Method for controlling an inertial drive

Abstract

A method for controlling an inertial drive on the basis of pulse trains is disclosed. The pulse trains include pulses having sections of different gradients and having variable amplitude and/or frequency. A pulse interval occurs between the individual pulses, wherein the selected pulse duration is so short that is substantially less than the cycle duration of the natural oscillation of the system to be driven.

Claims

1. A method for controlling an inertial drive on the basis of pulse trains that include sections having different gradients and having variable amplitude and frequency, the method comprising: providing pulse intervals of variable lengths between individual pulses, wherein a selected pulse duration is less than a cycle duration of a natural oscillation of a system to be driven; maintaining a constant pulse duration; determining a step frequency of a drive based on the variable lengths of the pulse intervals; and permitting continuous motion of the drive by superimposing a scanning motion and a step.

2. The method according to claim 1 wherein each pulse comprises a sequence having a first slowly rising edge, a rapidly falling edge and a second slowly rising edge, or having a first slowly falling edge, a rapidly rising edge and a second slowly falling edge.

3. The method according to claim 1 further comprising, when the drive changes direction, adjusting amplitude values to compensate for changing step sizes.

4. The method according to claim 3 further comprising readjusting the amplitude values to keep the step size constant.

5. The method according to claim 4 further comprising dynamically controlling the amplitude to maintain small step sizes less than 5 nm.

6. The method according to claim 1 further comprising: setting a drive speed based on a product of the step frequency and the step size; and filtering out resonant frequencies of the system to be driven.

7. The method according to claim 1, further comprising compensating mechanical and electrical properties of the system to be driven by pulse asymmetry in the respective pulse trains used for control.

8. The method according to claim 3, further comprising: correcting frequency-dependent variations in the step size by making adjustments to control amplitudes; and correcting the adjustments anticipatively, using a recorded series of measurements.

9. The method according to claim 3, further comprising: correcting frequency-dependent variations in the step size by making adjustments to control amplitudes; and correcting said adjustments dynamically.

10. The method according to claim 1 wherein more than one actuator is used per drive, the actuators selectively controllable by a timing offset.

11. The method according to claim 1 wherein the pulse duration of an individual pulse is less than 50 μs.

12. The method according to claim 1 wherein superimposing the scanning motion and the step includes performing the step when the scanning motion has reached a threshold value.

13. A method for controlling an inertial drive on the basis of pulse trains that include sections having different gradients and having variable amplitude and frequency, the method comprising: providing pulse intervals of variable lengths between individual pulses, wherein a selected pulse duration is less than a cycle duration of a natural oscillation of a system to be driven and wherein the selected pulse duration is at least one order of magnitude less than the cycle duration of a natural oscillation of the system to be driven.

14. The method according to claim 13 further comprising: when the drive changes direction, adjusting amplitude values to compensate for changing step sizes.

15. The method according to claim 14 further comprising readjusting the amplitude values to keep the step size constant.

16. The method according to claim 13, further comprising compensating mechanical and electrical properties of the system to be driven by pulse asymmetry in the respective pulse trains used for control.

17. The method according to claim 13, further comprising: correcting frequency-dependent variations in the step size by making adjustments to control amplitudes; and correcting the adjustments anticipatively, using a recorded series of measurements.

18. The method according to claim 13, further comprising: correcting frequency-dependent variations in the step size by making adjustments to control amplitudes; and correcting said adjustments dynamically.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) The method shall now be described in greater detail with reference to an embodiment and with the aid of Figures, in which

(2) FIG. 1 shows a schematic sketch of an inertial drive with a typical corresponding sawtooth control.

(3) FIG. 2 shows examples of prior art signal waveforms for controlling inertial drives.

(4) FIG. 3A shows a simplified view of a linear inertial drive.

(5) FIG. 3B shows a simplified view of a rotary inertial drive.

(6) FIG. 4 shows a typical movement of a friction member and a runner when controlled with sawtooth pulses according to the prior art, for example.

(7) FIG. 5A shows a comparative view of a normal sawtooth pulse, with a shortened sawtooth according to one embodiment described herein, having a pulse duration which is shorter than the cycle duration of the natural oscillation of the system.

(8) FIG. 5B shows a comparative view of a normal parabolic control signal, with a shortened parabolic step pulse according to one embodiment described herein, having a pulse duration which is shorter than the cycle duration of the natural oscillation of the system.

(9) FIG. 6A shows a simplified sketch of the experimental set-up for measuring the vibrations directly on the runner and on a reference object that is an elastically suspended in an unfavorable manner for vibrations.

