Flattening control method of piezoelectric deformable mirror

Abstract

The present invention relates to the technical field of wavefront aberration correction, and in particular to a piezoelectric deformable mirror flattening control method, comprising: designing a collaborative control framework based on a leader-follower mode to adjust the state of each slave piezoelectric actuator to be consistent with the position of a master piezoelectric actuator; designing a state observer for estimating the position state of the master piezoelectric actuator, with each slave piezoelectric actuator obtaining the position state of the master piezoelectric actuator through the state observer; designing a collaborative controller with coupling weights and combined with the state observer; inputting a control signal output by the collaborative controller into each slave piezoelectric actuator, and achieving flattening of the piezoelectric deformable mirror surface shape under the collaborative control between the slave piezoelectric actuators. The present invention achieves high-precision flattening of the initial surface shape of the piezoelectric deformable mirror through the organic combination of the state observer and the collaborative controller taking coupling weights into consideration, effectively solving the problem of uneven initial surface shape of the piezoelectric deformable mirror and significantly improving the accuracy of wavefront correction of the piezoelectric deformable mirror.

Description

Technical Field

[0001] The present invention belongs to the technical field of wavefront aberration correction, and in particular relates to a piezoelectric deformable mirror flattening control method. Background Art

[0002] Piezoelectric deformable mirrors have the advantages of high control accuracy, fast response speed, large dynamic range, and strong flexibility. As wavefront correctors, they play an important role in the field of wavefront aberration correction technology. Piezoelectric deformable mirrors are usually composed of multiple piezoelectric actuators. High-precision control of each piezoelectric actuator is a key factor in achieving surface flattening. However, the initial uneven surface shape of the piezoelectric deformable mirror seriously affects the wavefront correction effect. In the existing technology, although there have been studies focusing on the control strategies of each piezoelectric actuator, these methods do not consider the connection relationship between each piezoelectric actuator and the influence of their interaction; at the same time, the existing methods have difficulty in effectively handling the coupling relationship between piezoelectric actuators, resulting in insufficient piezoelectric accuracy and stability. Therefore, how to achieve high-precision flattening of the piezoelectric deformable mirror surface and improve the accuracy and reliability of wavefront correction is a technical problem that needs to be solved urgently in this field of technology. Summary of the Invention

[0003] In view of this, the present invention aims to provide a piezoelectric deformable mirror flattening control method, which is based on a collaborative control framework of the leader-follower mode, combined with a state observer of the master piezoelectric actuator, and takes into account the coupling weights between each slave piezoelectric actuator, to achieve high-precision flattening of the piezoelectric deformable mirror surface, significantly improving the accuracy and reliability of wavefront correction.

[0004] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0005] A piezoelectric deformable mirror flattening control method comprises the following steps:

[0006] S1: Design a collaborative control framework based on the leader-follower mode to adjust the position state of each slave piezoelectric actuator to the actual position state of the master piezoelectric actuator wherein, one is arbitrarily selected from all the piezoelectric actuators of the piezoelectric deformable mirror as a master piezoelectric actuator, and the remaining piezoelectric actuators are used as slave piezoelectric actuators;

[0007] The state space model of the master piezoelectric actuator and each slave piezoelectric actuator is expressed as:

[0008] ;

[0009] in, represents the state vector of the system, is the control input of the piezoelectric ceramic, is the output vector, A, B, C, DThey are the system matrix, input matrix, output matrix and direct transfer matrix respectively;

[0010] S2: Designed to estimate the position state of the master piezoelectric actuator Each slave piezoelectric actuator obtains the position state of the master piezoelectric actuator through the state observer ; Among them, the model of the state observer is expressed as:

[0011] ;

[0012] in, For the i The estimated error between the position state of the master piezoelectric actuator estimated by the slave piezoelectric actuator and the actual position state of the master piezoelectric actuator, is the state observation control quantity;

[0013] S3: Design a cooperative controller with coupling weights and combined with a state observer. The model of the cooperative controller is expressed as:

[0014] ;

[0015] in, The control signal output by the collaborative controller; is the coupling weight between the slave piezoelectric actuators, For the i The position state of the piezoelectric actuator itself and its estimated position state of the main piezoelectric actuator The error between ; For the j The position state of the piezoelectric actuator itself and its estimated position state of the main piezoelectric actuator The error between , Error and error The difference, that is , F is the control feedback matrix, For the i The feedback gain from the piezoelectric actuator, N The total number of master piezoelectric actuators and slave piezoelectric actuators;

[0016] S4: Inputting the control signal output by the cooperative controller into each slave piezoelectric actuator, and realizing flattening of the piezoelectric deformable mirror shape under the cooperative control between each slave piezoelectric actuator.

