Piezoelectric nanopositioning system control method, device, electronic device and storage medium based on rolling optimization

Abstract

The present invention proposes a control method, device, electronic device, and storage medium for a piezoelectric nanopositioning system based on rolling optimization, belonging to the field of precision electromechanical control technology. The method comprises: establishing a high-order transfer function model of a piezoelectric nanopositioning system and identifying the model parameters through a frequency sweep method; secondly, converting the model into a high-dimensional state space model, designing optimal control indicators, constructing a finite-time rolling optimization control problem, and improving the tracking capability of the piezoelectric nanopositioning system; finally, converting the rolling optimization control problem into a quadratic programming problem, and designing a coordinate descent method to accelerate the online calculation of the optimal control and ensure that the optimal control input satisfies the state and input constraints of the system. The method of the present invention can solve the problems of existing piezoelectric nanopositioning systems, such as the low order and limited expression capabilities of mathematical models, the narrow bandwidth of control methods, and the difficulty of digital implementation, thereby improving the ability of piezoelectric nanopositioning systems to track high-frequency reference instructions and being suitable for engineering applications.

Description

Technical Field

[0001] The present invention belongs to the field of precision electromechanical control technology, and in particular relates to a piezoelectric nanopositioning system control method, device, electronic equipment and storage medium based on rolling optimization, which is mainly used for high-precision servo tracking of high-bandwidth piezoelectric nanopositioning systems. Background Art

[0002] Over the past two or three decades, scanning tunneling microscopes and atomic force microscopes, based on nanoscience and nanopositioning technology, have fundamentally transformed research methods in a wide range of disciplines, including biology, materials science, chemistry, and physics. Furthermore, nanopositioning technology is also at the core of future lithography tools, playing an irreplaceable role in optical lithography systems.

[0003] Piezoelectric actuators are widely used in various fields of nanopositioning due to their advantages such as fast response, large output force and extremely high resolution, and have achieved many innovative application results.

[0004] With technological advancements, the performance demands of nanopositioning devices in areas such as high resolution and high bandwidth pose new challenges to control systems. However, inherent defects in piezoelectric actuators, such as creep and hysteresis nonlinearities, as well as vibrations caused by slightly damped resonant dynamics, limit the performance of piezoelectric nanopositioning systems. To overcome these shortcomings, various research institutions have begun modeling the principles of piezoelectric nanopositioning systems, studying the actuation mechanism and the impact of nonlinear factors on system performance. These efforts have led to the development of higher-order system models to improve the accuracy and bandwidth of nanopositioning systems. For example, the paper "High-Bandwidth Tracking Control of Piezoactuated Nanopositioning Stages via Active Modal Control" establishes a third-order model of a piezoelectric positioning system by considering damped resonance and nonlinear factors, thereby improving the control bandwidth of traditional second-order models. However, this approach suffers from inadequate modeling of the piezoelectric nanopositioning system and its inability to fully reflect the characteristics of the piezoelectric actuator. Furthermore, controller design adjustments require continuous debugging, relying on the engineer's experience, making it difficult to achieve optimal system performance.

[0005] Relatively speaking, establishing a higher-order piezoelectric nanopositioning system model is of greater significance for fully realizing the system's performance. In addition, rolling optimization control, as a multivariable control algorithm, is often used to track reference trajectories. It can significantly reduce tracking errors and improve the system's closed-loop bandwidth. Based on the nanopositioning system model, the optimal control index is designed, and the optimization control problem is constructed and combined with the rolling optimization control method. The reference instruction prediction information is applied to improve the drive tracking capability of the piezoelectric nanopositioning system, and the problem is converted into a quadratic programming problem to accelerate the online calculation speed, ultimately achieving high-precision, high-bandwidth tracking control of the piezoelectric nanopositioning system to meet the application requirements of the nanopositioning system. Summary of the Invention

