mechanical system comprising: a movably mounted body, a drive unit which can be operated by a medium, which drive unit is for driving the movably mounted body; a control valve for controlling a drive movement of the drive unit; a control unit which is configured to generate a control signal u(t) for actuating the control valve, wherein the control signal u(t) comprises a first switching pulse and a further switching pulse (S.sub.1, S.sub.3) each having a predefined pulse duration; the pulse duration of the first switching pulse (S.sub.1) is equal to the pulse duration of the further switching pulse (S.sub.3); a time interval (Δt.sub.1-3) between the start of the first switching pulse (S.sub.1) and the start of the further switching pulse (S.sub.3) and being adapted to an intrinsic period duration of the mechanical system.

16. A method according to claim 1, wherein the medium for operating the drive unit is an oil.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a mechanical system comprising a hydraulic cylinder with a drive piston, a movably mounted body, multiple control valves and a control unit;

(2) FIG. 2 shows an exemplary transfer function of the mechanical system from FIG. 1;

(3) FIG. 3 show three diagrams in which different control valve control signals are shown as a function of the time and associated time profiles of a position and speed of the drive piston, wherein

(4) FIG. 3A shows the control signal u(t) according to a first embodiment of the invention and a further control signal as a function of time;

(5) FIG. 3B shows the speed v(t) according to a first embodiment of the invention and a further speed as a function of time;

(6) FIG. 3C shows the position x(t) of the drive piston according to a first embodiment of the invention and a further position as a function of time;

(7) FIG. 4 show the same measurement diagrams as in FIG. 3, wherein

(8) FIG. 4A shows the same quantity measurement as a function of time as shown in FIG. 3A according to a first and a second embodiment of the invention;

(9) FIG. 4B shows the same speed measurement as a function of time as shown in FIG. 3B according to a first and a second embodiment of the invention;

(10) FIG. 4C shows the same position measurement of the entire piston as a function of time as in FIG. 3C according to a first and a second embodiment of the invention;

(11) FIG. 5 show the same measurement diagrams as in FIG. 3, wherein

(12) FIG. 5A shows the same quantity measurement as a function of time as shown in FIG. 3A according to the second embodiment of the invention;

(13) FIG. 5B shows the same speed measurement as a function of time as shown in FIG. 3B according to a second embodiment of the invention;

(14) FIG. 5C shows the same position of measurement of the entire piston as a function of time as in FIG. 3C according to a second embodiment of the invention;

(15) FIG. 6 show three diagrams, in which a valve piston position is shown as a function of the time and associated time profiles of a position and speed of the drive piston with a ballistic valve activation are shown;

(16) FIG. 6A shows the same quantity measurement as a function of time as shown in FIG. 5A with a ballistic valve actuator;

(17) FIG. 6B shows the same speed measurement as a function of time as shown in FIG. 5B with a ballistic valve actuator;

(18) FIG. 6C shows the same position of measurement of the entire piston as a function of time as in FIG. 5C with a ballistic valve actuator;

(19) FIG. 7 shows a coiler for winding up a metal strip comprising three mechanical systems each with a pressure roller and a hydraulic cylinder; and

(20) FIG. 8 shows a further mechanical system which comprises a hydraulic motor, a rotatably mounted body, a control valve and a control unit.

DESCRIPTION OF EMBODIMENTS

(21) FIG. 1 shows a schematic representation of a mechanical system 2.

(22) The mechanical system 2 comprises, among other things, a drive unit 4 that can be operated with a medium, in particular with oil. In the present exemplary embodiment, the drive unit 4 is designed as hydraulic cylinder.

(23) The drive unit 4 comprises a housing 6. In addition, the drive unit 4 comprises a linearly moveable drive piston 8 as its moveable drive element, wherein the drive piston 8 comprises a piston head 10 and a piston rod 12 that is connected to the piston head 10.

(24) Furthermore, the mechanical system 2 comprises a movably mounted body 14 which is driven by the drive unit 4. The movably mounted body 14 is connected to the drive piston 8, more precisely to the piston rod 12. In the present example, the movably mounted body 14 is mounted so as to be linearly moveable.

(25) Furthermore, the mechanical system 2 comprises a pressure source 16 and a pressure sink 18. The pressure source 16 in the present example is a pump which at its outlet provides the previously mentioned medium with a pressure of typically approximately 300 bar.

(26) In addition, the mechanical system 2 comprises a first control valve 20 which is designed as digital valve, and a second control valve 22, which is likewise designed as digital valve. In the present exemplary embodiment, the first and second control valve 20, 22 are embodied identically in construction and are therefore identical in their switching time t.sub.s. Here, the opening time of the respective control valve 20, 22 is referred to as closing time t.sub.s which at the same time corresponds to its closing time. Thus it is assumed that with respect to the control valves 20, 22 the opening time coincides with the closing time.

(27) In addition, the mechanical system 2 comprises a first fluid line 24, via which the first control valve 20 is connected to the pressure source 16, and a second fluid line 26, via which the second control valve 22 is connected to the pressure sink 18.

(28) In the present example, the previously mentioned pressure sink 18 is a tank which is preloaded in such a manner that in the second fluid line 26 at the second control valve 22, there is a pressure of typically approximately 20 bar.