(10) FIG. 6B shows a comparison of the vibrations triggered by a 20-nm step with a classic sawtooth pulse as shown in the upper one of the two curves, and by a shortened sawtooth pulse as shown in the lower one of the two curves, according to one embodiment described herein.

(11) FIG. 6C shows a comparison of the vibrations triggered by a 100-nm step using a classical parabolic signal waveform as shown in the upper two curves and using a shortened parabolic pulse train according to one embodiment described herein as shown in the lower curves.

(12) FIG. 7 shows a comparison of real and ideal step responses as responses of the driven system to a shortened sawtooth pulse according to one embodiment described herein.

(13) FIG. 8 shows a comparison of the vibrations of the drive when controlled using a classic sawtooth waveform and the vibrations occurring with a shortened sawtooth pulse according to one embodiment described herein.

(14) FIG. 9 shows a comparison of the variation in step size in relation to amplitude in the range of small steps, when a positioner jams due to lack of control being exercised, as indicated by black arrows, forming hysteresis, and the variation in step size when jamming is prevented by amplitude control, as indicated by the black-grey arrow showing a simple linear relationship.

(15) FIG. 10 shows a view of a filtered-out region of strong vibration, shown as shaded, with respectively selected step size and step frequency.

(16) FIG. 11A shows a comparison of a symmetrical shortened sawtooth pulse according to the invention and two asymmetric shortened sawtooth pulses, likewise according to one embodiment described herein.

(17) FIG. 11B shows a comparison of a short square wave signal according to one embodiment described herein and two short asymmetric square wave signal, likewise according to one embodiment described herein.

(18) FIG. 12 shows a representation of a superimposed scanning motion having shortened sawtooth waveforms according to one embodiment described herein and

(19) FIG. 13 shows time-shifted control signals for a plurality of piezoelectric actuators using shortened sawtooth signals according to one embodiment described herein.

DETAILED DESCRIPTION

(20) FIG. 1 shows a schematic sketch of a prior art inertial drive 100 with typical corresponding sawtooth control 102. In such drives, an actuator D is provided to which a periodic, sawtooth-like signal 104 is applied, and which produces an acceleration relative to a displaceably mounted runner E frictionally connected to the actuator D.

(21) FIG. 2 shows a selection of typical signal waveforms used for inertial drives. An important criterion is that high-acceleration phases alternate with low-acceleration phases.

(22) Waveform A: Classic sawtooth

(23) Waveform B: Exponential pulse train

(24) Waveform C: Parabolic pulse trains with cliff

(25) Waveform D: Sawtooth with intervals

(26) Waveform E: Sawtooth sequence with intervals between the sawteeth

(27) Waveform F: Parabolic curve.

(28) FIG. 3A shows a simplified linear inertial drive, including the typical components, namely the base 1a, an actuator 2a mounted on the base and controlled by the sawtooth signal, and the friction surface 3a on the actuator. The friction surface 3a is in constant friction contact with the runner 4a. The runner can be moved in direction 5a by controlling the actuator 2a accordingly. In this Figure, the runner 4a is guided by a guide 6a.

(29) FIG. 3B shows a simplified rotary inertial drive, including the typical components, namely the base 1b, an actuator 2b mounted on the base and controlled by the sawtooth signal, and the friction surface 3b on the actuator. The friction surface 3b is in constant friction contact with the runner 4b. The runner can be moved in direction 5b by controlling the actuator 2b accordingly. In this Figure, the runner 4b is guided rotationally by a bearing 6b.

(30) It can be seen from the view shown in FIG. 4 how a friction member 106 entrains a runner 108. The desired entrainment of the runner 108 is achieved on the rising flat edge 110 of the pulse. On the steep, falling edge 112, slip 114 occurs between the friction member 106 and the runner 108, although this slip 114 is not total. Rather, the runner is always pulled back a certain distance. When small steps are desired, the distance moved undesiredly backwards is greater not only in relation to the step size, but also in absolute terms, with the result that a reduction in the step size leads to an increase in undesired vibrations of the driven object.

(31) FIG. 5A illustrates the comparison of a traditional sawtooth pulse 116 and a shortened sawtooth pulse 118 according to one embodiment described. The differences in pulse duration are reduced so that both waveforms 116 and 118 can be shown in one diagram. In order to reduce the vibration amplitude, the control signal is changed to a sawtooth waveform with intervals 120, and the duration of the resulting shortened sawtooth pulse 118 is reduced to such an extent that it is substantially below the cycle duration of the natural oscillations of the positioner. The pulse durations of traditional sawtooth signals and the shortened sawtooth may well differ by several orders of magnitude.