[0017] Furthermore, in step S2, the state observation control quantity Designed to:

[0018] ;

[0019] in, t For time, For the j The estimated error between the position state of the master piezoelectric actuator estimated by the slave piezoelectric actuator and the actual position state of the master piezoelectric actuator, is the adjacency weight between each slave piezoelectric actuator, To obtain the master piezoelectric actuator status information, is the feedback gain of the state observer control.

[0020] Furthermore, in step S3, the collaborative controller for each slave piezoelectric actuator to meet the desired state is preliminarily designed as follows:

[0021] ;

[0022] Introducing coupling weights between piezoelectric actuators in the preliminary designed cooperative controller , the collaborative controller is finally designed as:

[0023] .

[0024] Furthermore, in step S2, a wavefront sensor is used to measure the initial aberration of the piezoelectric deformable mirror, and the analog signal of the wavefront sensor is converted into a digital quantity through the analog-to-digital conversion module and input into the collaborative controller to provide an initial value for the model of the main piezoelectric actuator. At this time, the model of the main piezoelectric actuator is:

[0025] .

[0026] Furthermore, in step S4, the control signal output by the collaborative controller is It is converted into analog quantity through the digital-to-analog conversion module and input into each slave piezoelectric driver to drive the piezoelectric deformable mirror to achieve surface flattening.

[0027] Furthermore, after step S4, the following steps are also included:

[0028] S5: Determine whether the surface shape of the piezoelectric deformable mirror is flattened; if it is flattened, end the control of the master piezoelectric actuator and each slave piezoelectric actuator; if it is not flattened, loop steps S2-S4 until the surface shape of the piezoelectric deformable mirror is flattened.

[0029] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0030] (1) By designing a state observer for the master piezoelectric actuator, the position state of the master actuator is estimated in real time, which solves the problem that the slave piezoelectric actuator cannot directly obtain the position state of the master piezoelectric actuator, thereby realizing coordinated control among the slave piezoelectric actuators.

[0031] (2) To address the complex coupling problem between multiple slave piezoelectric actuators, the present invention introduces coupling weights and optimizes a collaborative control strategy, effectively resolving the control difficulties caused by coupling relationships in the prior art. On this basis, by combining a state observer with a collaborative controller with coupling weights, high-precision flattening of the piezoelectric deformable mirror surface is achieved, significantly improving the accuracy of wavefront aberration correction and further enhancing the applicability and reliability of piezoelectric deformable mirrors in the field of high-precision wavefront correction. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0033] Figure 1 This is a flow chart of a piezoelectric deformable mirror flattening control method according to an embodiment of the present invention;

[0034] Figure 2 is a control logic diagram of a collaborative controller according to an embodiment of the present invention;

[0035] Figure 3 This is a logic block diagram of the hardware used in the piezoelectric deformable mirror flattening control method according to an embodiment of the present invention;

[0036] Figure 4 is a coupling weight diagram between the slave piezoelectric actuators according to an embodiment of the present invention;

[0037] Figure 5 is a position state curve diagram of each slave piezoelectric actuator and the master piezoelectric actuator according to an embodiment of the present invention;

[0038] Figure 6 is a position error curve diagram of each slave piezoelectric actuator and the master piezoelectric actuator according to an embodiment of the present invention;

[0039] Figure 7 3 is a surface diagram of the final flattened piezoelectric deformable mirror according to an embodiment of the present invention.

[0040] The reference numerals include: collaborative controller 1 , piezoelectric deformable mirror 2 , wavefront sensor 3 , analog-to-digital conversion module 4 , digital-to-analog conversion module 5 , piezoelectric driver 6 , state observer 7 , and main piezoelectric actuator 8 . DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0042] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0043] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second" and the like are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, features defined as "first", "second" and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0044] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal communication between two components. Those skilled in the art will be able to understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0045] The following will refer to Figure 1-Figure 7 The present invention is described in detail with reference to the embodiments.