(29) Apart from the foregoing, the mechanical system 2 comprises two pressure accumulators 28 which are partly filled with a gas. One accumulation is connected to the first fluid line 24 and the other one is connected to the second fluid line 26. By means of these two pressure accumulators 28, pressure peaks and/or cavitation during switching operations of the control valves 20, 22 can be avoided.

(30) Furthermore, the first control valve 20 is connected to the so-called piston side of the drive unit 4 via a third fluid line 30 of the mechanical system 2. The second control valve 22 is likewise connected to the piston side of the drive unit 4 via a fourth fluid line 32 of the mechanical system 2.

(31) The mechanical system 2 comprises a further control valve 34 which is designed as a proportional valve, in particular as a multi-way valve. The further control valve 34 is likewise connected to the piston side of the drive unit 4 via a fifth fluid line 36 of the mechanical system 2. Furthermore, the further control valve 34 is connected to the pressure sink 18 via a sixth fluid line 38 of the mechanical system 2. A seventh fluid line 40 of the mechanical system 2 connects the further control valve 34 to the pressure source 16.

(32) Each of the three control valves 20, 22, 34 comprises an electromagnetically controlled valve piston as a shut-off body and a valve spring.

(33) The further control valve 34 has a switching position in which the medium can flow from the drive unit 4 to the pressure sink 18. The further control valve 34 has a switching position in which the medium can flow from the pressure source 16 to the drive unit 4. In addition, the further control valve 34 has a switching position in which a medium flow through the further control valve 34 is prevented.

(34) The mechanical system 2 is equipped with a control unit 42 for controlling the control valves 20, 22, 34 and the unit is connected to each of the three control valves 20, 22, 34 in each case via a signal transmission line 44. The valve position of the respective control valve 20, 22, 34 is controlled by the control unit 42. For this purpose, the control unit 42 generates electrical control signals for the control valves 20, 22, 34 and passes the control signals on to the control valves 20, 22, 34 via the signal transmission lines 44.

(35) When the first control valve 20 is opened and the second control valve 22 is closed and the further control valve 34 is in the switching position in which a medium flow through the further control valve 34 is prevented, the medium provided by the pressure source 16 flows into the drive unit 4 via the first control valve 20. This moves the drive piston 8 out of the housing 6 of the drive unit 4.

(36) By contrast, when the first control valve 20 is closed, the second control valve 22 is opened and the further control valve 34 is in the switching position in which a medium flow through the further control valve 34 is prevented, the medium flows out of the drive unit 4 into the pressure sink 18 via the second control valve 22. This retracts the drive piston 8 into the housing 6 of the drive unit 4.

(37) The movement of the drive piston 8 represents a drive movement of the drive unit 4 through which the movably mounted body 14 is driven.

(38) On its so-called ring side 9, i.e. on that side on which the piston rod 12 of the drive piston 8 is located, the drive unit 4 is connected to a pressure regulating device which is not shown. The pressure regulating device ensures that a medium, which is present within the drive unit 4 on the ring side, can flow out of the drive unit 4 on the ring side 9 when, on the piston side 11 of the drive unit 4, a pressure increase takes place. In addition, the pressure regulating device ensures that in the case of a pressure decrease on the piston side 11, the medium on the ring side 9 can (again) flow into the drive unit 4. Alternatively or additionally, the drive unit 4 can comprise a return spring, which is not shown, in order to make possible a return movement of the drive piston 8 directed from the ring side 9 towards the piston side 11.

(39) The further control valve 34 is preferably utilized for realizing simple movements of the movably mounted body 14, during which vibrations of the movably mounted body 14 are uncritical. In a preferred manner, the further control valve 34 is activated by the control unit 42 by means of a PWM activation. It is possible, furthermore, that the first control valve 20 and/or the second control valve 22 are/is activated by the control unit 42 by means of a PWM activation in order to realize such a simple movement of the movably mounted body 14, during which vibrations of the movably mounted body 14 are uncritical.

(40) In addition, the mechanical system 2 comprises a position sensor 46 which is connected to the control unit 42 via a further signal transmission line 48. The position sensor 46 measures a position x of the drive piston 8 and passes the measured position x on to the control unit 42.

(41) The activation of the control valves 20, 22, 34 by the control unit 42 can take place as a function of the measured position x of the drive piston 8. Such a position regulation can be realized for example with the aid of the position sensor 46 in order to reduce residual errors during the positioning of the drive piston 8 carried out with the aid of the control valves 20, 22, 34.

(42) FIG. 2 shows a diagram in which an exemplary transfer function H(f) of the mechanical system 2 from FIG. 1 is shown as a function of a frequency f.

(43) On the abscissa of this diagram, the frequency f is plotted in logarithmic representation in the unit Hz, while on the ordinate of the diagram the transfer function H(f) is plotted in arbitrary units (“arbitrary units”=a.u.).

(44) As is evident in the transfer function H(f), the mechanical system 2 from FIG. 1 has multiple eigenfrequencies which are noticeable as peaks in the diagram. In the present exemplary embodiment, the dominant eigenfrequency of the mechanical system 2, which at the same time is the smallest eigenfrequency of the mechanical system, is around 14.4 Hz.

