Piezoelectric deformable mirror flattening control method

Abstract

The invention relates to the technical field of wavefront aberration correction, in particular to a piezoelectric deformable mirror flattening control method, which comprises the following steps of: designing a cooperative control framework based on a leader following mode, and adjusting the state of each slave piezoelectric actuator to be consistent with the position of a master piezoelectric actuator; a state observer used for estimating the position state of the main piezoelectric actuator is designed, and each slave piezoelectric actuator obtains the position state of the main piezoelectric actuator through the state observer; designing a cooperative controller which has a coupling weight and is combined with a state observer; and a control signal output by the cooperative controller is input into each slave piezoelectric actuator, and the shape of the piezoelectric deformable mirror is flattened under the cooperative control among the slave piezoelectric actuators. Through organic combination of the state observer and the cooperative controller considering the coupling weight, high-precision flattening of the initial surface shape of the piezoelectric deformable mirror is achieved, the problem that the initial surface shape of the piezoelectric deformable mirror is uneven is effectively solved, and the wavefront correction precision of the piezoelectric deformable mirror is remarkably improved.

Description

Technical Field

[0001] The 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 a wavefront corrector, 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 the 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 prior art, although some studies have focused 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 are difficult to effectively handle 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 the current field of this 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 a leader-follower mode, combined with a state observer of a 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 and significantly improve 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: A piezoelectric deformable mirror flattening control method comprises the following steps: 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 piezoelectric actuator is arbitrarily selected from all the piezoelectric actuators of the piezoelectric deformable mirror as a master piezoelectric actuator, and the remaining piezoelectric actuators are 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, 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 The state observer, and each slave piezoelectric actuator obtains the position state of the main piezoelectric actuator through the state observer ; Among them, the model of the state observer is expressed as: ; Among them, is the estimation error between the position state of the main piezoelectric actuator estimated by the i th slave piezoelectric actuator and the actual position state of the main piezoelectric actuator, is the state observation control quantity; S3: Design a cooperative controller combined with a state observer with coupling weights; among them, the model of the cooperative controller is expressed as: ; Among them, is the control signal output by the cooperative controller; is the coupling weight between each slave piezoelectric actuator, is the position state of the i th slave piezoelectric actuator itself and the position state of the main piezoelectric actuator estimated by it The error between them, that is ; is the position state of the j th slave piezoelectric actuator itself and the position state of the main piezoelectric actuator estimated by it The error between them, that is , is the error and the error The difference between them, that is , F is the control feedback matrix, is the feedback gain of the i th slave piezoelectric actuator, N is the total number of the main piezoelectric actuator and the slave piezoelectric actuators; S4: Input the control signal output by the cooperative controller into each slave piezoelectric actuator, and flatten the piezoelectric deformable mirror surface under the cooperative control between each slave piezoelectric actuator.

[0005] Furthermore, in step S2, the state observation control quantity is designed as: ; Among them, t is time, is the estimation error between the position state of the main piezoelectric actuator estimated by the j th slave piezoelectric actuator and the actual position state of the main piezoelectric actuator, is the adjacency weight between each slave piezoelectric actuator, is the permission to obtain the state information of the master piezoelectric actuator, is the feedback gain of the state observer control.

[0006] Furthermore, in step S3, the cooperative controller for each slave piezoelectric actuator to meet the desired state is preliminarily designed as: ; The coupling weight between the slave piezoelectric actuators is introduced into the preliminarily designed cooperative controller and the cooperative controller is finally designed as: .

[0007] 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 an analog-to-digital conversion module and input into the cooperative controller to provide an initial value for the model of the master piezoelectric actuator. At this time, the model of the master piezoelectric actuator is: .

[0008] Furthermore, in step S4, the control signal output by the cooperative controller is converted into an analog quantity through a digital-to-analog conversion module and input into each slave piezoelectric driver to drive the piezoelectric deformable mirror to achieve flat surface shape.