[0046] like Figure 1 As shown, the present invention provides a piezoelectric deformable mirror flattening control method, including the following steps:

[0047] S1: Design a collaborative control framework based on the leader-follower mode to adjust the position state of each slave piezoelectric actuator to the actual position state of the master piezoelectric actuator 8 consistent.

[0048] The state space model of the piezoelectric actuator is expressed as:

[0049] (1);

[0050] in, represents the state vector of the control system, is the control input of the piezoelectric ceramic, is the output vector, A, B, C, D They are the system matrix, input matrix, output matrix and direct transfer matrix respectively.

[0051] From all the piezoelectric actuators of the piezoelectric deformable mirror, one is randomly selected as the master piezoelectric actuator, and the remaining piezoelectric actuators are slave piezoelectric actuators. The present invention adopts a collaborative control framework of the leader-follower mode to achieve the flattening of the surface of the piezoelectric deformable mirror 2. Specifically, the collaborative control framework is used to adjust the position state of each slave piezoelectric actuator to the actual position state of the master piezoelectric actuator 8. Consistent, that is:

[0052] (2).

[0053] S2: Design the state observer 7 according to the main piezoelectric actuator 8.

[0054] Aiming at the problem that a certain slave piezoelectric actuator in the piezoelectric deformable mirror 2 cannot directly obtain the state information of the master piezoelectric actuator 8, thereby causing the cooperative control to be impossible, the present invention designs a state observer 7 of the master piezoelectric actuator 8 to estimate the position state of the master piezoelectric actuator 8 in real time, and each slave piezoelectric actuator obtains the position state of the master piezoelectric actuator 8 through the state observer 7. , thereby solving the problem that the slave piezoelectric actuator cannot directly obtain the position state of the master piezoelectric actuator 8, and realizing coordinated control between the slave piezoelectric actuators.

[0055] The model of the main piezoelectric actuator 8 is represented as:

[0056] (3);

[0057] The state observer 7 for estimating the position state of the main piezoelectric actuator 8 is designed as follows:

[0058] (4);

[0059] in, For the i an estimated error between the position state of the master piezoelectric actuator 8 estimated by the slave piezoelectric actuator and the actual position state of the master piezoelectric actuator 8, ; is the state observation control variable, which is used to enable the state observer 7 of each slave piezoelectric actuator to accurately obtain the true state of the master piezoelectric actuator 8, that is, .

[0060] The state observation control quantity Designed to:

[0061] (5);

[0062] in, t For time, For the j The estimated error between the position state of the master piezoelectric actuator estimated by the slave piezoelectric actuator and the actual position state of the master piezoelectric actuator, is the adjacency weight between each slave piezoelectric actuator; To obtain the status information of the master piezoelectric actuator 8, if i Each slave piezoelectric actuator can directly access the information of the master piezoelectric actuator 8, then ,on the contrary ; is the feedback gain controlled by the state observer 7.

[0063] S3: Design a cooperative controller 1 with coupling weights and combined with a state observer 7.

[0064] After each slave piezoelectric actuator of the piezoelectric deformable mirror 2 obtains the position state of the master piezoelectric actuator 8 through the state observer 7, the coordinated control of the piezoelectric deformable mirror 2 is achieved through state control. For the i The position state of the piezoelectric actuator itself The estimated position state of the main piezoelectric actuator 8 The error is:

[0065] (6);

[0066] The collaborative controller 1 that satisfies the desired state of each slave piezoelectric actuator is preliminarily designed as follows:

[0067] (7);

[0068] in, F is the control feedback matrix, For the i The feedback gain from the piezoelectric actuator.

[0069] In order to verify the stability of the control system, the equation (6) is derived and substituted into equations (6) and (7), and the closed-loop transfer function of the cooperative controller 1 for the state estimation of the main piezoelectric actuator 8 is obtained as follows:

[0070] (8);

[0071] By adjusting the gain, you can ensure The Hurwitz stability criterion is satisfied, thus ensuring the stability of the control system. Therefore, through equations (4) and (7), the coordinated control between the slave piezoelectric actuators can be achieved.

[0072] In practical applications, coupling between the slave piezoelectric actuators of the piezoelectric deformable mirror 2 is inevitable. Therefore, the present invention further considers the coupling effect between the slave piezoelectric actuators and designs the cooperative controller 1 on this basis.