(45) The following applies to the associated intrinsic period duration T.sub.1 i.e. for the reciprocal of this eigenfrequency:

(46) $T_1=\frac{1}{14.4\mathrm{Hz}}\approx 69.4\mathrm{ms}$

(47) The following presumes that the switching time t.sub.s of the first control valve 20 is shorter or equal to a sixth of the intrinsic period duration T.sub.1. Preferably, the switching time t.sub.s of the first control valve 20 is shorter than a sixth of the intrinsic period duration T.sub.1. It is particularly preferred when the switching time t.sub.s of the first control valve 20 is less than 5 ms.

(48) In order to realize, for example, a drive movement of the moveable drive element of the drive unit 4 with the aid of the first control valve 20, during which an excitation of undesirable vibrations of the mechanical system 2 is largely avoided, the control unit 42 activates the first control valve 20 with a digital electrical control signal u(t), the time profile of which can be mathematically expressed by the following formula (control signal u(t) in arbitrary units):

(49) $u\left(t\right)=\{\begin{array}{cc}1& \mathrm{for}0\le t\le {\tau }_1=\frac{T_1}{6}\\ 0& \mathrm{for}{\tau }_1<t<{\tau }_2=2{\tau }_1\\ p& \mathrm{for}{\tau }_2\le t\le {\tau }_3={\tau }_2+\frac{\Delta x-\Delta x_{\min }}{\stackrel{\_}{v}}\forall \Delta x\ge \Delta x_{\min }\\ 0& \mathrm{for}{\tau }_3<t<{\tau }_4={\tau }_3+{\tau }_1\\ 1& \mathrm{for}{\tau }_4\le t\le {\tau }_5={\tau }_4+{\tau }_1\\ 0& \mathrm{for}t>{\tau }_5\end{array}$

(50) With the following definition:

(51) $p=\{\begin{array}{cc}1& \mathrm{for}\Delta x>\Delta x_{\min }\\ 0& \mathrm{for}\Delta x=\Delta x_{\min }\end{array}$

(52) The quantity t stands for the time.

(53) From the formula for u(t), it follows that the control signal u(t) in the time 0≤t≤τ.sub.1 has a first switching pulse S.sub.1 and in the time τ.sub.4≤t≤τ.sub.5 has a further switching pulse S.sub.3.

(54) From the definition of the parameter p it follows, that the control signal u(t) between the first and the further switching pulse S.sub.1, S.sub.3 during the time interval τ.sub.2≤t≤τ.sub.3 has an additional switching pulse S.sub.2 in the case that Δx is greater than Δx.sub.min. If however Δx is equal to Δx.sub.min, the control signal u(t) between the first and the further switching pulse S.sub.1, S.sub.3 has no such additional switching pulse S.sub.2. Each of the switching pulses S.sub.1, S.sub.2, S.sub.3 causes the first control valve 20 to be opened.

(55) The quantity Δx stands for the desired travel of the movable drive element of the drive unit 4, i.e. for the set point value of the travel of the drive piston 8. Furthermore, Δx.sub.min stands for a predefined step width by which the drive piston 8 is moved when the control signal u(t) only has the first and further switching pulse S.sub.1, S.sub.3 and not the additional switching pulse S.sub.2.

(56) Furthermore, ν stands for the mean movement speed of the drive piston 8 with the first control valve 20 in the opened state. The mean movement speed ν is equal to the quotient of the mean volumetric flow Q of the medium which in the opened state flows through the first control valve 20, and the piston area A.sub.K of the piston head 10 (see FIG. 1). Thus the following applies:

(57) $\stackrel{\_}{v}=\frac{Q}{A_K}$
Δx.sub.min corresponds to the smallest possible step width that can be realized with the drive unit 4 when the first control valve 20 is activated with the said control signal u(t), wherein Δx.sub.min is given by:

(58) $\Delta x_{\min }=2\stackrel{\mathrm{.Math.}}{v}{\tau }_1=\frac{2Q{\tau }_1}{A_K}$
In FIGS. 3A, 3B and 3C, three diagrams are shown. The abscissas of these three diagrams each represent the time t, wherein the abscissas of all three diagrams cover the same period of time. The ordinates of the diagrams each represent another quantity in arbitrary units.

(59) The diagram of FIG. 3A shows the control signal u(t) as a function of the time t in the form of a continuous line, wherein the control signal u(t) is shown here for the case that the desired travel Δx is equal to Δx.sub.min.

(60) In the present case, the control signal u(t) has the previously mentioned first switching pulse S.sub.1 and the previously mentioned further switching pulse S.sub.3. However, the control signal u(t) in this case (i.e. with Δx=Δx.sub.min) does not have any additional switching pulse S.sub.2 between these two switching pulses S.sub.1, S.sub.3.

(61) The first switching pulse S.sub.1 causes an acceleration of the drive piston 8 (and thus also of the movably mounted body 14 attached to the drive piston 8), wherein because of its inertia, the mechanical system 2 reacts with a delay to the first switching pulse S.sub.1. The further switching pulse S.sub.3 prevents that the drive piston 8 rings after the end of the first switching pulse S.sub.1.