[0009] Furthermore, 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, the control of the master piezoelectric actuator and each slave piezoelectric actuator is ended; if it is not flattened, loop through steps S2 - S4 until the surface shape of the piezoelectric deformable mirror is flattened.

[0010] Compared with the prior art, the present invention can achieve the following beneficial effects: (1) By designing the state observer of the master piezoelectric actuator, the position state of the master actuator is estimated in real time, solving the problem that the slave piezoelectric actuators cannot directly obtain the position state of the master piezoelectric actuator, thereby realizing the cooperative control between the slave piezoelectric actuators.

[0011] (2) Aiming at the complex coupling problem between multiple slave piezoelectric actuators, the present invention introduces a coupling weight and optimizes the cooperative control strategy, effectively solving the control problem caused by the coupling relationship in the prior art. On this basis, by combining the state observer with the cooperative controller with coupling weight, the high-precision flattening of the surface shape of the piezoelectric deformable mirror is realized, significantly improving the accuracy of wavefront aberration correction and further enhancing the applicability and reliability of the piezoelectric deformable mirror in the field of high-precision wavefront correction. Description of the Drawings

[0012] The accompanying drawings, which form a part of the present invention, are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings: Figure 1 is a flowchart of the flattening control method for a piezoelectric deformable mirror according to an embodiment of the present invention; Figure 2 is a control logic diagram of a collaborative controller according to an embodiment of the present invention; Figure 3 is a logic block diagram of the hardware used in the flattening control method for a piezoelectric deformable mirror according to an embodiment of the present invention; Figure 4 is a coupling weight diagram between slave piezoelectric actuators according to an embodiment of the present invention; Figure 5 is a position state curve diagram between slave piezoelectric actuators and a main piezoelectric actuator according to an embodiment of the present invention; Figure 6 is a position error curve diagram between slave piezoelectric actuators and a main piezoelectric actuator according to an embodiment of the present invention; Figure 7 is a surface shape diagram of the finally flattened piezoelectric deformable mirror according to an embodiment of the present invention.

[0013] 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, main piezoelectric actuator 8. Detailed implementation manners

[0014] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be 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 to the present invention.

[0015] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0016] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is 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 thus should not be construed as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise stated, the meaning of "a plurality of" is two or more than two.

[0017] In the description of the present invention, it should be noted that unless otherwise clearly defined and limited, the terms "mounted", "connected", "coupled" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.

[0018] Next, reference will be made to Figures 1 - 7 and in combination with embodiments to describe the present invention in detail.

[0019] As Figure 1 shown, the embodiment of the present invention provides a method for flattening control of a piezoelectric deformable mirror, including the following steps: S1: Design a cooperative control framework based on the leader-follower mode, and adjust the position states of each slave piezoelectric actuator to be consistent with the actual position state of the master piezoelectric actuator 8.

[0020] The state space model of the piezoelectric actuator is expressed as: (1); wherein, represents the state vector of the control system, is the control input of the piezoelectric ceramic, is the output vector, A, B, C, D are the system matrix, input matrix, output matrix, and direct transmission matrix respectively.

[0021] Arbitrarily select one of all the piezoelectric actuators of the piezoelectric deformable mirror as the main piezoelectric actuator, and the remaining piezoelectric actuators as the slave piezoelectric actuators. The present invention adopts a collaborative control framework in a leader-following mode to flatten the surface shape of the piezoelectric deformable mirror 2. Specifically, the collaborative control framework is used to adjust the position states of the slave piezoelectric actuators to be consistent with the actual position state of the main piezoelectric actuator 8, that is: (2).

[0022] S2: Design a state observer 7 according to the main piezoelectric actuator 8.

