CN111290281A - Wavefront control method based on ADRC-Smith algorithm - Google Patents

Wavefront control method based on ADRC-Smith algorithm Download PDF

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CN111290281A
CN111290281A CN202010205762.0A CN202010205762A CN111290281A CN 111290281 A CN111290281 A CN 111290281A CN 202010205762 A CN202010205762 A CN 202010205762A CN 111290281 A CN111290281 A CN 111290281A
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adrc
smith
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孔令曦
程涛
杨平
王帅
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Institute of Optics and Electronics of CAS
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Abstract

The invention discloses a wave-front control method based on an ADRC-Smith algorithm, which is characterized in that the wave-front detection speed and the wave-front processing speed of an adaptive optical system are limited, so that the time delay of 2-3 times of a sampling period exists in the adaptive optical system, the ADRC (active disturbance rejection control) is a control method which has strong robustness and does not depend on a controlled system model, the ADRC algorithm and the Smith estimation algorithm are combined and applied to a wave-front control link of the adaptive optical system, the time delay existing in the adaptive optical system is compensated, and the system performance is improved.

Description

Wavefront control method based on ADRC-Smith algorithm
Technical Field
The invention relates to the technical field of wavefront control, in particular to a wavefront control method based on an ADRC-Smith algorithm.
Background
In an adaptive optics system with a sampling period of h, the speed of wavefront detection and wavefront processing is limited, so that a time delay tau of 2 h-3 h exists in the system. Using the approximate relationship, a simplified model of the adaptive optics system is obtained:
Figure BDA0002421036250000011
where s-J2 pi f is the Laplace operator and K is the total gain of the control loop (see li xinyang, zingiber hanense. effective bandwidth analysis of adaptive optics control systems [ J ] optics report 1997(12): 98-103.).
The time-lag system is characterized in that the output cannot reflect the control action applied to a controlled object in time, so that the phase lag of the controller is increased along with the increase of the frequency, the phase of a correction signal is the same as that of a disturbance signal, the negative feedback structure of the controller is damaged, and the system oscillation is broken. The traditional PI-Smith method has very limited perturbation tolerance to time delay in the system and cannot meet the actual requirement of the adaptive optical system, so time lag is an urgent problem to be solved in the adaptive optical system.
Disclosure of Invention
The invention provides a wavefront control technical method based on an ADRC-Smith algorithm, aiming at the problem that a PI + Smith algorithm in an adaptive optical system cannot adapt to delay perturbation in a wider range, so as to improve perturbation tolerance to system time delay and improve system performance.
In order to realize the purpose, the invention adopts the scheme that: a wavefront control method based on an ADRC-Smith algorithm comprises the following specific implementation steps:
step 1: fitting a transfer function of a controlled object to acquire time delay information in the system;
step 2: designing an ADRC-Smith compensation control structure;
and step 3: designing a nonlinear ESO (extended state observer) module according to the bearing capacity of the system;
and 4, step 4: and designing a nonlinear SEF (state error feedback) control law.
Wherein for the transfer function is Gp(s)＝Gc(s)e-τsSystem (e) of-τsBeing a pure hysteresis loop), a Smith compensation algorithm can be applied to match the time compensation function thereto, i.e.
Figure BDA0002421036250000021
When tau ismWhen τ is the exact compensation, the system transfer function is Gc(s)。
In the ADRC design, the selected controller order should match the transfer function form of the controlled object.
Wherein the nonlinear ESO is established based on the following formula (taking first order ADRC as an example):
Figure BDA0002421036250000022
wherein e is1As an observation error of ESO, z1、z2Is the output of ESO (z)2I.e. the dilated state), are observed estimates of the input signal r and the total disturbance f (-) respectively,
Figure BDA0002421036250000023
is z1、z2Y is the output signal of the system, gain β of the ESO1、β2Is an adjustable parameter; b0Is a compensation factor; and the nonlinear function fal (-) is defined as,
Figure BDA0002421036250000024
typically, 0< α <1, δ is n · h (h is the sampling step, n ≧ 1).
Wherein the control law is established based on the following formula (taking first order ADRC as an example):
Figure BDA0002421036250000025
wherein e is0To track errors, b1Is an adjustable gain factor.