(62) The first and the further switching pulses S.sub.1, S.sub.3 have the same pulse duration τ.sub.1, wherein the pulse duration τ.sub.1 of these two switching pulses S.sub.1, S.sub.3 is adapted to the intrinsic period duration T.sub.1 of the mechanical system 2. More precisely, the pulse duration τ.sub.1 of the two switching pulses S.sub.1, S.sub.3 corresponds to a sixth of the intrinsic period duration T.sub.1—in the present example, thus approximately 11.6 ms.

(63) Between the two switching pulses S.sub.1, S.sub.3, the control signal u(t) has a pause with a predefined pause duration, wherein the pause duration is twice as long as the pulse duration τ.sub.1 of the two switching pulses S.sub.1, S.sub.3. In the present case, the time interval Δt.sub.1-3 between the start of the first switching pulse S.sub.1 and the start of the further switching pulse S.sub.3 switching pulse thus corresponds to 3τ.sub.1=T.sub.1/2.

(64) In the diagram of FIG. 3C, the position x(t) of the drive piston 8 is shown as a function of the time t in the form of a continuous line. In this diagram, upon an activation of the first control valve 20 with the control signal u(t) shown in FIG. 3A (see continuous line in the diagram of FIG. 3A) the drive piston 8 moves by the distance Δx.sub.min, without any noteworthy vibration. Accordingly, the movably mounted body 14 attached to the drive piston 8 also moves by the distance Δx.sub.min without significant vibration.

(65) In the middle diagram of FIG. 3B, the speed v(t) of the drive piston 8 is shown in the form of a continuous line, and has a pulse-like profile.

(66) When the first control valve 20 is repeatedly activated with the control signal u(t), which is shown in the lower diagram of FIG. 3C (see continuous line in the lower diagram of FIG. 3C), the drive piston 8 in the process moves each time by the distance Δx.sub.min. In this way, a step drive (with the step width Δx.sub.min) can be realized.

(67) From the three diagrams of FIGS. 3A, 3B and 3C, because of the inertia of the mechanical system 2, it is evident that the drive piston 8 reacts with a delay to an acceleration by the first switching pulse S.sub.1. From the three diagrams it is evident, furthermore, that the movement of the drive piston 8 ends at the same time as the end of the further switching pulse S.sub.3.

(68) Furthermore, another control signal (not according to the invention) for the first control valve 20 is shown in the form of a dashed line for comparison in the lower diagram of FIG. 3C, which control signal only has a single switching pulse which starts at t=0 and the pulse duration of which is twice as long as the pulse duration τ.sub.1 of the first switching pulse S.sub.1. When the first control valve 20 is activated with this other control signal, the drive piston 8 likewise moves by the distance Δx.sub.min. However, the drive piston 8 in this case oscillates around the position x=Δx.sub.min (see dashed lines in the diagrams of FIGS. 3C, and 3B). Accordingly, with such an activation, the movably mounted body 14 of the mechanical system 2 attached to the drive piston 8 also oscillates.

(69) In FIG. 4, three diagrams 4A, 4B and 4C are likewise shown. These three diagrams show the same three quantities as a function of the time t which are also shown in FIGS. 3A, 3B and 3C as a function of the time t, namely the control signal u(t), the position x(t) of the drive piston and the speed v(t) of the drive piston 8.

(70) The diagram of FIG. 4A shows in the form of a continuous line the control signal u(t) for the first control valve 20 as a function of the time t, wherein the control signal u(t) is shown here for the case that the desired travel Δx is greater than Δx.sub.min.

(71) In the present case, i.e. with Δx>Δx.sub.min, the control signal u(t) has the first switching pulse S.sub.1 and the further switching pulse S.sub.3, the pulse duration τ.sub.1 of each of the two is equal to a sixth of the intrinsic period duration T.sub.1.

(72) In addition, the control signal u(t) between the first and the further switching pulse S.sub.1, S.sub.3 has the previously mentioned additional switching pulse S.sub.2. The pulse duration of the additional switching pulse S.sub.2 (i.e. of the middle switching pulse) is equal to the quotient (Δx−Δx.sub.min)/ν.

(73) Between the first and the additional switching pulse S.sub.1 and S.sub.2, the control signal u(t) has a first pause and between the additional and the further switching pulse S.sub.2 and S.sub.3 the control signal u(t) has a second pause, wherein the respective pause duration is equal to the pulse duration τ.sub.1 of the first and of the further switching pulses S.sub.1 and S.sub.3. In the present case, the time interval Δt.sub.1-3 between the start of the first switching pulse S.sub.1 and the start of the further switching pulse S.sub.3 consequently corresponds to 3τ.sub.1+(Δx−Δx.sub.min)/ν. The time interval Δt.sub.1-2 between the start of the first switching pulse S.sub.1 and the beginning of the additional switching pulse S.sub.2 amounts to 2τ.sub.1.