[0006] To overcome the problems of existing piezoelectric nanopositioning systems, such as their narrow control bandwidth and inability to track high-frequency reference instructions, the present invention proposes a piezoelectric nanopositioning system control method, device, electronic device, and storage medium based on rolling optimization. The present invention establishes a high-order transfer function model for the piezoelectric nanopositioning system and identifies the system model parameters using a frequency sweep method. Secondly, the transfer function model is converted into a high-dimensional state-space model, and the optimal control index is designed, constructing a finite-time rolling optimization control problem. This improves the tracking capability of the piezoelectric nanopositioning system by using future information about the reference instructions. Finally, the rolling optimization control problem is converted into a multi-parameter quadratic programming problem, accelerating the online calculation of the optimal control input and ensuring that the optimal control input satisfies the state and input constraints of the piezoelectric nanopositioning system. This invention can significantly improve the ability of a piezoelectric nanopositioning system to track high-frequency reference instructions, and has extremely high engineering application value.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] A first aspect of the present invention provides a piezoelectric nanopositioning system control method based on rolling optimization, comprising:

[0009] At each sampling moment, a reference instruction to be tracked and a state of the piezoelectric nanopositioning system are obtained;

[0010] Constructing a rolling optimization control problem using the reference instruction to be tracked, a high-dimensional state space model of the piezoelectric nanopositioning system, and a state;

[0011] According to the preset prediction time domain and control time domain, the rolling optimization control problem is solved using the quadratic programming method to obtain the optimal control input of the piezoelectric nanopositioning system to enable the piezoelectric nanopositioning system to track the given reference instruction.

[0012] In one embodiment of the present invention, the piezoelectric nanopositioning system is a single-degree-of-freedom linear piezoelectric nanopositioning system.

[0013] In one embodiment of the present invention, the inputs of the multi-parameter quadratic programming problem are the reference execution to be tracked and the state of the piezoelectric nanopositioning system.

[0014] In one embodiment of the present invention, the piezoelectric nanopositioning system is used to establish a transfer function model based on experimental data, construct a state space model, describe the rolling optimization control problem, and design a coordinate descent solution method.

[0015] A second aspect of the present invention provides a piezoelectric nanopositioning system control device based on rolling optimization control, comprising:

[0016] A sampling module is used to obtain the state of the piezoelectric nanopositioning system at each sampling moment;

[0017] A high-dimensional state-space model generation module for piezoelectric nanopositioning systems, used to identify high-order transfer function models of piezoelectric nanopositioning systems and further construct a high-dimensional state-space model of the piezoelectric nanopositioning system;

[0018] The piezoelectric nanopositioning system control input generation module is used to construct a rolling optimization control problem based on a given reference trajectory, a high-dimensional state space model of the piezoelectric nanopositioning system, and the current state. The rolling optimization problem is further transformed into a multi-parameter quadratic programming problem to accelerate the online calculation of the optimal control input of the piezoelectric nanopositioning system, and ultimately enable the piezoelectric nanopositioning system to track the given reference instructions.

[0019] A third aspect of the present invention provides an electronic device, comprising:

[0020] at least one processor; and a memory communicatively coupled to the at least one processor;

[0021] The memory stores instructions that can be executed by the at least one processor, and the instructions are configured to execute the above-mentioned piezoelectric nanopositioning system control method based on rolling optimization.

[0022] A fourth aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the above-mentioned piezoelectric nanopositioning system control method based on rolling optimization.

[0023] The characteristics and beneficial effects of the present invention are:

[0024] (1) The present invention establishes a high-dimensional state space model of a piezoelectric nanopositioning system, improving the model's expressive power;

[0025] (2) This paper constructs a finite-time rolling optimization control framework to improve the tracking capability of the piezoelectric nanopositioning system by referring to the future information of the trajectory;

[0026] (3) The present invention proposes a multi-parameter quadratic programming method and designs a coordinate descent method to accelerate the online solution of the rolling optimization control problem, and ensures that the optimal control input satisfies the state constraints and input constraints of the piezoelectric nanopositioning system. The control effect is good and very suitable for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Schematic diagram of the flow chart of the rolling optimization control method for a piezoelectric nanopositioning system in an embodiment of the present invention.

[0028] Figure 2 Schematic diagram of reference input signal for step response simulation of a piezoelectric nanopositioning platform in a specific embodiment of the present invention.