The principle of the invention is as follows: the Smith predictor is used for compensating the time delay in the adaptive optical system, but the algorithm has higher requirement on the accuracy of given compensation time parameters, the time delay in the system has perturbation of 2-3 times of a sampling period, and the pure Smith predictor control algorithm can cause system divergence and influence the system performance. The ADRC is a control technology with strong robustness, and the stability and the immunity of the ADRC are used for weakening the requirement of the Smith algorithm on the accuracy of a given compensation parameter, so that the tolerance of the system to the perturbation range of the delay time is expanded, and the performance of the system is improved.
Compared with the prior art, the invention has the advantages that:
(1) compared with optimal control algorithms such as a Linear Quadratic Gaussian (LQG) control algorithm and the like, the method does not need to establish a detailed mathematical model for the self-adaptive optical system, and is simpler in calculation;
(2) compared with a PI-Smith control algorithm, the method has strong robustness, and can ensure that the system realizes hysteresis compensation and stable control in a larger time lag parameter variation range.
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FIG. 1 is a schematic diagram of a wavefront control method based on the ADRC-Smith algorithm according to the present invention;
FIG. 2 is a graph of the residual signal for the system when the parameters given by ADRC-Smith are accurately compensated (τ ═ 0.002);
fig. 3 is a diagram of the residual signal of the system when the parameter given by ADRC-Smith is mismatched (τ ═ 0.0001);
fig. 4 is a diagram of the residual signal of the system when the parameter given by ADRC-Smith is mismatched (τ ═ 0.006);
FIG. 5 is a graph of the residual signal for a mismatch of a given parameter of ADRC-Smith outside a given perturbation range;
fig. 6 is a graph of the residual signal of the system when the given parameter of PI-Smith is accurately compensated (τ ═ 0.002);
fig. 7 is a diagram of the residual signal of the system when the given parameter of PI-Smith is mismatched (τ ═ 0.0015);
fig. 8 is a diagram of the residual signal of the system when the given parameter of PI-Smith is mismatched (τ ═ 0.0025);
fig. 9 is a graph of the residual signal for a given parameter mismatch of PI-Smith outside a given perturbation range.
Detailed Description
The present invention will be further described with reference to the accompanying drawings by taking the control of the tilting mirror in the adaptive optics system as an example.
As shown in fig. 1, in an adaptive optics system with a sampling period of h ═ 0.001s, the wavefront control method based on the ADRC-Smith algorithm of the present invention sets the tilt mirror equivalent transfer function to Gc(s)＝K＝1。
The time delay in the system is set to 0.002s, and the low-frequency beam dither signal r is set to 10 sinx.
The method comprises the following concrete steps:
step 1: combining the tilting mirror equivalent transfer function, the function of the controlled object can be written as follows:
Gp(s)＝e-τs
step 2: designing a controller by adopting a first-order ADRC according to an equivalent transfer function of the tilting mirror, wherein the part of a time compensation function of the Smith compensation algorithm is
Figure BDA0002421036250000031
According to the parameter setting, assigning taum＝0.002s。
Step 3 given an ESO parameter of β1＝1，
Figure BDA0002421036250000032
b0＝20。
And 4, step 4: given the SEF control law parameter as b1＝15。
As shown in fig. 2, the system delay is accurately compensated, i.e., τ ═ τmA simulation result graph when the time is 0.002 s; fig. 3 is a diagram showing simulation results when the system delay compensation mismatch, i.e., τ is 0.0001 s; fig. 4 is a graph showing the simulation result when the system delay compensation mismatch, i.e., τ ═ 0.006 s. As can be seen from the simulation results, when the perturbation range of the delay time is within the tau epsilon [0.0001,0.006]When the perturbation range is within the range of (1), the system is in a stable convergence state, the residual signal intensity | epsilon | is less than or equal to 0.05, and the perturbation range completely covers the requirement of the adaptive optical system for time perturbation of 2-3 h, namely 0.002-0.003. Beyond this range, the residual signal strength increases, but the control algorithm also has some suppression of system beam jitter, as shown in fig. 5.
For comparison, the conventional PI-Smith method was used as a control and simulated in the same system. As can be seen from the simulation results shown in FIGS. 6, 7 and 8, the perturbation range tau epsilon [0.0015,0.0025], namely 1.5 h-2.5 h, of the system delay time of the PI-Smith method is beyond the range, and the system diverges as shown in FIG. 9.
The simulation results show that in the same set of adaptive optical system, for low-frequency beam jitter signals, the ADRC-Smith algorithm expands the range of the system to time delay perturbation by 6 times compared with the PI-Smith algorithm.

Claims (5)