(74) In the upper diagram of FIG. 4C, the position x(t) of the drive piston 8 as a function of the time t is shown in the form of a continuous line. As is evident from this diagram, upon an activation of the first control valve 20 with the control signal u(t) shown in FIG. 4 (see continuous line in the lower diagram of FIG. 4), the drive piston 8 moves by the distance Δx without oscillating significantly in the process. Accordingly, the movably mounted body 14 attached to the drive piston 8 also moves by the distance Δx without oscillating significantly.

(75) The first and the further switching pulse S.sub.1 and S.sub.3 jointly cause the drive piston 8, and thereby also the movably mounted body 14 of the mechanical system 2 attached to the drive piston 8, to move by the distance Δx.sub.min. The additional switching pulse S.sub.2 causes the drive piston 8, and thus also the movably mounted body 14 attached to the drive piston 8, to (additionally) move by the difference (Δx−Δx.sub.min). Together, the three switching pulses S.sub.1, S.sub.2, S.sub.3 thus cause the drive piston 8, and thus also the movably mounted body 14 attached to the drive piston 8, to move by the distance Δx.

(76) From the middle diagram of FIG. 4B, in which the speed v(t) of the drive piston 8 is shown in the form of a continuous line, during the additional switching pulse S.sub.2 it is evident that the drive piston 8 moves with an approximately stationary speed. (Minor high-frequency vibrations of the speed v(t) can be attributed to high-frequency eigenfrequencies of the mechanical system 2.) The speed of the drive piston 8 simultaneously corresponds to that of the movably mounted body 14 of the mechanical system 2 attached to the drive piston 8.

(77) For comparison, the control signal u(t) from FIG. 3C and the associated position x(t) of the drive piston 8 and the associated speed v(t) of the drive piston as a function of the time t are each shown in the form of a dashed line in the diagrams of FIG. 4.

(78) Three diagrams are also shown in FIGS. 5A, 5B and 5C. These three diagrams show the same three quantities as a function of the time t, as are also shown in FIGS. 3A, 3B and 3C and FIGS. 4A, 4B and 4C as a function of the time t, namely the control signal u(t), the position x(t) of the drive piston and the speed v(t) of the drive piston 8.

(79) The time profiles of the control signal u(t), the position x(t) of the drive piston 8 and the speed v(t) of the drive piston 8 each shown in FIGS. 5A, 5B and 5C in the form of a continuous line are identical to the time profiles of these quantities each shown in FIGS. 4A, 4B and 4C in the form of a continuous line.

(80) For comparison, another control signal (not according to the invention) for the first control valve 20 is shown in the form of a dashed line in the lower diagram of FIG. 5A, which control signal only has a single switching pulse which begins at t=0 and the pulse duration T.sub.0 of which corresponds to the sum of the three previously mentioned switching pulses S.sub.1, S.sub.2, S.sub.3. When the first control valve 20 is activated with this other control signal, the drive piston 8 likewise moves by the distance Δx, however the drive piston 8 in this case oscillates around the position Δx=Δx or on its way there (see dashed lines in the diagrams of FIGS. 5B and 5C). Accordingly, the movably mounted body 14 of the mechanical system 2 attached to the drive piston 8 also oscillates during such activation.

(81) With the time profiles shown in FIG. 3A to FIG. 5C it was presumed that the switching time t.sub.s of the first control valve 20 is shorter than a sixth of the intrinsic period duration T.sub.1.

(82) In the case that this presumption is not satisfied, i.e. in the case that the switching time t.sub.s is longer than a sixth of the intrinsic period duration T.sub.1, the first control valve 20 is ballistically activated, wherein other pulse durations for the switching pulses are adjusted.

(83) In FIG. 6, three diagrams FIGS. 6A, 6B and 6C are again shown. The upper and the middle diagram of FIGS. 6B and 6C show, as already in FIG. 3 to FIG. 5, the position x(t) of the drive piston 8 or the speed v(t) of the drive piston 8 as a function of the time t.

(84) In connection with FIGS. 6A, 6B and 6C, it is assumed that the switching time t.sub.s of the first control valve 20 amounts to for example 15 ms, i.e. is longer than a sixth of the intrinsic period duration T.sub.1. In this case, the first control valve 20 is ballistically activated.

(85) Other than in FIG. 3A to FIG. 5C, the lower diagram of FIG. 6C shows a position s(t) of the valve piston of the first control valve 20 as a function of the time t. There, the value “1” in this diagram stands for a position of the valve piston in which the first control valve 20 is completely opened, while the value “0” stands for a position of the valve piston in which the first control valve 20 is completely closed. Accordingly, values between 0 and 1 relate to intermediate positions of the valve piston between these two positions.

(86) The time profile of the position s(t) of the valve piston with the ballistic activation of the first control valve 20 is shown in the diagram of FIG. 6A in the form of a continuous line.