(32) FIG. 5B illustrates the comparison of a traditional parabolic control signal 122 and a shortened parabolic waveform 124. In order to reduce the vibration amplitude, the control signal is changed to a pulse with intervals 126, and the duration of the shortened pulse is reduced to such an extent that it is substantially below the cycle duration of the natural oscillations of the positioner. The pulse durations of the traditional waveform and the shortened control signal may well differ by several orders of magnitude.

(33) FIG. 6A, FIG. 6B, and FIG. 6C illustrate the effect of the shortened pulse trains, using sample measurements on an inertial drive, by comparing the latter with those obtained in the case of a traditional sawtooth waveform FIG. 6B and in the case of a traditional parabolic signal waveform FIG. 6C. To allow a direct comparison, the sawtooth waveforms and the parabolic waveforms for the control signals, traditional versus shortened were compared directly.

(34) FIG. 6A shows a simplified sketch of an inertial drive apparatus 127.

(35) A runner 5a guided inside the guide 5b is driven by supplying a sawtooth signal to the actuators. A small mirror 5c is mounted on runner 5a, the position of the mirror being monitored with the laser 5d of a laser interferometer.

(36) To show the effect of oscillations of the runner 5a on an object which is coupled to the runner unfavorably in regard to vibrations, another mirror 5f is mounted on top of a thin rod 5e on the runner 5a. Since the rod 5e is thin and the mirror 5f has a relatively high mass, the mirror 5f can be easily made to vibrate. The movements of the mirror 5f are monitored using a second laser beam 5g of the laser interferometer.

(37) FIG. 6B shows real measurements which were obtained using the experimental set-up 127 described above and shown in FIG. 6A.

(38) In each case, the runner 5a was driven to perform a 20-nm step.

(39) In the case of the upper two graphs 128 and 130, respectively, a traditional sawtooth signal 131 was used, whereas in the case of the lower two graphs, 132 and 134 respectively, a shortened sawtooth pulse 136 according to the invention was used.

(40) The graph 128 shows clearly that the carriage converted only a very small portion of the movement performed by the actuator into a step 20 nm; most of the movement is merely oscillation of the runner 5a on the order of 400 nm.

(41) The effect of the oscillation of the runner 5a on the mirror 5f is shown in the graph 130, where the mirror 5f can be observed oscillating with an amplitude of approximately 700 nm, followed by a long period of transient oscillations with a clearly discernible beat. If, instead of the mirror construction 5e+5f, a needle had been used in order to perform nanoscale manipulations, then such vibrations would have made it very difficult in practical terms to approach the object with fine steps.

(42) As can be seen from FIG. 6B, the drive response is different when control is effected using the shortened sawtooth pulses 136 as disclosed herein.

(43) In graph 132, the measured position is shown directly on the runner 5a. One can see a 20-nm step. The resolution of FIG. 5B is not sufficient to assess transient oscillations that may be present. It can be clearly seen that the oscillations are much less prominent than when a step is performed using a conventional sawtooth signal 131. The same is true for the vibration of the mirror 5f, shown in graph 134. The 20-nm step can be seen, followed by very small and rapid transient oscillations. This behavior is significantly better than when a conventional sawtooth 131 is used.

(44) With such positioning behavior, a needle of the kind referred to above may be used very well for nano-manipulations.

(45) FIG. 6c shows real measurements which were obtained using the experimental set-up 127 described above and shown in FIG. 6A.

(46) The runner 5a was driven in each case using parabolic signals to perform a 100-nm step.

(47) In the case of the graphs 138 and 140, a standard parabolic signal 142 was used, whereas in the case of the graphs 144 and 146, a shortened parabolic pulse 148 was used.

(48) The graph 138 shows clearly that the carriage converted only a very small portion of the movement performed by the actuator into a step of size about 100 nm; most of the movement is merely oscillation of the runner 5a in the order of several microns.

(49) The effect of the oscillation of the runner 5a on the mirror 5f is shown in the graph 140, where the mirror 5f can likewise be observed oscillating with an amplitude of several microns, followed by a long period of transient oscillations.

(50) As can be seen from FIG. 6C, the situation is different when control is effected using the shortened parabolic pulse pulses 142 as disclosed herein.

(51) In the graph 144, the measured position is shown directly on the runner 5a. One can see a 100-nm step. The resolution of FIG. 6C is not sufficient to assess transient oscillations that may be present. It can be clearly seen that the oscillations are much less prominent than in the case of a positioner driven with a normal parabolic signal 142. The same is true for the vibration of the mirror 5f, shown in the graph 146. The 100-nm step can be seen, followed by very small and rapid transient oscillations. This behavior is again significantly better than when a conventional parabolic signal is used.