[0029] Figure 3 A schematic diagram of the simulation results of the constrained step response control quantity output of a piezoelectric nanopositioning platform in a specific implementation case is disclosed.

[0030] Figure 4 Schematic diagram of the simulation results of the constrained step response of the piezoelectric nanopositioning platform in a specific embodiment of the present invention.

[0031] Figure 5 A schematic diagram of a reference input signal for a sinusoidal response simulation of a piezoelectric nanopositioning platform in a specific implementation case is disclosed.

[0032] Figure 6 This is a schematic diagram of the simulation results of the constrained sinusoidal response control quantity output of the piezoelectric nanopositioning platform in a specific implementation case of the present invention.

[0033] Figure 7 Schematic diagram of the simulation results of the unconstrained sinusoidal response of a piezoelectric nanopositioning platform in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other. The present invention proposes a piezoelectric nanopositioning system control method, device, electronic device and storage medium based on rolling optimization, which are further described in detail below with reference to the accompanying drawings and specific examples.

[0035] The first aspect of the present invention proposes a control method for a piezoelectric nanopositioning system based on rolling optimization. First, a high-order transfer function model of the piezoelectric nanopositioning system is established, and the model parameters are identified by a frequency sweep method. Then, the transfer function model is converted into a state space model. A rolling optimization problem is constructed based on state constraints and input constraints. The rolling optimization problem is then converted into a multi-parameter quadratic programming problem to accelerate the online solution of the optimal control input. The overall process of the method is as follows: Figure 1 As shown, the following steps are included:

[0036] Step (1) Obtain frequency response data of the piezoelectric nanopositioning system through a frequency analyzer, and use this to identify the nth-order transfer function model of the actuator:

[0037]

[0038] Among them, the operator z has a clear physical meaning (z -k represents a delay of k sampling periods), a i and b i , i = 0, 1, ..., n-1 are the model coefficients to be identified, Y(z) and U(z) are the discrete time transforms of the electric displacement output y(k) and the control input u(k) of the piezoelectric nanopositioning system, respectively. In the embodiment of the present invention, the model order n = 5, and b0 = 0.2536, b1 = 0.3351, b2 = 0.2654, b3 = 0.8734, b4 = 0.9523, a0 = -0.09212, a1 = 0.1754, a2 = 0.5851, a3 = 0.3625, a4 = 0.6599;

[0039] Step (2) defines the state x(k) of the piezoelectric nanopositioning system at time k as follows:

[0040]

[0041] in, Then the transfer function model of the piezoelectric nanopositioning system in step (1) can be transformed into the following state space form:

[0042] x(k+1)=Ax(k)+Bu(k)

[0043] y(k)=Cx(k)

[0044] In the above formula, the transfer matrix A, input matrix B and measurement matrix C of the piezoelectric nanopositioning system have the following forms:

[0045]

[0046]

[0047] In the embodiment of the present invention, β1=0.9523, β2=0.2450, β3=-0.2414, β4=-0.1516, β5=0.1308;

[0048] Step (3) Given the reference trajectory r(i) of the piezoelectric nanopositioning system, i=1, 2, ..., predict the time domain N p (N p =20), control time domain N c (N c =10), the upper limit of the electric displacement output of the piezoelectric nanopositioning system y max , lower limit y min , the upper limit u of the control input of the piezoelectric nanopositioning system max , lower limit u min , based on the state space model of the piezoelectric nanopositioning system in step (2), the following rolling optimization control problem is constructed:

[0049]

[0050] satisfy:

[0051] x(0|k)=x(k)

[0052] u(-1|k)=u(k-1)

[0053] x(i+1|k)=Ax(i|k)+Bu(i|k)

[0054] y(i|k)=Cx(i|k)

[0055] u(i|k)=u(i-1|k)+Δu(i|k)

[0056]

[0057] y(i|k)∈[y min ,y max ]

[0058] u(i|k)∈[u min ,u max ]