(87) The control signal ũ(t), with which the first control valve 20 is activated upon the ballistic activation, can be mathematically expressed by the following formula (control signal ũ(t) in arbitrary units):

(88) $\tilde{u}\left(t\right)=\{\begin{array}{cc}1& \mathrm{for}0\le t\le \widetilde{{\tau }_1}=\frac{1}{2}\left(\frac{T_1}{6}+t_S\right)\\ 0& \mathrm{for}\widetilde{{\tau }_1}<t<\widetilde{{\tau }_2}=2\widetilde{{\tau }_1}\\ p^{\prime }& \mathrm{for}\widetilde{{\tau }_2}\le t\le \widetilde{{\tau }_3}=\widetilde{{\tau }_2}+\frac{\Delta x-\Delta x_{\min }^{\prime }}{\tilde{v}}\forall \Delta x\ge \Delta x_{\min }^{\prime }\\ 0& \mathrm{for}\widetilde{{\tau }_3}<t<\widetilde{{\tau }_4}=\widetilde{{\tau }_3}+\widetilde{{\tau }_1}\\ 1& \mathrm{for}\widetilde{{\tau }_4}\le t\le \widetilde{{\tau }_5}=\widetilde{{\tau }_4}+\widetilde{{\tau }_1}\\ 0& \mathrm{for}t>\widetilde{{\tau }_5}\end{array}$

(89) With the following definition:

(90) $p^{\prime }=\{\begin{array}{cc}1& \mathrm{for}\Delta x>\Delta x_{\min }^{\prime }\\ 0& \mathrm{for}\Delta x=\Delta x_{\min }^{\prime }\end{array}$

(91) From the formula for ũ(t), it follows that the control signal ũ(t) in the time interval 0≤t≤{tilde over (τ)}.sub.1 has a first switching pulse and in the time interval ≤t≤ has a further switching pulse.

(92) From the definition of the parameter p′ it follows that the control signal ũ(t) between the first and the further switching pulses in the time interval ≤t≤ has an additional switching pulse if Δx is greater than Δx.sub.min′. When, by contrast Δx is equal to Δx.sub.min′, the control signal ũ(t) does not have any such additional switching pulse between the first and the further switching pulses.

(93) In the present case, the first and the further switching pulses have a different pulse duration than upon an activation according to FIG. 3 or FIG. 4. For the pulse duration of the first and further switching pulse the following applies in the present case:

(94) $\widetilde{{\tau }_1}=\frac{1}{2}\left({\tau }_1+t_S\right)=\frac{1}{2}\left(\frac{T_1}{6}+t_S\right)$

(95) The pulse duration of the first and further switching pulses thus corresponds to the arithmetic mean value from the switching time t.sub.s of the first control valve 20 and a sixth of the intrinsic period duration T.sub.1.

(96) Accordingly, the following applies to the smallest possible step width Δx.sub.min′ of the drive unit 4, by which the movable drive element of the drive unit 4 moves when the control signal ũ(t) only has the first and the further switching pulses and not the additional switching pulse:

(97) $\Delta x_{\min }^{\prime }=2\stackrel{\_}{v}\widetilde{{\tau }_1}=\frac{2Q\widetilde{{\tau }_1}}{A_K}$

(98) In the case shown in FIG. 6, it is presumed that the set point value of the travel of the drive piston 8 should have the same amount Δx as with the valve activation according to FIG. 4 and FIG. 5. In the present case, the control signal ũ(t) between its first and its further switching pulses additionally has the additional switching pulse.

(99) From the lower diagram of FIG. 6C, it is evident that the first and the further switching pulse of the control signal ũ(t) have such a short pulse duration that, by way of the pulse-like actuation of the first control valve 20 through the first or further switching pulse, the valve piston is thrust in the opening direction without the valve piston reaching its end position with full opening of the control valve 20. Then the valve piston subsequently falls back again in the direction of its closed end position under the effect of the valve spring of the first control valve 20 and/or under the effect of flow forces. The pulse duration of the additional switching pulse of the control signal ũ(t) by contrast is long enough for the valve piston to reach its end position with full opening of the control valve 20.

(100) For comparison, the position of the valve piston as a function of the time t upon the activation according to FIG. 4C and FIG. 5C is shown in the lower diagram of FIG. 6C, in which it is presumed that t.sub.s≤T.sub.1/6 applies, in the form of a dashed line. In addition, the time profile of the position x(t) of the drive piston 8 or the time profile of the speed v(t) of the drive piston 8 from FIGS. 4A and 4B and FIGS. 5A and 5B are shown in the upper and middle diagram of FIGS. 6A and 6B in the form of a dashed line.

(101) From the diagrams of FIGS. 6A, 6B and 6C it is evident that in the case of the ballistic activation of the first control valve 20 with the adapted pulse duration the drive piston 8 covers the same distance Δx as in the case of the activation described in connection with FIGS. 4A, 4B and 4C and FIGS. 5A, 5B and 5C (with which however t.sub.s≤T.sub.1/6 was presumed).

(102) With the ballistic activation of the first control valve 20, the drive piston 8, and thus also the movably mounted body 14 attached to the drive piston 8, also moves

(103) without vibrating significantly. However, in the case of the ballistic activation with the adapted pulse duration because of the longer switching time t.sub.s) the movement of the drive piston 8 takes place with a short time delay relative to the movement of the drive piston 8 shown in FIG. 4C and FIG. 5C.

(104) When the case that the set point value of the travel Δx of the drive piston 8 is to be equal to Δx.sub.min′, the additional switching pulse in the control signal ũ(t) is missing.

