CN105301956A - Control method of pneumatic optic deformable mirror system - Google Patents

Control method of pneumatic optic deformable mirror system Download PDF

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Publication number
CN105301956A
CN105301956A CN201510812247.8A CN201510812247A CN105301956A CN 105301956 A CN105301956 A CN 105301956A CN 201510812247 A CN201510812247 A CN 201510812247A CN 105301956 A CN105301956 A CN 105301956A
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lens system
distorting lens
displacement
pneumatic optical
output quantity
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CN105301956B (en
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李朋志
李佩玥
赵磊
东立剑
葛川
隋永新
杨怀江
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Abstract

A control method of a pneumatic optic deformable mirror system belongs to the field of control of ultra-precise optic applications. The method firstly fits a linear relation between input data and output data of the system under an open-loop stable state in order to determine a feed-forward coefficient of a feed-forward controller, then calculates an output quantity of the feed-forward controller according to an expected displacement of the system, then compares the expected displacement and an actual displacement obtained by a displacement sensor in order to obtain a displacement error, then determines a scale, an integral and a differential coefficient of a PID controller by a trial-and-error method, then calculates an output quantity of the PID controller by the displacement error, then determines a pulse transfer function of a notching filter according to vibration characteristics of the system and finally overlays the output quantity of the feed-forward controller and the output quantity of the PID controller and carries out smoothing of the overlaid quantity by the pulse transfer function to obtain a control output quantity so as to control entry of the output quantity into the system and realize control of the system. By the method, a displacement adjustment steady-state error will be less than 80 nm within 0.1 s.

