Piezoelectric positioning device and positioning method by means of such a piezoelectric positioning device

Abstract

A piezoelectric positioning device (1) has at least one piezoelectric actuator (3) having a first connection contact (4) and a second connection contact (5). A control device (6) with digital/analog converters (12, 16) connected to the connection contacts (4, 5) is used to control the at least one piezoelectric actuator (3). In comparison with a coarse converter (12), a fine converter (16) has a comparatively smaller voltage range and lower voltage levels, with the result that a high degree of positioning accuracy can be achieved.

Claims

1. A piezoelectric positioning device comprising: at least one piezoelectric actuator comprising, respectively, a first connection contact and a second connection contact, a control device configured to control the at least one piezoelectric actuator, and comprising: a first digital/analog converter connected to the first connection contact and providing a first analog converter output voltage U.sub.1 in a first voltage range ΔU.sub.1 in first voltage levels Δu.sub.1, a second digital/analog converter connected to the second connection contact and providing a second analog converter output voltage U.sub.2 in a second voltage range ΔU.sub.2 in second voltage levels Δu.sub.2,
where: ΔU.sub.1>ΔU.sub.2≧Δu.sub.1>Δu.sub.2.

2. The positioning device as claimed in claim 1, wherein the first voltage levels Δu.sub.1 have a maximum voltage inaccuracy Δu.sub.d, where: ΔU.sub.2≧Δu.sub.1+Δu.sub.d and/or ΔU.sub.2≦64.Math.Δu.sub.1.

3. The positioning device as claimed in claim 1 further comprising a first voltage amplifier arranged downstream of the first digital/analog converter and a second voltage amplifier is arranged downstream of the second digital/analog converter.

4. The positioning device as claimed in claim 1, further comprising a non-reactive resistor connected between the second digital/analog converter and the second connection contact.

5. The positioning device as claimed in claim 3, further comprising a low-pass filter connected between the first digital/analog converter and the first voltage amplifier.

6. The positioning device as claimed in claim 1, further comprising a position measuring sensor configured to measure an actual position (x) regulated via the at least one piezoelectric actuator.

7. The positioning device as claimed in claim 6, wherein the control device comprises a position regulating unit regulating the actual position (x).

8. The positioning device as claimed in claim 7, wherein the position regulating unit comprises a desired value filter.

9. The positioning device as claimed in claim 7, wherein the control device comprises a position pilot control unit which interacts with the position regulating unit.

10. The positioning device as claimed in claim 6, wherein the control device comprises a detection unit configured to generate a control signal (S) if the absolute value of a position control error (e.sub.X) undershoots a predefined control error limit value.

11. The positioning device as claimed in claim 1, wherein the control device comprises a calculation unit calculating a first input value (d.sub.1) for the first digital/analog converter and a second input value (d.sub.2) for the second digital/analog converter from a desired voltage value (U.sub.S).

12. The positioning device as claimed in claim 11, wherein the calculation unit is programmed to replace a first voltage value (U.sub.1S) calculated in an instantaneous time step (k) with a first voltage value (U.sub.A) calculated in an earlier time step (k−1) if a difference absolute value (ΔU) of the desired voltage value (U.sub.S) and of the first voltage value (U.sub.A) in the earlier time step (k−1) exceeds a limit value (L).

13. The positioning device as claimed in claim 11, wherein the calculation unit changes the limit value (L) in accordance with the control signal (S).

14. The positioning device as claimed in claim 4, further comprising a voltage measuring sensor determining a measurement voltage (u.sub.m) corresponding to a voltage (U.sub.m) dropped across the non-reactive resistor.

15. The positioning device as claimed in claim 14, wherein the control device comprises a charge regulating unit regulating an actual state of charge (Q) of the at least one piezoelectric actuator designed to determine the actual state of charge (Q) from the measurement voltage (Q.sub.m) and to compare the actual state of charge with a desired state of charge (Q.sub.S).

16. The positioning device as claimed in claim 14, wherein the desired state of charge (Q.sub.S) is predefined by the position regulating unit.

17. A positioning method, comprising: providing a piezoelectric positioning device as claimed in claim 1, and actuating the piezoelectric positioning device by applying the first analog converter output voltage (U.sub.1) and the second analog converter output voltage (U.sub.2) to the at least one piezoelectric actuator.