(105) To realize a drive movement of the drive unit 4 with the aid of the second control valve 22, with which an excitation of undesirable vibrations of the mechanical system 2 is largely avoided, the second control valve 22 can be activated by the control unit 42 analogously to the manner described in connection with FIG. 3 to FIG. 6. In other words, the above explanations concerning the activation of the first control valve 20 analogously apply to the second control valve 22.

(106) The descriptions of the following exemplary embodiments are each primarily limited to the differences from the preceding exemplary embodiment, to which reference is made regarding constant features and functions For serving the purpose, elements which are substantially the same or correspond to one another are marked with the same reference signs and features which are not mentioned and are taken over in the following exemplary embodiments without being described again.

(107) FIG. 7 shows a schematic representation of a coiler 50 for winding up a metal strip 52 into a coil.

(108) The coiler 50 comprises among other things a rotatably mounted coiler drum 54. Furthermore, the coiler 50 in the present exemplary embodiment comprises three mechanical systems 56 of identical design.

(109) Each of these three mechanical systems 56 comprises a drive unit 4 that is operable with a medium, which drive unit 4 is a hydraulic cylinder and comprises a moveable drive piston 8 as its drive element. In addition, each of the three mechanical systems 56 comprises a movably mounted body 14 which is driven with the aid of the drive unit 4, and a pivotable pivot arm unit 58 attached to a foundation, which is connected to the drive piston 8 of the drive unit 4 and forms a vibratory part of the mechanical system 56.

(110) In this present exemplary embodiment, the movably mounted body 14 of the respective mechanical system is a pressure roller for pressing the metal strip 52 on the drum against the coiler drum 54 or against the already wound-up part of the metal strip 52, wherein the pressure roller is rotatably mounted on the pivot arm unit 58 of the respective mechanical system 56. Otherwise, the respective mechanical system 56 of the coiler 50 is configured like the mechanical system 2 in FIG. 1. This means, in particular, that each of the three mechanical systems 56 comprises a first control valve 20, a second control valve 22 and a further control valve 34 for controlling a drive movement of the drive unit 4, wherein each of the first and second control valves 20, 22 is a digital valve and the further control valve 34 is a proportional valve.

(111) In FIG. 7, components of only one of the three mechanical systems 56 are shown exemplarily for the control of the drive movement of the drive unit 4. The other two mechanical systems 56 of the coiler 50, include components that are not shown for clarity of FIG. 7.

(112) During a winding-up operation of the metal strip 52 during which the metal strip 52 is wound onto the rotating coiler drum 54, the pressure roller of each of the three mechanical systems 56 of the coiler 50 is pressed against the metal strip 52 with the aid of the drive unit 4 of the respective mechanical system 56.

(113) For as long as fewer than n windings of the metal strip 52 have been wound onto the coiler drum 54 during the winding-up operation of the metal strip 52, there is an instant for each of the mechanical systems 56 at which the strip beginning 60 of the metal strip 52 lying on the coiler drum 54 is situated between the rotary axis of the coiler drum 54 and the rotary axis of the pressure roller of the respective mechanical system 56. The pressure roller is lifted off the metal strip 52 at a predefined period of time before the instant and after a predefined period of time the pressure roller is again set onto the metal strip 52. This avoids the inner n windings of the metal strip 52 being pressed against the strip beginning 60, wherein n is a natural number. Typically, n is 3, 4 or 5.

(114) The lifting-off and setting-down of the respective pressure roller is controlled with the aid of the first and second control valves 20, 22 of the respective mechanical system 56. In order to avoid the respective pressure roller being excited to vibrate during lifting-off and/or setting down the roller, the first and second control valves 20, 22 of the respective mechanical system 56 are activated with one of the previously described control signals u(t), ũ(t), wherein the pulse duration of the first and further switching pulses is adapted to a eigenfrequency or an intrinsic period duration of the respective mechanical system 56.

(115) Simple movements of the respective pressure roller, for example pivoting it in and out, can be controlled for example with the aid of the further control valve 34 of the respective mechanical system 56, particularly by means of a PWM activation of the further control valve 56.

(116) The coiler 50 need not necessarily comprise precisely three mechanical systems 56. The coiler 50 may have a different number of such mechanical systems 56, for example four, which are controlled in the manner described above.

(117) FIG. 8 shows a schematic representation of a further mechanical system 62.

(118) This mechanical system 62 likewise comprises a rotary drive unit 64 that is operable with a medium and a movably mounted body 14 which is driven by the drive unit 64. The drive unit 64 compromises a hydraulic motor which comprises a rotor as moveable drive element which is not shown by FIGS. Furthermore, the movably mounted body 14 in this embodiment is rotatably mounted.

(119) The mechanical system 62 comprises a pressure source 16 comprised of a pump and a pressure sink 18 comprised of a tank.

(120) The mechanical system 62 FIG. 8 further comprises a control valve 20 which is a digital valve and is controlled from a control unit 42 of the mechanical system 62, wherein the control valve 20 is connected to the control unit 42 via a signal transmission line 44.

(121) The control valve 20 is connected to the drive unit 64 via a first fluid line 66 of the mechanical system 62. The control valve 20 is connected to the pressure source 16 by a second fluid line 68 of the mechanical system 62, wherein a pressure accumulator 28 partially filled with a gas is connected to the second fluid line 68.