[0073] First, the coupling weight between the piezoelectric actuators is introduced , the model of the main piezoelectric actuator 8 is formula (3), and the state observer 7 is preliminarily defined as formula (4). Then, the cooperative controller 1 considering the coupling weights between the piezoelectric actuators and combined with the state observer 7 is designed as:

[0074] (9);

[0075] in, is the coupling weight between each slave piezoelectric actuator; Error and error The difference, that is , For the j The position state of the piezoelectric actuator itself The estimated position state of the main piezoelectric actuator 8 The error between , N The total number of master and slave piezoelectric actuators.

[0076] The cooperative controller 1 realizes the cooperative control of mirror flattening taking into account the coupling between the slave piezoelectric actuators.

[0077] S4: Input the control signal output by the cooperative controller 1 into each slave piezoelectric actuator, and realize the flattening of the surface shape of the piezoelectric deformable mirror 2 under the cooperative control between the slave piezoelectric actuators.

[0078] Example 1

[0079] Combine Figure 2 and Figure 3The piezoelectric deformable mirror 2 includes a master piezoelectric actuator 8 and six slave piezoelectric actuators. The hardware used in the piezoelectric deformable mirror flattening control method includes a collaborative controller 1, a piezoelectric deformable mirror 2, a wavefront sensor 3, an analog-to-digital conversion module 4, a digital-to-analog conversion module 5, a piezoelectric driver 6, a state observer 7, and a master piezoelectric actuator 8. The flattening control method of the piezoelectric deformable mirror 2 includes the following steps:

[0080] Step 1: Use the wavefront sensor 3 to measure the initial aberration of the piezoelectric deformable mirror 2, and convert the analog signal of the wavefront sensor 3 into a digital quantity through the analog-to-digital conversion module 4, input it into the collaborative controller 1, and provide an initial value for the model of the main piezoelectric actuator 8.

[0081] At this time, the model of the main piezoelectric actuator 8 is:

[0082] (10).

[0083] Step 2: Each slave piezoelectric actuator estimates the position state of the master piezoelectric actuator 8 in real time through the state observer 7 , state observation control quantity Designed to:

[0084] (11).

[0085] Step 3: The position state observed by the state observer 7 The actual position state of the main piezoelectric actuator 8 Subtract and get the state error ;

[0086] Step 4: Introduce coupling weights between piezoelectric actuators , and the state error As the input value of the cooperative controller 1, the cooperative controller 1 considering the coupling weight is finally designed as:

[0087] (12).

[0088] From the coupling weight between the piezoelectric actuator like Figure 4 As shown, Figure 4 1, 2, 3, 4, 5, and 6 refer to the first slave piezoelectric actuator, the second slave piezoelectric actuator, the third slave piezoelectric actuator, the fourth slave piezoelectric actuator, the fifth slave piezoelectric actuator, and the sixth slave piezoelectric actuator, respectively.

[0089] Step 5: The control signal output by the collaborative controller 1 The digital-to-analog conversion module 5 converts the data into analog quantities and inputs them into the piezoelectric driver 6. The piezoelectric driver 6 drives all the piezoelectric actuators (the master piezoelectric actuator 8 and six slave piezoelectric actuators) of the piezoelectric deformable mirror 2 to achieve surface flattening.

[0090] Step 6: Determine whether the surface shape of the piezoelectric deformable mirror 2 is flattened; if not, return to step 2 and continue closed-loop control until the surface shape of the piezoelectric deformable mirror 2 is flattened; if it is flattened, end the control process.

[0091] Determining whether the surface shape of the piezoelectric deformable mirror 2 is flattened is a prior art and will not be described in detail here.

[0092] like Figure 5 As shown, under the control method, the first slave piezoelectric actuator, the second slave piezoelectric actuator, the third slave piezoelectric actuator, the fourth slave piezoelectric actuator, the fifth slave piezoelectric actuator, and the sixth slave piezoelectric actuator can accurately track the dynamic equation: The position state of the master piezo actuator 8 is described.