18. A piezoelectric positioning device comprising: at least one piezoelectric actuator comprising, respectively, a first connection contact and a second connection contact, a control device configured to control the at least one piezoelectric actuator, and comprising: a first digital/analog converter connected to the first connection contact and providing a first analog converter output voltage U.sub.1 in a first voltage range ΔU.sub.1 in first voltage levels Δu.sub.1, a second digital/analog converter connected to the second connection contact and providing a second analog converter output voltage U.sub.2 in a second voltage range ΔU.sub.2 in second voltage levels Δu.sub.2,
where: ΔU.sub.1>ΔU.sub.2≧Δu.sub.1>Δu.sub.2, a first voltage amplifier arranged downstream of the first digital/analog converter and a second voltage amplifier arranged downstream of the second digital/analog converter, a non-reactive resistor connected between the second voltage amplifier and the second connection contact, and a low-pass filter connected between the first digital/analog converter and the first voltage amplifier.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Further features, advantages and details of the invention can be gathered from the following description of an exemplary embodiment. In the figures:

[0022] FIG. 1 shows a schematic illustration of the structure of a piezoelectric positioning device having a piezoelectric actuator which is controlled using a first digital/analog converter and a second digital/analog converter,

[0023] FIG. 2 shows a schematic illustration of the characteristic curves of the digital/analog converters,

[0024] FIG. 3 shows a signal flow diagram of position regulation for the piezoelectric actuator with a calculation unit for calculating voltage values for the digital/analog converters, and

[0025] FIG. 4 shows a signal flow diagram of the calculation unit for calculating a first voltage value for the first digital/analog converter and a second voltage value for the second digital/analog converter.

DETAILED DESCRIPTION

[0026] A piezoelectric positioning device 1 has a piezoelectric actuator 3 for positioning a kinematic system 2. In electrical terms, the piezoelectric actuator 3 acts as a capacitor with a capacitance C and changes a longitudinal dimension on the basis of an actual state of charge. The change in the longitudinal dimension is denoted Δx. The piezoelectric actuator 3 is known and conventional and is in the form of a piezo stack, for example.

[0027] The piezoelectric actuator 3 is connected to a control device 6 via connection contacts 4, 5. The control device 6 has a digital signal processor 7. A first converter/amplifier circuit 8 has a signal connection to the digital signal processor 7, but is DC-isolated from the latter by a first isolation element 11. The first converter/amplifier circuit 8 is connected to the first connection contact 4. A second converter/amplifier circuit 9 is connected to the second connection contact 5 via a non-reactive series resistor 10. The series resistor 10 has the resistance value R. The second converter/amplifier circuit 9 has a signal connection to the digital signal processor 7, but is DC-isolated from the latter by a second isolation element 11′.

[0028] The first converter/amplifier circuit 8 has a first digital/analog converter 12 which is connected to a first voltage amplifier 14 via a low-pass filter 13. The first digital/analog converter 12 has a first voltage range ΔU.sub.1 and provides a first analog converter output voltage U.sub.1 in first voltage levels Δu.sub.1. The first converter/amplifier circuit 8 is connected to a first voltage source 15 which provides a first shift voltage. The first shift voltage shifts a reference potential of the first converter/amplifier circuit 8 with respect to the reference potential (GROUND GND). This requires the DC isolation by the isolation element 11′ between the digital signal processor 7 and the first converter/amplifier circuit 8.

[0029] The second converter/amplifier circuit 9 has a second digital/analog converter 16 which is connected to a second voltage amplifier 17. The second digital/analog converter 16 has a second voltage range ΔU.sub.2 and provides a second analog converter output voltage U.sub.2 in second voltage levels Δu.sub.2. The second converter/amplifier circuit 9 is connected to a second voltage source 18 which provides a second shift voltage. The second shift voltage shifts a reference potential of the second converter/amplifier circuit 9 with respect to the reference potential. This requires the DC isolation by the isolation element 11′ between the digital signal processor 7 and the second converter/amplifier circuit 9. If the second shift voltage is 0 V, the second isolation element 11′ is not required. However, DC isolation by the isolation element 11′ may be useful for safety reasons since, in the event of a fault, the digital signal processor 7 is electrically separated in this manner from components of the second converter/amplifier circuit 9 which possibly carry high voltage. A corresponding situation applies to the first shift voltage and the first isolation element 11.