(122) Furthermore, the pressure sink 18 is connected to the drive unit 64 via a third fluid line 70 of the mechanical system 62. A fourth fluid line 72 of the mechanical system 62 connects the pressure sink to the pressure source 16.

(123) When the control valve 20 is opened, the medium provided by the pressure source 16 flows via the control valve 20 to the drive unit 64 and drives its rotor which drives the movably mounted body 14. The medium exiting the drive unit 64 flows to the pressure sink 18 from where the medium is delivered to the control valve 20 from the pressure source 16 formed as a pump.

(124) To realize a drive movement of the drive unit 64 with the aid of the control valve 20, during which excitation of undesirable vibrations of the mechanical system 62 is largely avoided, the control unit 42 activates the control valve 20 with a digital electrical control signal w(t). The time profile of the signal can be mathematically expressed by the following formula (control signal w(t) in arbitrary units):

(125) 0$w\left(t\right)=\{\begin{array}{cc}1& \mathrm{for}0\le t\le {\kappa }_1\\ 0& \mathrm{for}{\kappa }_1<t<{\kappa }_2=2{\kappa }_1\\ p& \mathrm{for}{\kappa }_2\le t\le {\kappa }_3={\kappa }_2+\frac{\Delta \phi -{\mathrm{\Delta \phi }}_{\min }}{\stackrel{\_}{\omega }}\forall \mathrm{\Delta \phi }\ge {\mathrm{\Delta \phi }}_{\min }\\ 0& \mathrm{for}{\kappa }_3<t<{\kappa }_4={\kappa }_3+{\kappa }_1\\ 1& \mathrm{for}{\kappa }_4\le t\le {\kappa }_5={\kappa }_4+{\kappa }_1\\ 0& \mathrm{for}t>{\kappa }_5\end{array}$

(126) With the following definition:

(127) $p=\{\begin{array}{cc}1& \mathrm{for}\Delta \phi >\Delta {\phi }_{\min }\\ 0& \mathrm{for}\Delta \phi =\Delta {\phi }_{\min }\end{array}$

(128) From the formula for w(t), it follows that the control signal w(t) in the time interval 0≤t≤K.sub.1 has a first switching pulse with the pulse duration K.sub.1 and in the time interval K.sub.4≤t≤K.sub.5 has a further switching pulse with the same pulse duration K.sub.1.

(129) The pulse duration K.sub.1 of the first and second switching pulses is equal to a sixth of the dominant intrinsic period duration of the mechanical system 62 when the switching time t.sub.s of the control valve 20 is maximally as long as a sixth of the dominant intrinsic period duration. By contrast, when the switching time t.sub.s of the control valve 20 is longer than a sixth of the dominant intrinsic period duration of the mechanical system 62, the pulse duration K.sub.1 of the first and second switching pulses is equal to the arithmetic mean from a sixth of the dominant intrinsic period duration of the mechanical system 62 and the switching time t.sub.s of the control valve 20.

(130) From the definition of the parameter P it follows, furthermore, that the control signal w(t) between the first and the further switching pulses in the time K.sub.2≤t≤K.sub.3 has an additional switching pulse if Δφ is greater than Δφ.sub.min. By contrast, if Δφ is equal to Δφ.sub.min, the control signal w(t) does not have any such additional switching pulse between the first and the further switching pulses.

(131) The quantity Δφ stands for the rotation angle to be covered by the movable drive element of the drive unit 64 during its drive movement, i.e. for the set point value of the rotation angle of the rotor. Furthermore, the quantity Δφ.sub.min stands for a predefined (angular) step width by which the rotor rotates when the control signal w(t) only has the first and the further switching pulse and not the additional switching pulse. Δφ.sub.min corresponds to the smallest possible (angular) step width that can be realized with the drive unit 64 when the control valve 20 is activated with the control signal w(t).

(132) Furthermore, w stands for the mean angular velocity of the rotor of the drive unit 64 in the opened state of the control valve 20.

(133) Although the invention has been illustrated and described in more detail by the preferred exemplary embodiments, the invention is not restricted by the disclosed examples and other versions can be derived from this without leaving the protected scope of the invention.

LIST OF REFERENCE SIGNS

(134) 2 System 4 Drive unit 6 Housing 8 Drive piston 9 Ring side 10 Piston head 11 Piston side 12 Piston rod 14 Body 16 Pressure source 18 Pressure sink 20 Control valve 22 Control valve 24 Fluid line 26 Fluid line 28 Pressure accumulator 30 Fluid line 32 Fluid line 34 Control valve 36 Fluid line 38 Fluid line 40 Fluid line 42 Control unit 44 Signal transmission line 46 Position sensor 48 Signal transmission line 50 Coiler 52 Metal strip 54 Coiler drum 56 System 58 Pivot arm unit 60 Strip beginning 62 System 64 Drive unit 66 Fluid line 68 Fluid line 70 Fluid line 72 Fluid line S.sub.1 Switching pulse S.sub.2 Switching pulse S.sub.3 Switching pulse