Time delay control method and system based on error compensation type extended state observer

Abstract

The application discloses a time delay control method and system based on an error compensation type extended state observer, which comprises the following steps: a time delay controller acquires input signals and each output state of a tracking differentiator, and outputs a first control signal; an estimation error model of a displacement is constructed for an extended state observer; based on the first control signal, a total disturbance signal and an estimation error of the extended state observer, a controlled object is converted into an integrator series type form, and a displacement signal is output based on the controlled object; the displacement signal is input into the tracking differentiator to obtain real-time estimation values of each state of a nano-positioning stage; and the real-time estimation values of each state are fed back to the time delay controller. By introducing the extended state observer, the application solves the problem that the stability of a control system is easily affected by the uncertainty of a control input matrix; by introducing the tracking differentiator, the application solves the difficult problem that high-order system states and their derivatives required by time delay control are not easy to obtain.

Description

Technical Field

[0001] This invention relates to the field of control technology, and in particular to a time delay control method and system based on an error-compensated extended state observer. Background Technology

[0002] Nanostages are core components in precision engineering, playing a crucial role in micro / nano manufacturing, micro / nano robotics, and precision servo systems. Piezoelectric ceramic actuators, with their advantages of high output, high resolution, and fast response, are ideal for driving the motion of nanostages. However, the inherent hysteresis and creep nonlinearity of piezoelectric materials severely affect positioning accuracy. Furthermore, the low damping characteristics of the platform itself make it easy to excite low-order resonant modes of the nanostage, leading to mechanical resonance. Moreover, the coupling of hysteresis and mechanical resonance at high frequencies further reduces positioning accuracy. These problems significantly hinder the improvement of nanostage performance.

[0003] Time-delay-based disturbance compensation methods have been widely applied in industrial systems, but are limited to low-order systems such as motors. This is because time-delay control requires complete knowledge of the system state and its derivative at the previous sampling time, while traditional numerical differentiation methods, due to the introduction of significant noise, struggle to meet the requirements of time-delay control for high-order systems. Furthermore, time-delay control is highly sensitive to the uncertainty of the control input matrix; when the uncertainty is large, the time-delay control system is prone to divergence. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a time delay control method and system based on an error-compensated extended state observer.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] A time-delay control method based on an error-compensated extended state observer includes the following steps:

[0007] The time delay controller acquires the input signal and tracks the various output states of the differentiator, and outputs the first control signal;

[0008] An estimation error model of the output displacement by the extended state observer is constructed. Based on the first control signal, the total disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type, and the output displacement signal is based on the controlled object.

[0009] The displacement signal is input into the tracking differentiator to obtain real-time estimates of each state of the nano-positioning stage;

[0010] The real-time estimates of each state are fed back to the delay controller.

[0011] As one possible implementation, constructing the displacement estimation error model for the extended state observer includes the following steps:

[0012] Acquire the first control signal and total disturbance information to determine the output displacement of the nano-positioning stage;

[0013] Based on the output displacement, system order, and third control signal, a corresponding extended state observer is constructed, and the relevant parameters and bandwidth of the extended state observer are obtained.

[0014] The output displacement of the nanostage is combined with the first estimated state of the extended state observer to obtain the estimation error of the extended state observer about the first state.

[0015] The first state estimation error is combined with the first control signal to obtain the second control signal;

[0016] The second control signal is combined with the full disturbance signal to obtain the third control signal;

[0017] By performing a Laplace transform on the error equations of the extended state observer with respect to all states, a frequency domain expression for the estimation error of the extended state observer with respect to the first state is obtained.

[0018] As one possible implementation, the state-space model of the nanopositioning stage is represented as follows:

[0019] in, This represents the known part of the state-space model. Represents the control signal distribution matrix. Let represent the total disturbance information, C represent the system output matrix, y represent the system output displacement, u represent the time delay controller output, f represent the unknown disturbance information, and n represent the system order.

[0020] As one possible implementation, the actual state of the system is defined as the output displacement and its derivatives, expressed as x1 = y,...,x n =y (n-1) ,x n+1 =f

[0021] The corresponding extended state observer is represented as:

[0022]

[0023] Among them, z i (i = 1...n+1) represent the output states of the extended state observer. ω represents the parameters of the extended state observer. oThis represents the bandwidth of the extended state observer, where u represents the first control signal, and when ω o When the output states of the extended state observer approach the preset threshold, they approximate the actual states of the linear active disturbance rejection controller, i.e., z i →x i (i = 1...n).