[0030] The second converter/amplifier circuit 9 is preferably operated symmetrically with respect to the reference potential, with the result that it is possible to dispense with DC isolation by the second isolation element 11′. For this purpose, the second shift voltage is set to 0 V. This is advantageous, on the one hand, since a current measurement via the non-reactive series resistor 10 is usually carried out using a digital/analog converter with a differential input or a corresponding preamplifier, the common-mode signal of the differential input or differential preamplifier usually being limited to ±5 V with respect to the reference potential. On the other hand, it is advantageous, for safety reasons, to leave the voltage potential of a connection contact 4, 5 in the vicinity of the reference potential. If one of the connection contacts 4, 5 inadvertently makes contact with the reference potential or the frame ground of the piezoelectric positioning device 1, for example during a start-up measurement, this does not result in depolarization or destruction of the piezoelectric actuator 3.

[0031] If the operating range of the piezoelectric actuator 3 is, for example, −20 V to 120 V and the first voltage range ΔU.sub.1 is 0 V to 135 V and the second voltage range ΔU.sub.2 is −2.5 V to 2.5 V, the first shift voltage is set to −17.5 V and the second shift voltage is set to 0 V. This ensures that, in the event of a fault—irrespective of which connection contact 4, 5 touches the reference potential or the frame ground, at most −17.5 V to 117.5 V are applied across the piezoelectric actuator 3, that is to say the voltage applied in the event of a fault is in the operating range of the piezoelectric actuator 3.

[0032] The first digital/analog converter 12 has n bits, with the result that a first digital input can accept 2.sup.n input values d.sub.1. The first voltage levels Δu.sub.1 are determined by the first voltage range ΔU.sub.1 and the 2.sup.n digital input values d.sub.1. The second digital/analog converter 16 accordingly has m bits, with the result that a second digital input can accept 2.sup.m input values d.sub.2. The second voltage levels Δu.sub.2 are determined by the second voltage range ΔU.sub.2 and the 2.sup.m input values d.sub.2. The first digital/analog converter 12 is used to provide the converter output voltage U.sub.1 in a large voltage range ΔU.sub.1 and in high voltage levels Δu.sub.1, whereas the second digital/analog converter 16 is used to provide the second converter output voltage U.sub.2 in a smaller voltage range ΔU.sub.2 and in lower voltage levels Δu.sub.2. Accordingly, the first digital/analog converter 12 is also referred to as a coarse converter 12 below, whereas the second digital/analog converter 16 is also referred to as a fine converter 16 below. The following accordingly applies:

ΔU.sub.1>ΔU.sub.2 and Δu.sub.1>Δu.sub.2.

[0033] In addition, the second voltage range ΔU.sub.2 covers at least one first voltage level Δu.sub.1, with the result that the following applies:

ΔU.sub.2≧Δu.sub.1.

[0034] These relationships are illustrated in FIG. 2.

[0035] The first voltage levels Δu.sub.1 in practice have a voltage inaccuracy. A maximum voltage inaccuracy Δu.sub.d is illustrated by way of example in FIG. 2. In the worst-case scenario, the maximum voltage inaccuracy Δu.sub.d can occur in a negative direction in one voltage level Δu.sub.1 and can occur in a positive direction in a subsequent voltage level Δu.sub.1. This is illustrated by way of example for the voltage levels Δu.sub.1 and 2.Math.Δu.sub.1in FIG. 2. Voltage inaccuracies which occur are also known as differential non-linearities in digital/analog converters. The following preferably accordingly applies to the second voltage range ΔU.sub.2:

ΔU.sub.2≦Δu.sub.1+Δu.sub.d, in particular ΔU.sub.2≧Δu.sub.1+2.Math.u.sub.d.

[0036] The positioning accuracy of the piezoelectric actuator 3 is dependent on the second voltage levels Δu.sub.2, that is to say the resolution of the fine converter 16. The positioning accuracy is accordingly higher, the lower the second voltage levels Δu.sub.2. The following preferably applies to the second voltage range ΔU.sub.2:

ΔU.sub.2≦64.Math.Δu.sub.1, in particular ΔU.sub.2≦32.Math.Δu.sub.1.

[0037] This ensures second voltage levels Aug which are as low as possible for a given number of bits m.

[0038] In order to measure an actual position x to be regulated, the positioning device 1 has a position measuring sensor 19. The position measuring sensor 19 measures, for example, the actual position x of a component of the kinematic system 2 to be positioned. The position measuring sensor 19 can also measure, for example, the actual position x or the adjustment travel of the piezoelectric actuator 3. The position measuring sensor 19 has a signal connection to the control device 6 and provides the digital signal processor 7 with digital measured values x.sub.m of the actual position x via a first analog/digital converter 20.