Description

The control method of Pneumatic optical distorting lens system
Technical field
The invention belongs to the control field in ultra-precise optical application, be specifically related to a kind of control method of Pneumatic optical distorting lens system.
Background technology
Photoetching projection objective lens due to absorbing laser energy, makes image quality degradation in exposure process.The picture element deterioration with non-axis symmetry characteristic is then needed to be compensated by optical skew mirror system etc.Lens element in optical skew mirror system produces horse-saddle distortion, thus compensates the asymmetric multiplying power and constant term astigmatism introduced by thermal aberration.Optical skew mirror system in photoetching projection objective lens needs to reach high-precision adjustment of displacement in the short period of time, thus ensures that the quick high accuracy face shape of wherein optical lens components regulates.Existing document does not also relate to the closed-loop control of Pneumatic optical distorting lens system, and especially quick high accuracy controls.Often require that regulation time is at about 0.1s fast, high precision then means that adjustment of displacement precision is at ± about 150nm usually.
Summary of the invention
For solving the problems of the technologies described above, the invention provides a kind of Pneumatic optical distorting lens system control method.
It is that the technical scheme that problem adopts is as follows that the present invention solves above-mentioned technology.
The control method of Pneumatic optical distorting lens system, comprises the following steps:
Step one, Pneumatic optical distorting lens system allow input analog voltage range in, input analog voltage when stablizing under obtaining this system open loop and output displacement data, take input analog voltage as horizontal ordinate, with output displacement data for ordinate, the linear relationship of the input analog voltage that matching obtains and output displacement data, inverse is got to the linear coefficient that matching obtains, obtains the feed-forward coefficients k of feedforward controller f;
Step 2, expectation displacement y according to Pneumatic optical distorting lens system dwith the feed-forward coefficients k of the feedforward controller that step one obtains f, calculate the output quantity u of feedforward controller f=k f× y d;
In step 3, acquisition Pneumatic optical distorting lens system, the actual displacement y of displacement transducer, obtains displacement error amount e=y d-y;
The scale-up factor k of the PID controller in step 4, employing trial and error determination Pneumatic optical distorting lens system p, integral coefficient k iwith differential coefficient k d;
The scale-up factor k of the PID controller that step 5, the displacement error amount obtained according to step 3 and step 4 obtain p, integral coefficient k iwith differential coefficient k d, calculate the output quantity u of PID controller p;
Step 6, vibration characteristics according to Pneumatic optical distorting lens system, selectedly need the external disturbance frequency f of carrying out trap process 0, and determine that Pneumatic optical distorting lens system is to this external disturbance frequency f 0attenuation amplitude, then according to the coefficient k of attenuation amplitude determination notch filter n, pulsed transfer function F (z) of notch filter is then calculated according to formula (2);
F ( z ) = z 2 - 2 cos ( 2 πf 0 / 1000 ) z + 1 z 2 - 2 k n cos ( 2 πf 0 / 1000 ) z + k n 2 - - - ( 2 )
In formula, z represents complex variable;
Step 7, by the output quantity u of feedforward controller fwith the output quantity u of PID controller psuperposition, and by the pulsed transfer function of notch filter, filtering is carried out to superposition amount, re-use difference equation method and calculate control output quantity u;
Step 8, the analog voltage that control output quantity u is converted to identical numerical value, input the pneumatic servo valve of Pneumatic optical distorting lens system, thus realize the control of Pneumatic optical distorting lens.
Further, in described step one, adopt the linear relationship of least square fitting input analog voltage and output displacement data.
Further, in described step one, input analog voltage when stablizing under the open loop of acquisition and output displacement data are at least three groups.
Further, in described step 3, adopt the actual displacement y in A/D analog to digital converter collection acquisition Pneumatic optical distorting lens system.
Further, in described step 4, interfering frequency f 0for the vibration frequency corresponding to the peak value of the oscilating characteristic of Pneumatic optical distorting lens system.
Further, in described step 5, the output quantity u of PID controller pcalculated by formula (1);
u p = k p × e + k i × ( Σ j = 0 k ( e ( j ) × T s ) ) + k d × ( e ( k ) - e ( k - 1 ) ) ÷ T s - - - ( 1 )
In formula, k is sampling sequence number, T sfor the sampling period.
Further, in described step 8, adopt D/A digital to analog converter that control output quantity u is converted to the analog voltage of identical numerical value.
Compared with prior art, beneficial effect of the present invention is:
1, Pneumatic optical distorting lens system of the present invention control method adopt feedforward controller and notch filter based on Pneumatic optical distorting lens system real data and determine, effectively can promote this control method speed, realize controlling fast, adopt trial and error determination PID controller, in conjunction with the filter action of notch filter, effectively can improve the precision of this control method, realize high precision to control, through experimental verification, adopt method of the present invention to control Pneumatic optical distorting lens system, adjustment of displacement steady-state error can be made in 0.1s to be less than 80nm;
2, the feedforward controller of the control method of Pneumatic optical distorting lens system of the present invention, PID controller and notch filter realize comparatively simple, and stability is good.
Accompanying drawing explanation
Fig. 1 is the theory diagram of the control method of Pneumatic optical distorting lens system of the present invention;