[0024] As one possible implementation, assume the first control signal is represented as:

[0025]

[0026] The first output displacement is obtained by combining the output displacement model, and the first output displacement is expressed as:

[0027]

[0028] The error of the first extended state observer corresponding to the output displacement is expressed as:

[0029]

[0030] Applying a Laplace transform to the first-state estimation error of the extended state observer yields the observation error of the extended state observer:

[0031] Where E1(s) and D1(s) are the Laplace transforms of e1 and d1, respectively, l n e1 is a low-frequency approximation of the residual perturbation d1.

[0032] As one possible implementation, if the perturbation value at the previous sampling time is used as the estimated perturbation value at the current time, then:

[0033]

[0034] Where t represents the current time and L represents a sampling period;

[0035] The mathematical model of the nanostation including the extended state observer is expressed as follows:

[0036]

[0037] Where x represents the system state after introducing the error-type extended state observer, This represents the system matrix of the state-space model at this point; This indicates the input distribution matrix at this point; d r This indicates residual disturbances that were not completely eliminated;

[0038] Therefore, the control law model given by time delay control is:

[0039]

[0040] Among them, B + = (B T B) -1 B T A m and B m Let be the system matrix and input matrix of the desired model, respectively, and r be the desired trajectory;

[0041] t represents the current time, L represents the sampling time interval, x represents the system state after introducing the error-type extended state observer, and B + This represents the pseudo-inverse matrix of B;

[0042] The state-space model of the tracking differentiator is represented as follows:

[0043]

[0044] in, The system matrix represents the tracking differentiator. v represents the input distribution matrix of the tracking differentiator. T =[v1...v n ] 1×n ω represents the state vector of the differentiator; y represents the output displacement of the nanostage; ω represents the output displacement of the nanostage. td This indicates the bandwidth of the tracking differentiator.

[0045] As one possible implementation method, the controlled object is represented as follows:

[0046]

[0047] Where B+ represents the pseudo-inverse matrix of B, t represents the current time, L represents the sampling time interval, x represents the system state after introducing the error state observer, A represents the system matrix after introducing the error state observer, B represents the control input distribution matrix after introducing the error state observer, v represents the estimated value of each state by the tracking differentiator, u represents the control input signal, and A m and B m Let be the system matrix and input matrix of the desired model, respectively, and r be the desired trajectory.

[0048] A time-delay control system based on an error-compensated extended state observer includes a first module, a second module, a third module, and a fourth module;

[0049] The first module is configured to: acquire the input signal and track the various output states of the differentiator, and output the first control signal;

[0050] The second module is used to construct an estimation error model of the extended state observer for the output displacement. Based on the first control signal, the total disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into an integrator series form, and the output displacement signal is based on the controlled object.

[0051] The third module is used to input the displacement signal into the tracking differentiator to obtain real-time estimates of each state of the nanopositioning stage.

[0052] The fourth module is used to feed back the real-time estimates of each state to the delay controller.

[0053] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0054] A time delay control device based on an error-compensated extended state observer includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the method described above.

[0055] This invention, by adopting the above technical solutions, has significant technical effects:

[0056] This invention solves the problem that the stability of the control system is easily affected by the uncertainty of the control input matrix by introducing an error-compensated extended state observer;

[0057] By introducing a tracking differentiator, the problem of obtaining the high-order system state and its derivative required for time delay control is solved. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart of the overall method of the present invention;

[0060] Figure 2 This is a schematic diagram illustrating the construction process of the extended state observer;

[0061] Figure 3 This is a schematic diagram of the extended state observer;

[0062] Figure 4 This is a schematic diagram of time delay control based on an extended state observer;

[0063] Figure 5 This is a diagram comparing the performance of different control schemes;

[0064] Figure 6 This is a structural block diagram provided in this application;

[0065] Figure 7 This is a schematic diagram of the system of the present invention;

[0066] Figure 8 This application provides a schematic diagram of an electronic device structure. Detailed Implementation

[0067] The present invention will be further described in detail below with reference to the embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following embodiments.

[0068] A time-delay control method based on an error-compensated extended state observer, such as Figure 1 As shown, it includes the following steps:

[0069] S100: The time delay controller acquires the input signal and tracks the various output states of the differentiator, and outputs the first control signal;

[0070] S200. Construct an estimation error model of the output displacement for the extended state observer. Based on the first control signal, the total disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type, and the output displacement signal is based on the controlled object.

[0071] S300. Input the displacement signal into the tracking differentiator to obtain the real-time estimated values ​​of each state of the nano-positioning stage;

[0072] S400, Feed back the real-time estimated values ​​of each state to the delay controller.