[0039] The series resistor 10 is used as a shunt or measuring resistor in order to determine the current which has flowed to the piezoelectric actuator 3. For this purpose, the positioning device 1 has a voltage measuring sensor 21 which measures a voltage U.sub.m dropped across the series resistor 10. The voltage measuring sensor 21 has a signal connection to the control device 6 and provides the digital signal processor 7 with digital measured values u.sub.m of the voltage U.sub.m via a second analog/digital converter 22.

[0040] The control device 6 is used to regulate the actual position x and an actual state of charge Q of the piezoelectric actuator 3. The charge regulation forms an internal control loop, whereas the position regulation forms an external control loop which is superimposed on the internal control loop. In order to regulate the position and charge, the digital signal processor 7 forms a position regulating unit 23, a position pilot control unit 24, a charge regulating unit 25, a calculation unit 26 and a detection unit 27.

[0041] A desired position X.sub.S is first of all supplied to a desired value limiter 28 and any limited desired position X.sub.S′ is supplied to a desired value filter 29 in the position regulating unit 23. The desired value filter 29 has the function of a path generator and takes into account physical limits of the piezoelectric actuator 3, in particular. The desired value filter 29 provides a calculated second desired position x.sub.S on the output side. Using a first adder 31, the measured and digitized actual position x.sub.m is subtracted from the desired position x.sub.S and a position control error e.sub.X is calculated. Any dead times of the kinematic system 2 and/or of the positioning device 1 can be taken into account using a dead time element 30 upstream of the adder 31. The position control error ex is supplied to a prefilter 32 and to a downstream position regulator 33. The position regulator 33 provides a regulation manipulated variable u.sub.R on the output side. The position regulating unit 23 interacts with the position pilot control unit 24. For this purpose, the desired position x.sub.S, as a pilot control manipulated variable, is added to the regulation manipulated variable u.sub.R, using of a second adder 34, to form an overall manipulated variable u.sub.P.

[0042] The manipulated variable u.sub.P provides a desired state of charge Q.sub.S for the charge regulating unit 25. The charge regulating unit 25 is also supplied with the digitized measurement voltage u.sub.m which is converted, in a conversion element 35 having the resistance value R, into a current i.sub.m which is filtered in a prefilter 36 and is then integrated by an integrator 37. The integrator 37 provides an actual state of charge Q of the piezoelectric actuator 3 on the output side. The actual state of charge Q is subtracted from the desired state of charge Q.sub.S by a third adder 38, with the result that the third adder 38 outputs a charge control error e.sub.Q on the output side. The charge control error e.sub.Q is converted, in a second conversion element 39, into a desired voltage value U.sub.S which is intended to be output by the digital/analog converters 12, 16 as a sum of the analog converter output voltages U.sub.1 and U.sub.2.

[0043] The desired voltage value U.sub.S is supplied to the calculation unit 26 which calculates the digital input values d.sub.1 and d.sub.2 for the digital/analog converters 12 and 16. The calculation unit 26 is also supplied with a control signal S which is generated by the detection unit 27. For this purpose, the detection unit 27 is supplied with the desired positions X.sub.S, X.sub.S′ and x.sub.S and the position control error e.sub.X. The detection unit 27 is designed in such a manner that a control signal S is generated if X.sub.S=x.sub.s or X.sub.S′=x.sub.S and the absolute value of the position control error ex undershoots a predefined control error limit value for a minimum period. In this case, the detection unit 27 detects a stable or steady state of the position regulation. If a steady state is detected for example, S=1 applies to the control signal S, otherwise S=0.

[0044] The calculation unit 26 is illustrated in detail in FIG. 4. In order to illustrate time steps, the instantaneous time step is indicated as [k] and the previous time step is indicated by [k−1]. A required first voltage value U.sub.1S[k] for the coarse converter 12 is calculated from the desired voltage value U.sub.S[k] by a conversion element 39. The first voltage value U.sub.1S[k] takes into account the parameters of the coarse converter 12, for example the first voltage range ΔU.sub.1 and the first voltage levels Δu.sub.1 and/or the resolution. This first voltage value U.sub.1S[k] is supplied to a first selection element 40. The selection element 40 is also supplied with an output voltage value U.sub.A[k−1] of the selection element 40, which output voltage value is stored in a memory element 41.

[0045] The selection element 40 selects between U.sub.1S[k] and U.sub.A[k−1] on the basis of a switching signal S.sub.A[k]. If S.sub.A[k]=1, the selection element 40 selects the first voltage value U.sub.1S[k] as the instantaneous output voltage value U.sub.A[k] and otherwise selects the earlier output voltage value U.sub.A[k−1], that is to say if S.sub.A[k]=0. The output voltage value U.sub.A[k] specifies the analog first converter output voltage U.sub.1to be output by the coarse converter 12, in which case the corresponding digital input value d.sub.1 for the coarse converter 12 is calculated in the calculation element 42.