[0023] Aiming at the problem that the state information of the main piezoelectric actuator 8 cannot be directly obtained for a certain slave piezoelectric actuator in the piezoelectric deformable mirror 2, resulting in the inability to achieve collaborative control, the present invention designs a state observer 7 for the main piezoelectric actuator 8 to estimate the position state of the main piezoelectric actuator 8 in real time. Each slave piezoelectric actuator obtains the position state of the main piezoelectric actuator 8 through the state observer 7 , thus solving the problem that the slave piezoelectric actuators cannot directly obtain the position state of the main piezoelectric actuator 8 and realizing the collaborative control among the slave piezoelectric actuators.

[0024] The model of the main piezoelectric actuator 8 is expressed as: (3); Design the state observer 7 for estimating the position state of the main piezoelectric actuator 8 as: (4); Among them, is the estimation error between the position state of the main piezoelectric actuator 8 estimated by the i th slave piezoelectric actuator and the actual position state of the main piezoelectric actuator 8, ; is the state observation control quantity, which is used to enable the state observer 7 of each slave piezoelectric actuator to accurately obtain the true state of the main piezoelectric actuator 8, that is .

[0025] Design the state observation control quantity as: (5); Among them, t is time, is the estimation error between the position state of the main piezoelectric actuator estimated by the j th slave piezoelectric actuator and the actual position state of the main piezoelectric actuator 8, is the adjacency weight among the slave piezoelectric actuators; is the permission to obtain the state information of the main piezoelectric actuator 8. If the iIf an individual piezoelectric actuator can directly access the information of the main piezoelectric actuator 8, then , conversely ; is the feedback gain controlled by the state observer 7.

[0026] S3: Design the cooperative controller 1 with coupling weights and combined with the state observer 7.

[0027] After each individual piezoelectric actuator of the piezoelectric deformable mirror 2 obtains the position state of the main piezoelectric actuator 8 through the state observer 7, the cooperative control of the piezoelectric deformable mirror 2 is realized through state control. Define as the position state of the i th individual piezoelectric actuator itself and the error between its estimated position state of the main piezoelectric actuator 8 , that is: (6); The cooperative controller 1 for each individual piezoelectric actuator to meet the desired state is preliminarily designed as: (7); Among them, F is the control feedback matrix, is the feedback gain of the i th individual piezoelectric actuator.

[0028] In order to verify the stability of the control system, take the derivative of Equation (6) and substitute it into Equation (6) and Equation (7), and the closed-loop transfer function of the cooperative controller 1 for the state estimation of the main piezoelectric actuator 8 can be obtained as: (8); By adjusting the gain, it can be ensured that meets the Hurwitz stability criterion, thereby ensuring the stability of the control system. Therefore, through Equation (4) and Equation (7), the cooperative control between each individual piezoelectric actuator can be realized.

[0029] In practical applications, the coupling between the individual piezoelectric actuators of the piezoelectric deformable mirror 2 is inevitable. Therefore, the present invention further considers the coupling effect between the individual piezoelectric actuators and designs the cooperative controller 1 on this basis.

[0030] First, introduce the coupling weight between the individual piezoelectric actuators. The model of the main piezoelectric actuator 8 is Equation (3), and the state observer 7 is preliminarily defined as Equation (4). Then, the cooperative controller 1 considering the coupling weight between the piezoelectric actuators and combined with the state observer 7 is designed as: (9); Among them, is the coupling weight between each slave piezoelectric actuator; is the error The difference between the error is, that is , is the j position state of the nth slave piezoelectric actuator itself and the position state of the master piezoelectric actuator 8 estimated by it The error between them is, that is , N is the total number of the master piezoelectric actuator and the slave piezoelectric actuators.

[0031] The collaborative controller 1 is used to achieve the mirror flattening collaborative control considering the coupling between each slave piezoelectric actuator.

[0032] S4: Input the control signal output by the collaborative controller 1 into each slave piezoelectric actuator, and realize the flattening of the surface shape of the piezoelectric deformable mirror 2 under the collaborative control between each slave piezoelectric actuator.