[0059] In the above problem, x(i|k) and y(i|k) represent the state and electric displacement output of the piezoelectric nanopositioning system at time k, respectively, predicted i steps ahead, u(i|k) represents the control input of the piezoelectric nanopositioning system at time k, r(i|k) = r(k+i) represents the reference trajectory of the piezoelectric nanopositioning system at time k, predicted i steps ahead, and u(·|k) = {u(0|k), ..., u(N p -1|k)} means predicting N at time kp The control input sequence of steps is Δu(i|k)=u(i|k)-u(i-1|k) represents the difference between u(i|k) and u(i-1|k), ρ represents the penalty coefficient of the control input, the transfer matrix A, the input matrix B and the observation matrix C are all given in step (2); in the embodiment of the present invention, a step signal and a sinusoidal signal are used as the reference trajectory r(i) for simulation experiments, wherein the step signal adopts a combination of signals with different amplitudes, such as Figure 2 As shown, the mathematical expression of the sinusoidal signal is: y(t) = 2sin(600πt) + 0.9sin(1000πt) + 0.5sin(1400πt) + 0.6sin(1600πt), as shown in Figure 5 In addition, the prediction time domain N p =20, control time domain N c =10, the upper limit of the electric displacement output of the piezoelectric nanopositioning system y max =3, lower limit y min =-3, the upper limit of the control input of the piezoelectric nanopositioning system u max =3, lower limit u min =-3, the penalty coefficient of control input ρ = 0.5;

[0060] Step (4) defines the following variables based on the rolling optimization control problem in step (3):

[0061]

[0062]

[0063] The constraints of the above control problem can be used to obtain the following compact prediction model for the piezoelectric nanopositioning system:

[0064] ΔU=ΨU-∑u(k-1)

[0065] Y=Φx(k)-ΓU

[0066] in,

[0067]

[0068]

[0069] Step (5) Based on the above-mentioned piezoelectric nanopositioning system prediction model, the rolling optimization control problem in step (3) is transformed into the following quadratic programming problem:

[0070]

[0071] Satisfies: WU≤b,

[0072] Among them, U* To express the optimal solution to the above problem, the weight matrix H, weight vector h, bias g, coefficient matrix W, and boundary vector b have the following forms:

[0073]

[0074]

[0075]

[0076] also, represents the identity matrix;

[0077] Step (6) constructs the dual problem of the quadratic programming problem in step (5):

[0078]

[0079] Satisfies: μ ≥ 0

[0080] The weight matrix P and weight vector p have the following forms:

[0081] P=WH -1 W T , p=b+WH -1 h;

[0082] Step (7) sets the current moment to k=1, and instructs the piezoelectric nanopositioning system to track a given reference trajectory r(i), i=k, k+12, ..., and proceeds to step (7-1);

[0083] (7-1) At time k, the state x(k) of the piezoelectric nanopositioning system and the control input u(k-1) at the previous time are obtained, and the matrices H, W, P and vectors h, b, p in steps (5) and (6) are calculated, and the matrix T = WH -1 , given the number of iterations M, and let the current iteration count m = 1, the initial value of the given vector μ(m) is 2(N p +N c ) is a zero vector, and the initial value of the vector v(m) is a length of N c The zero vector of the embodiment of the present invention, the number of iterations M = 10, enter step (7-2),

[0084] (7-2) Determine m. If m≤M, proceed to step (7-2). Otherwise, proceed to step (7-5).

[0085] (7-3) Let the counting variable j = 1, and make a judgment on j. If j> 2 (N p +N c), then go to step (7-4), otherwise use the coordinate descent method to solve the dual problem in step (6), let the vector t j represents the jth row of matrix T, vector w j represents the jth column of the matrix W, the scalar p j Represents the jth element of the weight vector p, vector p j represents the jth row of the matrix P, and the scalar μ j (m) represents the jth element of the vector μ(m), and the scalar p jj =t j w j ,and:

[0086]

[0087] For the jth element μ of vector μ(m) j (m) Update as follows:

[0088] μ j (m) = μ j (m)-Δ j

[0089] Update the vector v(m) as follows:

[0090] v(m)=v(m)+Δ j w j

[0091] Let j = j + 1 and go back to step (7-2);

[0092] (7-4) Let m = m + 1, μ(m) = μ(m-1), v(m) = v(m-1), and proceed to step (7-2).