(52) FIG. 7 illustrates the response of the driven system to a shortened sawtooth pulse 149 as disclosed herein. The graph 150 shows the real step response, in comparison with the graph 152 representing the ideal step response.

(53) FIG. 8 shows that the vibrations of an inertial drive driven with a traditional control signal become greater as the step sizes become smaller as shown in graph 154, which makes it technically impossible to use very small step sizes.

(54) The situation is different when the inertial drive is controlled by the shortened control pulses. As can be seen from graph 156, the vibrations also become smaller when the step sizes become smaller, which makes it technically feasible to use small steps of the inertial drive.

(55) FIG. 9 shows the typical behavior of an inertial drive at very small step sizes with and without amplitude control.

(56) When the amplitude is reduced, the step sizes 158 become increasingly smaller until no step is performed. When the amplitudes are then increased again, steps are not performed again immediately; instead, the amplitude 159 must be increased until the drive performs a large, erratic step 160. As soon as such a step 160 has been performed, the step size 158 can be controlled again by varying the amplitude.

(57) In the case of amplitude control, the step size 158 can be used continuously in a linear relationship down to a step size of zero, since the “jamming” described above is prevented by a fast control loop. No hysteresis occurs, so the small steps can be put to technical and meaningful uses.

(58) It can be seen from FIG. 10 how areas of strong vibrations indicated by a grey area 162 can be filtered out for a specimen positioner by selecting suitable step sizes and frequencies. The black line 164 is a possible control curve that avoids those combinations of step frequency and step size that result in overly strong vibrations.

(59) FIG. 11A shows three sawtooth pulses 166, 168, and 170, having different symmetries. The topmost pulse shows a symmetrical sawtooth control signal 166. The areas 172 and 174 enclosed by the sawtooth control signal 166 and the average value 176 are identical above and below the average value 176 of the sawtooth control signal 166.

(60) In the two other waveforms 168 and 170, the areas above and below the average value differ. For example, the area above the average value, 178, is larger than the area below the average value, 180. Asymmetry can also be produced in the other direction in which the area below the average value is greater.

(61) It can be shown that asymmetry can be produced using various methods. For the middle case 168, the asymmetry is set using different amplitude levels, whereas in the bottom case 170, asymmetry is produced using different edge gradients.

(62) Such asymmetry can compensate for the fact that the amplifier electronics, the actuators and the mechanics might not be able to follow a fast step perfectly, which then lead to asymmetric behavior at the point of friction, which leads in turn to undesired vibrations.

(63) FIG. 11B shows three square pulse sequences, 182, 184, and 186 having different symmetries. The topmost pulse sequence 182 shows a symmetrical square pulse sequence. The areas enclosed by the square wave signals and the dotted line, 188 and 190, respectively are identical above and below the average value 192 of the symmetrical square pulse control signal 182.

(64) In the two other waveforms, the areas above and below the average value 192 differ. The area above the average value 192 is larger. Asymmetry can also be produced in the other direction in which the area below the average value 192 is greater.

(65) It can be shown that asymmetry can be produced using various methods. For the middle case 184, the asymmetry is set using different amplitude levels, whereas in the bottom case 186, asymmetry is produced using different durations for the interval between slip phases.

(66) Such asymmetry can compensate in the event that the amplifier electronics, the actuators and the mechanics might not be able to follow a fast step perfectly, which then lead to asymmetric behavior at the point of friction, which leads in turn to undesired vibrations.

(67) FIG. 12 shows sawtooth pulses 194 superimposed on a scanning movement. A slowing rising line 196, interrupted by the sawtooth pulses 194, can be seen. Such a control signal allows continuous scanning motion to be performed with a runner.

(68) The scanning motion results from semi-static control that changes slowly in comparison with the edges of the step. Superimposition may be realized in such a way that a step is performed as soon as the scanning motion has reached a threshold value. After the step, the voltage applied to the actuator is again at the same level as before the first scan, so scanning can start anew. Because these cycles can be repeatedly performed, the possible stroke length is theoretically unlimited.

(69) FIG. 13 shows shortened sawtooth waveforms 198, 200, and 202, with which a drive having three actuators, in this case, can be controlled. The sawteeth 204 are produced with the same frequency, but with a timing offset 206, so not all the actuators perform a step simultaneously. By means of such multi-actuator drives, it is possible to realize powerful actuators with very uniform operating behavior.