1. A wave front control method based on ADRC-Smith algorithm is characterized in that: the method comprises the following concrete steps:
step 1: fitting a transfer function of a controlled object to acquire time delay information in the system;
step 2: designing an ADRC-Smith compensation control structure;
and step 3: designing a nonlinear ESO (namely, an extended state observer) module according to the bearing capacity of the system;
and 4, step 4: and designing a nonlinear SEF (state error feedback) control law.
2. An ADRC-Smith algorithm based wavefront control method according to claim 1, characterised in that: for a transfer function of Gp(s)＝Gc(s)e-τsSystem of (e) e-τsFor pure hysteresis, the Smith compensation algorithm can be applied to match the time compensation function thereto, i.e.
Figure FDA0002421036240000015
When tau ismWhen τ is the exact compensation, the system transfer function is Gc(s)。
3. An ADRC-Smith algorithm based wavefront control method according to claim 1, characterised in that: in the ADRC design, the selected controller order should match the transfer function form of the controlled object.
4. An ADRC-Smith algorithm based wavefront control method according to claim 1, characterised in that: the nonlinear ESO is established based on the following equation:
Figure FDA0002421036240000011
wherein e is1As an observation error of ESO, z1、z2Is the output of ESO (z)2I.e. the dilated state), are observed estimates of the input signal r and the total disturbance f (-) respectively,
Figure FDA0002421036240000012
is z1、z2Y is the output signal of the system, gain β of the ESO1、β2Is an adjustable parameter; b0Is a compensation factor; and the nonlinear function fal (-) is defined as,
Figure FDA0002421036240000013
typically, 0< α <1, δ is n · h (h is the sampling step, n ≧ 1).
5. An ADRC-Smith algorithm based wavefront control method according to claim 1, characterised in that: the control law is established based on the following formula:
Figure FDA0002421036240000014
wherein e is0To track errors, b1Is an adjustable gain factor.
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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112180737A (en) * 2020-10-20 2021-01-05 郑州大学 Control system control method based on active disturbance rejection control and similar Smith estimation
CN112684710A (en) * 2021-01-22 2021-04-20 中国科学院光电技术研究所 Light beam jitter suppression method based on LQG + PI mixed control strategy
CN113300766A (en) * 2021-04-13 2021-08-24 西安理工大学 Self-adaptive distortion wavefront corrector based on LQG and method thereof
CN113311712A (en) * 2021-05-28 2021-08-27 哈工大卫星激光通信股份有限公司 Identification method for hysteresis characteristic of rapid tilting mirror
CN114993591A (en) * 2022-04-15 2022-09-02 中南大学 LADRC-based seismic simulation vibrating table control method and system
CN115469555A (en) * 2022-11-14 2022-12-13 中国科学院光电技术研究所 Space image prediction and image quality optimization method for sensor chip projection lithography machine
CN115509121A (en) * 2022-10-27 2022-12-23 中国科学院光电技术研究所 Method for setting parameters of PI-Smith controller in pure time-lag system
CN115685757A (en) * 2022-10-27 2023-02-03 中国科学院光电技术研究所 Active disturbance rejection pre-estimation control method based on filtering in pure time lag system

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109143863A (en) * 2018-09-13 2019-01-04 武汉科技大学 The quick self study of nonlinear system improves ADRC control method
CN110554603A (en) * 2019-08-05 2019-12-10 西安工业大学 photoelectric stabilized sighting platform control method based on disturbance observation fractional order controller

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109143863A (en) * 2018-09-13 2019-01-04 武汉科技大学 The quick self study of nonlinear system improves ADRC control method
CN110554603A (en) * 2019-08-05 2019-12-10 西安工业大学 photoelectric stabilized sighting platform control method based on disturbance observation fractional order controller

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
XIANGYANG LI等: "ADRC with Feedfoward Control For Time-Delay Systems", 《2018 IEEE 7TH DATA DRIVEN CONTROL AND LEARNING SYSTEMS CONFERENCE》 *
刘川来 等: "Smith自抗扰控制器在过程时滞系统中的应用", 《青岛科技大学学报（自然科学版）》 *

Cited By (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112180737A (en) * 2020-10-20 2021-01-05 郑州大学 Control system control method based on active disturbance rejection control and similar Smith estimation
CN112180737B (en) * 2020-10-20 2022-04-19 郑州大学 Control system control method based on active disturbance rejection control and similar Smith estimation
CN112684710A (en) * 2021-01-22 2021-04-20 中国科学院光电技术研究所 Light beam jitter suppression method based on LQG + PI mixed control strategy
CN112684710B (en) * 2021-01-22 2022-08-23 中国科学院光电技术研究所 Light beam jitter suppression method based on LQG + PI mixed control strategy
CN113300766A (en) * 2021-04-13 2021-08-24 西安理工大学 Self-adaptive distortion wavefront corrector based on LQG and method thereof
CN113311712A (en) * 2021-05-28 2021-08-27 哈工大卫星激光通信股份有限公司 Identification method for hysteresis characteristic of rapid tilting mirror
CN114993591A (en) * 2022-04-15 2022-09-02 中南大学 LADRC-based seismic simulation vibrating table control method and system
CN115509121A (en) * 2022-10-27 2022-12-23 中国科学院光电技术研究所 Method for setting parameters of PI-Smith controller in pure time-lag system
CN115685757A (en) * 2022-10-27 2023-02-03 中国科学院光电技术研究所 Active disturbance rejection pre-estimation control method based on filtering in pure time lag system
CN115469555A (en) * 2022-11-14 2022-12-13 中国科学院光电技术研究所 Space image prediction and image quality optimization method for sensor chip projection lithography machine
CN115469555B (en) * 2022-11-14 2023-03-31 中国科学院光电技术研究所 Space image prediction and image quality optimization method for sensor chip projection lithography machine

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