[0046] The output voltage value U.sub.A[k] is also supplied to a compensation low-pass filter 50. The compensation low-pass filter 50 ensures that the dynamic response of the first converter/amplifier circuit 8, which has been subjected to low-pass attenuation on account of the low-pass filter 13, is compensated for by the second converter/amplifier circuit 9. This means that the entire dynamic response is available for compensating for interference during the small-signal behavior for the voltage at the piezoelectric actuator 3. The cut-off frequency of the low-pass filter 13 and therefore also the cut-off frequency of the compensation low-pass filter 50 are determined from the required maximum movement speed of the piezoelectric actuator 3.

[0047] Using a fourth adder 43, the low-pass-filtered output voltage value U.sub.A[k] for the coarse converter 12 is subtracted from the desired voltage value U.sub.S[k], with the result that the adder 43 outputs a second voltage value U.sub.2S[k] which is intended to be output by the fine converter 16 as a second analog converter output voltage U.sub.2. This second voltage value U.sub.2S[k] is converted into the digital input value d.sub.2 for the fine converter 16 in a calculation element 44.

[0048] In order to calculate the switching signal S.sub.A[k], the output voltage value U.sub.A[k−1] from the previous time step, which is stored in a memory element 46, is subtracted from the desired voltage value U.sub.S[k] by a fifth adder 45. The adder 45 outputs a voltage difference, for which a difference absolute value ΔU[k] is formed by an absolute value formation unit 47. The difference absolute value ΔU[k] is supplied to a comparator 48 which compares it with a limit value L[k]. If the difference absolute value ΔU[k] exceeds the limit value L[k], the switching signal S.sub.A[k]=1 is output and results in the selection of the first voltage value U.sub.1S[k] in the selection element 40. Otherwise, the switching signal S.sub.A[k]=0 is output and results in the selection of the earlier output voltage value U.sub.A[k−1] in the selection element 40.

[0049] A second selection element 49 selects between a first limit value Lu and a second limit value L.sub.S on the basis of the control signal S[k] provided by the detection unit 27 and provides the instantaneous limit value L[k] on the basis of the selection. The first limit value L.sub.U is selected if the control signal S[k] characterizes an unstable or dynamic state of the position regulation, whereas the second limit value L.sub.S is selected if the control signal S[k] characterizes a stable or steady state of the position regulation. The following holds true:

L.sub.U<L.sub.S.

[0050] This ensures that a change in the first converter output voltage U.sub.1 becomes unlikely in a stable state of the position regulation.

[0051] The piezoelectric positioning device 1 is part of a projection exposure apparatus, for example, at least one component of the projection exposure apparatus, for example a mirror, a lens element and/or a plate to be bent, being able to be positioned in a highly accurate manner with the piezoelectric positioning device 1.

[0052] The method of operation of the positioning device 1 is as follows:

[0053] In order to set a desired position X.sub.S, a suitable trajectory and the associated desired position x.sub.S are calculated by the desired value limiter 28 and the desired value filter 29. The position control error ex is determined from the desired position x.sub.S and the digitized actual position x.sub.m, which was determined by the position measuring sensor 19, and is supplied, via the prefilter 32, to the position regulator 33 which outputs the regulation manipulated variable u.sub.R. The position regulator 33 is in the form of a PID regulator, for example. The desired position x.sub.S is additionally added via the position pilot control unit 24 and the resulting desired state of charge Q.sub.S of the piezoelectric actuator 3 is supplied to the charge regulating unit 25.

[0054] The charge regulating unit 25 calculates a charge control error e.sub.Q and outputs, on the output side, the required desired voltage value U.sub.S which must be converted by the digital/analog converters 12 and 16 into the analog converter output voltages U.sub.1 and U.sub.2. In order to calculate the charge control error e.sub.Q, the digitized measurement voltage u.sub.m is converted into a current i.sub.m and is integrated to form the actual state of charge Q.

[0055] In the manner already described, the calculation unit 46 is used to calculate the digital input values d.sub.1 and d.sub.2 for the digital/analog converters 12, 16 from the desired voltage value Us. In this case, the position regulation is initially in a dynamic state, with the result that the detection unit 27 transmits a corresponding control signal S to the calculation unit 26 which uses the first limit value L.sub.U for the comparator 48.