[0093] (7-5) Let the optimal control input U * =-H -1 (h+W T )μ(m), and U * The first component is applied to the piezoelectric nanopositioning system in step (2), and the piezoelectric nanopositioning system performs corresponding movement to the next moment;

[0094] (7-6) Let k = k + 1, and then return to step (7-1) to realize the tracking of the given reference trajectory r(i), i = k, k + 1, ... by the piezoelectric nanopositioning system.

[0095] The piezoelectric nanopositioning system used in the method of the embodiment of the present invention is a conventional model device; those skilled in the art can implement the method through programming.

[0096] The present invention is further described below with reference to a specific embodiment.

[0097] Simulation experiment

[0098] (1) Simulation settings:

[0099] In this embodiment, the simulation step size is set to 0.0001s (i.e., 10KHz), and the total simulation time is 0.1s; the piezoelectric nanopositioning system model order n=5, the model parameters are: b0=0.2536, b1=0.3351, b2=0.2654, b3=0.8734, b4=0.9523, a0=-0.09212, a1=0.1754, a2=0.5851, a3=0.3625, a4=0.6599; In addition, the prediction time domain N of the rolling horizon optimization control p =20, control time domain N c =10, the upper limit of the electric displacement output of the piezoelectric nanopositioning system y max =3, lower limit y min =-3, the upper limit of the control input of the piezoelectric nanopositioning system u max =3, lower limit u min = -3, the penalty coefficient of control input ρ = 0.5, the number of iterations M = 10;

[0100] (2) Step reference trajectory tracking

[0101] ①Simulation settings: Design a step reference trajectory signal, which contains step signals of different amplitudes (see Figure 2 ), including a maximum amplitude of ±3μm, which exceeds the displacement output amplitude limit of the piezoelectric nanopositioning system. Step response simulations were performed to verify the simulation effect of the constrained step response control variable output.

[0102] ②Simulation results: The step response control output results are as follows: Figure 3 As shown in the figure, it can be seen that through the rolling optimization control including input and state constraints, the output of the control signal is effectively limited to between -3μm and +3μm, achieving the expected control input limiting goal. The constrained step response simulation results are shown in Figure 2. Figure 4 Show, according to Figure 4 The control system stabilization time is 0.2×10 -3 s, and the control system effectively limits the output amplitude of the piezoelectric nanopositioning system to within ±3μm, achieving the expected control effect.

[0103] (3) Sine reference trajectory tracking

[0104] ①Simulation settings: Assume a sinusoidal jump reference trajectory signal. The reference signal is synthesized using sinusoidal signals of 300Hz, 500Hz, 700Hz and 800Hz, with corresponding amplitudes of 2μm, 0.9μm, 0.5μm and 0.6μm respectively. The mathematical expression of the reference signal is: y(t) = 2sin(600πt) + 0.9sin(1000πt) + 0.5sin(1400πt) + 0.6sin(1600πt), as shown in Figure 1. Figure 5 The maximum input and output of the signal are -3.3μm and +3.3μm, respectively, exceeding the output amplitude limit of the piezoelectric nanopositioning system. Sinusoidal response simulations were performed to verify the output simulation results of the constrained sinusoidal response control variable.

[0105] ②Simulation results: The output of the sinusoidal response control quantity is as follows Figure 6 As shown in the figure, it can be seen that through the rolling optimization control including input and state constraints, the output of the control signal is effectively limited to between -3μm and +3μm, achieving the expected goal. The simulation results of the constrained sinusoidal response are shown in Figure 7 According to Figure 7 The control system can quickly track the changes in the credit signal input, and the system tracking lag can be ignored. The control system effectively limits the output amplitude of the piezoelectric nanopositioning system to within ±3μm, achieving the expected control effect.

[0106] To implement the above embodiment, a second embodiment of the present invention provides a piezoelectric nanopositioning system control device, comprising:

[0107] A sampling module is used to obtain the state of the piezoelectric nanopositioning system at each sampling moment;

[0108] A high-dimensional state-space model generation module for piezoelectric nanopositioning systems, used to identify high-order transfer function models of piezoelectric nanopositioning systems and further construct a high-dimensional state-space model of the piezoelectric nanopositioning system;

[0109] The piezoelectric nanopositioning system control input generation module is used to construct a rolling optimization control problem based on a given reference instruction, a high-dimensional state space model of the piezoelectric nanopositioning system, and the current state. The rolling optimization problem is further transformed into a multi-parameter quadratic programming problem to accelerate the online calculation of the optimal control input of the piezoelectric nanopositioning system, and ultimately enable the piezoelectric nanopositioning system to track the given reference instruction.