Fig. 2 is the design sketch adopting control method of the present invention to control Pneumatic optical distorting lens.
Embodiment
The present invention is further illustrated below in conjunction with accompanying drawing.
As described in Figure 1, the control method of Pneumatic optical distorting lens system of the present invention is carried out for Pneumatic optical distorting lens system, and this system forms primarily of pneumatic servo valve, gas piping, corrugated tube, physical construction, lens element and displacement transducer.The analog voltage that controller exports enters pneumatic servo valve, and pneumatic servo valve exports the gas of corresponding air pressure.Gas enters corrugated tube through gas piping, and the gas of different air pressure can make corrugated tube that different stretching motion amounts occurs.Corrugated tube driving device structure does corresponding displacement movement, thus makes the optical lens components in physical construction that the deformation of corresponding face occur.The actual displacement of physical construction is obtained by displacement transducer.Controller used in the present invention forms primarily of feedforward controller, PID controller, notch filter, A/D analog to digital converter and D/A digital to analog converter, specifically can by digital signal processor (DigitalSignalProcessor, DSP) realize, servo period T sfor 1ms.
The control method of Pneumatic optical distorting lens system of the present invention, step is as follows:
Step one, Pneumatic optical distorting lens system allow input analog voltage range in, input different analog voltages, input analog voltage when stablizing under obtaining this system open loop situation and output displacement data, then be horizontal ordinate with input analog voltage, with output displacement data for ordinate, the output displacement obtained by MATLABR2009b software application least square fitting and the linear relationship of input analog voltage, inverse is got to the linear coefficient that matching obtains, obtains the feed-forward coefficients k for feedforward controller f;
In upper process, for reducing the error of the linear relationship of input analog voltage and output displacement data, so input analog voltage when obtaining stablize under open loop case and output displacement data are generally at least three groups;
Step 2, expectation displacement y according to Pneumatic optical distorting lens system dwith the feed-forward coefficients k of the feedforward controller that step one obtains f, calculate the output quantity u of feedforward controller f=k f× y d;
Step 3, employing A/D analog to digital converter timing acquiring obtain the reading of the actual displacement y in Pneumatic optical distorting lens system, and general collection period is 1ms, by expecting displacement y dwith actual displacement y, thus obtain displacement error amount e=y d-y;
Step 4, characteristic according to Pneumatic optical distorting lens system, consider stability and precision, adopts the scale-up factor k of trial and error determination PID controller p, integral coefficient k iwith differential coefficient k d;
The scale-up factor k of the PID controller that step 5, the displacement error amount e utilizing step 3 to obtain and step 4 obtain p, integral coefficient k iwith differential coefficient k d, calculate the output quantity u of PID controller p, specifically can adopt following formula:
u p = k p × e + k i × ( Σ j = 0 k ( e ( j ) × T s ) ) + k d × ( e ( k ) - e ( k - 1 ) ) ÷ T s
In formula, k is sampling sequence number, T sfor the sampling period;
Step 6, according to user demand, need the external disturbance frequency f of carrying out trap process according to Pneumatic optical distorting lens system vibration performance (under varying environment, Pneumatic optical distorting lens system vibration performance is different) is selected 0(unit is Hz), and determine Pneumatic optical distorting lens system external portion interfering frequency f 0attenuation amplitude, thus determine the coefficient k of notch filter n, and then the pulsed transfer function of this notch filter is obtained according to following formula;
F ( z ) = z 2 - 2 cos ( 2 πf 0 / 1000 ) z + 1 z 2 - 2 k n cos ( 2 πf 0 / 1000 ) z + k n 2
In formula, the complex variable that z defines in complex number plane, can be described as z transformation operator; Be generally and make the control effects of control method of the present invention obtain better precision, interfering frequency f 0be preferably the vibration frequency corresponding to peak value of the oscilating characteristic of Pneumatic optical distorting lens system;
Step 7, output quantity u to the feedforward controller that step 2 obtains fwith the output quantity u of the PID controller that step 5 obtains psuperpose, utilize notch filter F (z) that step 6 obtains, to superposition amount (u f+ u p) carry out filtering, use difference equation method to calculate control output quantity u;
Step 8, use D/A digital to analog converter are converted to the analog voltage of identical numerical value by controlling output quantity u, the pneumatic servo valve of input Pneumatic optical distorting lens system, thus the quick high accuracy realizing this system controls.
Embodiment 1
Adopt the Pneumatic optical distorting lens system of the analog voltage range 0-6V of input, be increased to the analog voltage of 6V successively according to the voltage increment of interval 0.25V from 0V, input analog voltage when stablizing under obtaining this system open loop situation and output displacement data, determine the feed-forward coefficients k of feedforward controller f=0.4407.Adopt the k of trial and error determination PID controller p=0.2, k i=0.01, k d=0.001.Arranging A/D analog to digital converter to the sampling period of actual displacement is 1ms.According to the vibration characteristics of Pneumatic optical distorting lens system, determine f 0=50, attenuation amplitude is-52.25dB, k n=0.9696.According to above-mentioned control method, Pneumatic optical distorting lens system is controlled, control result as shown in Figure 2, as can be seen from the figure, control method of the present invention can make adjustment of displacement steady-state error be less than 80nm in 0.1s, thus achieves the Pneumatic optical distorting lens system Bit andits control of (0.1s) high precision (steady-state error is less than 80nm) fast.