[0033] Embodiment 1 Combined with Figure 2 and Figure 3 , the piezoelectric deformable mirror 2 includes a master piezoelectric actuator 8 and six slave piezoelectric actuators. The hardware used in the flattening control method of the piezoelectric deformable mirror 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. Then, the flattening control method of the piezoelectric deformable mirror 2 includes the following steps: 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, and input it into the collaborative controller 1 to provide an initial value for the model of the master piezoelectric actuator 8.

[0034] At this time, the model of the master piezoelectric actuator 8 is: (10).

[0035] Step 2: Each slave piezoelectric actuator estimates the position state of the master piezoelectric actuator 8 in real time through the state observer 7 , and the state observation control quantity is designed as: (11).

[0036] Step 3: Subtract the position state observed by the state observer 7 from the actual position state of the master piezoelectric actuator 8 to obtain the state error ; Step 4: Introduce the coupling weight between the slave piezoelectric actuators , and taking the state error as the input value of the cooperative controller 1, the cooperative controller 1 considering the coupling weights is finally designed as: (12).

[0037] From the coupling weights between the piezoelectric actuators such as Figure 4 shown, Figure 4 1, 2, 3, 4, 5, 6 in

[0038] Step Five: Convert the control signal output by the cooperative controller 1 into an analog quantity through the digital-to-analog conversion module 5, and input it to the piezoelectric actuator 6. The piezoelectric actuator 6 drives all the piezoelectric actuators (the main piezoelectric actuator 8 and six slave piezoelectric actuators) of the piezoelectric deformable mirror 2 to act, so as to realize the flattening of the surface shape.

[0039] Step Six: Judge whether the surface shape of the piezoelectric deformable mirror 2 is flattened; if not, return to Step Two and continue the closed-loop control until the surface shape of the piezoelectric deformable mirror 2 is flattened; if it is flattened, end the control process.

[0040] Judging whether the surface shape of the piezoelectric deformable mirror 2 is flattened is a prior art, so it will not be elaborated here.

[0041] such as Figure 5 shown, under the action of 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 accurately track the position state described by the main piezoelectric actuator 8 whose dynamic equation is .

[0042] such as Figure 6As shown, the first error refers to the position error curve between the first slave piezoelectric actuator and the main piezoelectric actuator, the second error refers to the position error curve between the second slave piezoelectric actuator and the main piezoelectric actuator, the third error refers to the position error curve between the third slave piezoelectric actuator and the main piezoelectric actuator, the fourth error refers to the position error curve between the fourth slave piezoelectric actuator and the main piezoelectric actuator, the fifth error refers to the position error curve between the fifth slave piezoelectric actuator and the main piezoelectric actuator, and the sixth error refers to the position error curve between the sixth slave piezoelectric actuator and the main 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 main piezoelectric actuator 8, with a tracking error less than 1 nanometer. The surface shape of the finally flattened piezoelectric deformable mirror 2 is as Figure 7 shown.

[0043] It should be understood that various forms of the processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in the disclosure of the present invention can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solution disclosed in the present invention can be achieved. No limitations are imposed herein.

[0044] The above specific embodiments do not constitute a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the protection scope 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 piezoelectric actuator is arbitrarily selected from all the piezoelectric actuators of the piezoelectric deformable mirror as a master piezoelectric actuator, and the remaining piezoelectric actuators are 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, 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, is 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 The estimated position state of the main piezoelectric actuator The error between ; For the j The position state of the piezoelectric actuator itself The estimated position state of the main piezoelectric actuator The error between , Error With error The difference is , F is the control feedback matrix, For the i The feedback gain from the piezoelectric actuator, N is 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 the flattening of the piezoelectric deformable mirror shape under the cooperative control between the slave piezoelectric actuators.

2. The piezoelectric deformable mirror flattening control method according to claim 1, characterized in that: In step S2, the state observation control quantity Designed for: ； 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.

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: ； 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 an 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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