[0110] To implement the above embodiment, a third aspect of the present invention provides an electronic device, including:

[0111] at least one processor; and a memory communicatively coupled to the at least one processor;

[0112] The memory stores instructions that can be executed by the at least one processor, and the instructions are configured to execute the above-mentioned piezoelectric nanopositioning system control method based on rolling optimization.

[0113] A fourth aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the above-mentioned piezoelectric nanopositioning system control method based on rolling optimization.

[0114] It should be noted that the computer-readable medium described above in the present invention may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or component, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more conductors, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device, or component. In the present invention, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. This propagated data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium may be transmitted using any suitable medium, including but not limited to wires, optical cables, RF (radio frequency), etc., or any suitable combination thereof.

[0115] The computer-readable medium may be included in the electronic device or may exist independently, without being incorporated into the electronic device. The computer-readable medium carries one or more programs that, when executed by the electronic device, cause the electronic device to perform the piezoelectric nanopositioning system control method described in the above embodiment.

[0116] Computer program code for performing the operations of the present invention may be written in one or more programming languages, or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on the remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0117] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0118] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. Throughout the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0119] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application belong.

[0120] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and a portable compact disc read-only memory (CDROM). Furthermore, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or otherwise processing it in a suitable manner if necessary, and then storing it in a computer memory.

[0121] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, any one of the following technologies known in the art or a combination thereof can be used to implement the present invention: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0122] Those skilled in the art will appreciate that all or part of the steps in the method for implementing the above-mentioned embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0123] In addition, the functional units in the various embodiments of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into a module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0124] The storage medium mentioned above may be a read-only memory, a magnetic disk, or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application. Persons skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

[0125] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A piezoelectric nanopositioning system control method based on rolling optimization, characterized in that: include: At each sampling moment, the reference instruction to be tracked and the state of the piezoelectric nanopositioning system are obtained, including: (1) Obtain the frequency response data of the piezoelectric nanopositioning system through a frequency analyzer and use it to identify the actuator Order transfer function model: in, is the operator, Indicates a delay of k sampling periods, and , are the model coefficients to be identified, and They are the electric displacement outputs of the piezoelectric nanopositioning system and control inputs Discrete-time transform of ; (2) Definition of piezoelectric nanopositioning system State of the moment In the following form: in, ; Then the transfer function model of the piezoelectric nanopositioning system in step (1) can be transformed into the following state space form: In the above formula, the transfer matrix of the piezoelectric nanopositioning system is , input matrix and the observation matrix They have the following forms: , , ； Constructing a rolling optimization control problem using the reference instruction to be tracked, a high-dimensional state space model of the piezoelectric nanopositioning system, and a state; According to the preset prediction time domain and control time domain, the rolling optimization control problem is solved using the quadratic programming method to obtain the optimal control input of the piezoelectric nanopositioning system to enable the piezoelectric nanopositioning system to track the given reference instruction.

2. The piezoelectric nanopositioning system control method based on rolling optimization according to claim 1, characterized in that: The construction rolling optimization control problem includes: Given the reference trajectory of the piezoelectric nanopositioning system , , prediction time domain , control time domain , , the upper limit of the electric displacement output of the piezoelectric nanopositioning system , lower limit ,The upper limit of the control input of the piezoelectric nanopositioning system , lower limit ,Based on the state space model of the piezoelectric nanopositioning system, the following rolling optimization control problem is constructed: satisfy: ， In the above rolling optimization control problem, and Respectively expressed in Always predict ahead The state and electric displacement output of the piezoelectric nanopositioning system are Indicates Always predict ahead Step-by-step piezoelectric nanopositioning system control input, Indicates Always predict ahead The reference trajectory of the piezoelectric nanopositioning system is express Always predict ahead The control input sequence of the step, express and The difference, Represents the penalty coefficient of the control input; step signal and sine signal are used as reference trajectory A simulation experiment is carried out, in which the step signal adopts a signal group with different amplitudes.