Claims (7)

1. the control method of Pneumatic optical distorting lens system, is characterized in that, comprises the following steps:
Step one, Pneumatic optical distorting lens system allow input analog voltage range in, input analog voltage when stablizing under obtaining this system open loop and output displacement data, take input analog voltage as horizontal ordinate, with output displacement data for ordinate, the linear relationship of the input analog voltage that matching obtains and output displacement data, inverse is got to the linear coefficient that matching obtains, obtains the feed-forward coefficients k of feedforward controller f;
Step 2, expectation displacement y according to Pneumatic optical distorting lens system dwith the feed-forward coefficients k of the feedforward controller that step one obtains f, calculate the output quantity u of feedforward controller f=k f× y d;
In step 3, acquisition Pneumatic optical distorting lens system, the actual displacement y of displacement transducer, obtains displacement error amount e=y d-y;
The scale-up factor k of the PID controller in step 4, employing trial and error determination Pneumatic optical distorting lens system p, integral coefficient k iwith differential coefficient k d;
The scale-up factor k of the PID controller that step 5, the displacement error amount obtained according to step 3 and step 4 obtain p, integral coefficient k iwith differential coefficient k d, calculate the output quantity u of PID controller p;
Step 6, vibration characteristics according to Pneumatic optical distorting lens system, selectedly need the external disturbance frequency f of carrying out trap process 0, and determine that Pneumatic optical distorting lens system is to this external disturbance frequency f 0attenuation amplitude, then according to the coefficient k of attenuation amplitude determination notch filter n, pulsed transfer function F (z) of notch filter is then calculated according to formula (2);
F ( z ) = z 2 - 2 c o s ( 2 πf 0 / 1000 ) z + 1 z 2 - 2 k n c o s ( 2 πf 0 / 1000 ) z + k n 2 - - - ( 2 )
In formula, z represents complex variable;
Step 7, by the output quantity u of feedforward controller fwith the output quantity u of PID controller psuperposition, and by the pulsed transfer function of notch filter, filtering is carried out to superposition amount, re-use difference equation method and calculate control output quantity u;
Step 8, the analog voltage that control output quantity u is converted to identical numerical value, input the pneumatic servo valve of Pneumatic optical distorting lens system, thus realize the control of Pneumatic optical distorting lens.
2. the control method of Pneumatic optical distorting lens system according to claim 1, is characterized in that, in described step one, adopts the linear relationship of least square fitting input analog voltage and output displacement data.
3. the control method of Pneumatic optical distorting lens system according to claim 1, is characterized in that, in described step one, input analog voltage when stablizing under the open loop of acquisition and output displacement data are at least three groups.
4. the control method of Pneumatic optical distorting lens system according to claim 1, is characterized in that, in described step 3, adopts the actual displacement y in A/D analog to digital converter collection acquisition Pneumatic optical distorting lens system.
5. the control method of Pneumatic optical distorting lens system according to claim 1, is characterized in that, in described step 4, and interfering frequency f 0for the vibration frequency corresponding to the peak value of the oscilating characteristic of Pneumatic optical distorting lens system.
6. the control method of Pneumatic optical distorting lens system according to claim 1, is characterized in that, in described step 5, and the output quantity u of PID controller pcalculated by formula (1):
u p = k p × e + k i × ( Σ j = 0 k ( e ( j ) × T s ) ) + k d × ( e ( k ) - e ( k - 1 ) ) ÷ T s - - - ( 1 )
In formula, k is sampling sequence number, T sfor the sampling period.
7. the control method of Pneumatic optical distorting lens system according to claim 1, is characterized in that, in described step 8, adopts D/A digital to analog converter that control output quantity u is converted to the analog voltage of identical numerical value.
CN201510812247.8A 2015-11-20 2015-11-20 The control method of Pneumatic optical distorting lens system Expired - Fee Related CN105301956B (en)

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