[0056] The digital/analog converters 12, 16 provide the desired analog converter output voltages U.sub.1 and U.sub.2 in a manner corresponding to the input values d.sub.1 and d.sub.2 and their characteristic curves. The converter output voltage U.sub.1 is filtered by the low-pass filter 13 and is then applied to the piezoelectric actuator 3 in a form amplified in a desired manner by the voltage amplifier 14. A noise signal of the coarse converter 12 is attenuated by the low-pass filter 13 and the series resistor 10. In comparison, the converter output voltage U.sub.2 is amplified by the second voltage amplifier 17 without a low-pass filter and is applied to the piezoelectric actuator 3 since the second voltage levels Δu.sub.2 are considerably lower than the first voltage levels Δu.sub.1. The positioning accuracy of the piezoelectric actuator 3 is therefore determined by the second voltage levels Δu.sub.2.

[0057] As a result of the converter output voltages U.sub.1 and U.sub.2 which have been set, the piezoelectric actuator 3 changes its longitudinal extent by Δx and therefore sets the desired actual position x. If a substantially steady state of the position regulation is achieved, the detection unit 27 detects this and provides the calculation unit 26 with a corresponding control signal S. The calculation unit 26 accordingly uses the larger, second limit value L.sub.S for the comparator, as a result of which the coarse converter 12 changes its set converter output voltage U.sub.1 again only when a change in the desired voltage value Us cannot be set using the fine converter 16.

[0058] The first limit value L.sub.U is ΔU.sub.2/4, for example, as a result of which changes to the coarse converter 12 are forced in the dynamic state of the position regulation. In contrast, the second limit value L.sub.S is ΔU.sub.2/2, for example, as a result of which the second voltage range ΔU.sub.2 of the fine converter 16 is optimally utilized.

[0059] The positioning device according to the invention and the two-stage digital/analog converter concept according to the invention having a coarse converter and a fine converter therefore enable highly accurate position regulation of piezoelectric actuators, in particular piezo stacks, using voltage or charge control. The entire adjustment range or movement range is preferably enabled via the longitudinal extent of a single piezo stack. As a result of the fact that piezo stacks react immediately and directly to voltage or charge changes, highly dynamic position regulation is also enabled. The at least one piezoelectric actuator or the at least one piezo stack preferably consists of a ceramic which is not conductive. As a result, the piezoelectric actuator can be operated in a potential-free manner, in particular. As a result of the measurement at the series resistor, it is also possible to diagnose system faults, for example cable breaks and/or short circuits. As a result of the subdivision into a coarse converter and a fine converter, it is possible to deliberately avoid differential non-linearities since small position control errors can always be compensated for using the fine converter and the converter output voltage of the coarse converter is changed only in the case of comparatively large position changes. The control concept for the coarse converter and for the fine converter is fundamentally such that a changed desired voltage value is intended to be set using the fine converter if possible, with the result that there is no need to change the coarse converter. If this is not possible, both the coarse converter and the fine converter are changed and set in such a manner that the fine converter is as close as possible to its central position or is in the center of its voltage range. This is ensured by the calculation unit. The number of desired value changes of the coarse converter is minimized by the calculation unit, with the result that the differential non-linearity of the coarse converter acts only in an isolated manner as a one-off interference variable in the position control loop and can be compensated for by the position control loop without any problems. Linking the calculation unit to the detection unit also ensures that a change in the coarse converter does not occur in a steady state of the position regulation, that is to say if the actual position set is intended to be retained exactly. Combining the desired value distribution among the coarse converter and the fine converter with the path generator of the position regulation adjusts or readjusts the coarse converter in such a manner that a voltage range which is as identical as possible in the positive and negative directions is available with the fine converter. As a result, voltage changes needed to retain the actual position in a highly accurate manner can be applied by the fine converter alone.

[0060] Selecting the supply voltages makes it possible to easily adapt the positioning device according to the invention to the voltage range of the piezoelectric actuator and to reliably protect the latter from overvoltages. The digital charge regulation makes it possible to substantially avoid hysteresis effects of the piezoelectric actuator. If piezo stacks made of low-voltage ceramics are used, a power-saving and highly integrated structure of the positioning device is possible. The number of components is comparatively small, with the result that an adverse effect caused by noise, thermal drift, or component variances is small.

[0061] Overall, the positioning device according to the invention enables highly accurate and highly dynamic position regulation in a simple and reliable manner. The positioning device according to the invention is suitable, in principle, for positioning any desired kinematic systems or their components.