3. The piezoelectric nanopositioning system control method based on rolling optimization according to claim 2, characterized in that: Based on the above mentioned rolling optimization control problem, the following constraints are defined: , , , ; The constraints of the above rolling optimization control problem give rise to the following compact prediction model for the piezoelectric nanopositioning system: in, ， , , 。 4. The piezoelectric nanopositioning system control method based on rolling optimization according to claim 3, characterized in that: The method of solving the rolling optimization control problem using a quadratic programming method according to the preset prediction time domain and control time domain to obtain the optimal control input of the piezoelectric nanopositioning system includes: According to the above state model of the piezoelectric nanopositioning system, the rolling optimization control problem is transformed into the following quadratic programming problem: satisfy: , in, Represents the optimal solution to the above problem, the weight matrix , weight vector , offset , coefficient matrix and boundary vectors They have the following forms: ， , , , ， also, Represents the identity matrix.

5. The piezoelectric nanopositioning system control method based on rolling optimization according to claim 4, characterized in that: Construct the dual problem of the quadratic programming problem: satisfy: Among them, the weight matrix and weight vector They have the following forms: , 。 6. The piezoelectric nanopositioning system control method based on rolling optimization according to claim 5, characterized in that: The method of implementing the tracking of a given reference instruction by the piezoelectric nanopositioning system includes: Let the current moment be , and make the piezoelectric nanopositioning system track the given reference trajectory , , and go to step (7-1); (7-1) In At this moment, obtain the status of the piezoelectric nanopositioning system and the control input at the previous moment , from which the matrices in steps (5) and (6) are calculated and vector 、 、 , and calculate the matrix , given the number of iterations , and let the current iteration count , given a vector The initial value is length The zero vector of The initial value is length The zero vector of the embodiment of the present invention is the number of iterations , go to step (7-2); (7-2) Yes Make a judgment, if Then go to step (7-2), otherwise go to step (7-5); (7-3) Let the counting variable , and Make a judgment, if , then go to step (7-4), otherwise use the coordinate descent method to solve the dual problem in step (6), let the vector Representation matrix No. Row, vector Representation matrix No. Column, scalar Represents the weight vector No. elements, vector Representation matrix No. Row, scalar Represents a vector No. elements, scalar ,and: Pair Vector No. Elements Make the following updates: Pair Vector Make the following updates: make And go back to step (7-2); (7-4) Command , , go to step (7-2); (7-5) Let the optimal control input be , and The first component of is applied to the piezoelectric nanopositioning system in step (2), and the piezoelectric nanopositioning system performs corresponding movement to the next moment; (7-6) Command , and then return to step (7-1) to realize the piezoelectric nanopositioning system for a given reference trajectory , tracking.

7. A control device for implementing the piezoelectric nanopositioning system control method based on rolling optimization according to any one of claims 1 to 6, characterized in that: include: A sampling module is used to obtain the state of the piezoelectric nanopositioning system at each sampling moment; A high-dimensional state-space model generation module for piezoelectric nanopositioning systems, used to identify high-order transfer function models of piezoelectric nanopositioning systems and further construct a high-dimensional state-space model of the piezoelectric nanopositioning system; The piezoelectric nanopositioning system control input generation module is used to construct a rolling optimization control problem based on a given reference instruction, a high-dimensional state space model of the piezoelectric nanopositioning system, and the current state. The rolling optimization problem is further transformed into a multi-parameter quadratic programming problem to accelerate the online calculation of the optimal control input of the piezoelectric nanopositioning system, and ultimately enable the piezoelectric nanopositioning system to track the given reference instruction.

8. An electronic device, characterized in that: include: at least one processor; and a memory communicatively coupled to the at least one processor; The memory stores instructions that can be executed by the at least one processor, and the instructions are configured to execute a piezoelectric nanopositioning system control method based on rolling optimization as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the piezoelectric nanopositioning system control method based on rolling optimization as described in any one of claims 1-6.

Images