[0093] like Figure 6 As shown, the first error refers to the position error curve between the first slave piezoelectric actuator and the master piezoelectric actuator, the second error refers to the position error curve between the second slave piezoelectric actuator and the master piezoelectric actuator, the third error refers to the position error curve between the third slave piezoelectric actuator and the master piezoelectric actuator, the fourth error refers to the position error curve between the fourth slave piezoelectric actuator and the master piezoelectric actuator, the fifth error refers to the position error curve between the fifth slave piezoelectric actuator and the master piezoelectric actuator, and the sixth error refers to the position error curve between the sixth slave piezoelectric actuator and the master piezoelectric actuator. Through this control method, the first slave piezoelectric actuator, the second slave piezoelectric actuator, the third slave piezoelectric actuator, the fourth slave piezoelectric actuator, the fifth slave piezoelectric actuator, and the sixth slave piezoelectric actuator can all achieve error-free tracking of the master piezoelectric actuator 8, with a tracking error of less than 1 nanometer. The final flattened surface of the piezoelectric deformable mirror 2 is as follows: Figure 7 shown.

[0094] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved. This is not limited herein.

[0095] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A piezoelectric deformable mirror flattening control method, characterized in that: The steps include: S1: Design a collaborative control framework based on the leader-follower mode to adjust the position state of each slave piezoelectric actuator to the actual position state of the master piezoelectric actuator wherein, one is arbitrarily selected from all the piezoelectric actuators of the piezoelectric deformable mirror as a master piezoelectric actuator, and the remaining piezoelectric actuators are used as slave piezoelectric actuators; The state space model of the master piezoelectric actuator and each slave piezoelectric actuator is expressed as: ； in, represents the state vector of the system, is the control input of the piezoelectric ceramic, is the output vector, t For time, A, B, C, D They are the system matrix, input matrix, output matrix and direct transfer matrix respectively; S2: Designed to estimate the position state of the master piezoelectric actuator Each slave piezoelectric actuator obtains the position state of the master piezoelectric actuator through the state observer ; Among them, the model of the state observer is expressed as: ； in, For the i The estimated error between the position state of the master piezoelectric actuator estimated by the slave piezoelectric actuator and the actual position state of the master piezoelectric actuator, is the state observation control quantity; S3: Design a cooperative controller with coupling weights and combined with a state observer. The model of the cooperative controller is expressed as: ； in, The control signal output by the collaborative controller; is the coupling weight between the slave piezoelectric actuators, For the i The position state of the piezoelectric actuator itself and its estimated position state of the main piezoelectric actuator The error between ; For the j The position state of the piezoelectric actuator itself and its estimated position state of the main piezoelectric actuator The error between , Error and error The difference, that is , F is the control feedback matrix, For the i The feedback gain from the piezoelectric actuator, N The total number of master piezoelectric actuators and slave piezoelectric actuators; S4: Inputting the control signal output by the cooperative controller into each slave piezoelectric actuator, and realizing flattening of the piezoelectric deformable mirror shape under the cooperative control between each slave piezoelectric actuator.

2. The piezoelectric deformable mirror flattening control method according to claim 1, characterized in that: In step S2, the state observation control quantity Designed to: ； in, For the j The estimated error between the position state of the master piezoelectric actuator estimated by the slave piezoelectric actuator and the actual position state of the master piezoelectric actuator, is the adjacency weight between each slave piezoelectric actuator, To obtain the master piezoelectric actuator status information, is the feedback gain of the state observer control.

3. The piezoelectric deformable mirror flattening control method according to claim 1, characterized in that: In step S3, the cooperative controller for each slave piezoelectric actuator to meet the desired state is preliminarily designed as follows: ； Introducing coupling weights between piezoelectric actuators in the preliminary designed cooperative controller , the collaborative controller is finally designed as: 。 4. The piezoelectric deformable mirror flattening control method according to claim 1, characterized in that: In step S2, the initial aberration of the piezoelectric deformable mirror is measured using a wavefront sensor, and the analog signal of the wavefront sensor is converted into a digital quantity through the analog-to-digital conversion module and input into the collaborative controller to provide an initial value for the model of the main piezoelectric actuator. At this time, the model of the main piezoelectric actuator is: 。 5. The piezoelectric deformable mirror flattening control method according to claim 1, characterized in that: In step S4, the control signal output by the cooperative controller is It is converted into analog quantity through the digital-to-analog conversion module and input into each slave piezoelectric driver to drive the piezoelectric deformable mirror to achieve surface flattening.

6. The piezoelectric deformable mirror flattening control method according to claim 1, characterized in that: After step S4, the following steps are also included: S5: Determine whether the surface shape of the piezoelectric deformable mirror is flattened; if it is flattened, end the control of the master piezoelectric actuator and each slave piezoelectric actuator; if it is not flattened, loop steps S2-S4 until the surface shape of the piezoelectric deformable mirror is flattened.

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