[0073] In one embodiment, an estimation error model for displacement by an extended state observer is constructed, such as... Figure 2 As shown, it includes the following steps:

[0074] S210. Obtain the first control signal and full disturbance information, and determine the output displacement of the nano-positioning stage;

[0075] S220. Based on the output displacement, system order, and third control signal, construct the corresponding extended state observer and obtain the relevant parameters and bandwidth of the extended state observer.

[0076] S230. Combine the output displacement of the nano-positioning stage with the first estimated state of the extended state observer to obtain the estimation error of the extended state observer about the first state.

[0077] S240. Combine the first state estimation error with the first control signal to obtain the second control signal;

[0078] S250. Combine the second control signal with the full disturbance signal to obtain the third control signal;

[0079] S260. Perform a Laplace transform on the error equations of the extended state observer with respect to all states to obtain the frequency domain expression of the estimation error of the extended state observer with respect to the first state.

[0080] The state-space model of the nanopositioning stage is represented as follows:

[0081] in, This represents the known part of the state-space model. Represents the control signal distribution matrix. Let represent the total disturbance information, C represent the system output matrix, y represent the system output displacement, u represent the time delay controller output, f represent the unknown disturbance information, and n represent the system order.

[0082] y represents the system output displacement, u is the controller output, and for the nanostation parameter b, it represents the estimated value of the control signal gain, which is a known quantity. Define the system state x. p The output is the displacement and its derivatives, i.e.: x p,1 =y,...,x p,n =y (n-1) Let the augmented state x p,n+1 If f = , then the extended state observer for this system is:

[0083]

[0084] Among them, z i (i = 1...n+1) represents the states of the observer, and the parameters of the observer... ω o This represents the bandwidth of the extended state observer.

[0085] Set the control input as follows:

[0086]

[0087] Substituting into formula (1), then

[0088]

[0089] At this point, the error of the extended state observer is:

[0090]

[0091] Therefore, we can conclude that:

[0092]

[0093] Taking the Laplace transform of equation (6), we get:

[0094]

[0095] Formula (7) Explanation l n e1 is a low-frequency approximation of the residual perturbation d1. Therefore, l n Feeding e1 back to the input can significantly improve the estimation capability of traditional extended state observers. The specific structure is as follows: Figure 3 As shown.

[0096] Figure 3 The mathematical model of the nanostation with an error-type extended state observer can be expressed as:

[0097]

[0098] in

[0099] This represents the system matrix of the state-space model at this point;

[0100] This indicates that the input distribution matrix is ​​being used at this point;

[0101] d r This indicates residual disturbances that were not completely eliminated;

[0102] Due to the introduction of the extended state observer, B in the state-space model (1) p The uncertainty of the matrix is ​​almost completely eliminated, and it is included in d in formula (9). r middle.

[0103] The core of time delay control lies in using the disturbance value at the previous sampling time as an estimate of the disturbance at the current time, that is:

[0104]

[0105] Where t represents the current time and L represents a sampling period. The control law given by the time delay control is:

[0106]

[0107] Among them B + = (B T B) -1 B T A m and B m Let be the system matrix and input matrix of the desired model, respectively, and r be the desired trajectory.

[0108] To obtain the states and their derivatives in the control law (11), a tracking differentiator is introduced, whose state-space model is expressed as:

[0109]

[0110] in:

[0111] The system matrix represents the tracking differentiator;

[0112] This represents the input distribution matrix of the tracking differentiator;

[0113] v T =[v1...v n ] 1×n , represents the state vector of the differentiator; y represents the output displacement of the nanostation.

[0114] Where ω td This represents the bandwidth of the tracking differentiator. After obtaining estimates of each system state using the tracking differentiator, the control input can be rewritten as:

[0115]

[0116] This control input is used as the input to the observer tracking the expanded state of the differentiator. A schematic diagram of the overall structure can be found in the appendix. Figure 4 As shown.

[0117] Time-delay control was designed based on an error-compensated extended state observer and applied to trajectory tracking of a nanostation. The nanostation has a resonant frequency of 100Hz, a damping ratio of 0.02, an ESO bandwidth of 200Hz, a control bandwidth of 100Hz, and a tracking differentiator bandwidth of 1kHz. Figure 5 As shown in the figure, the dotted line represents the reference signal of the input system, the dashed line represents the control result using active disturbance rejection control combined with an error-compensated extended state observer, and the solid line represents the triangular wave tracking result using time delay control combined with an error-compensated extended state observer. A comparison of the two shows that, when the observer bandwidth and control bandwidth are exactly the same, the time delay control scheme of the nanostation proposed in this invention is significantly superior to the active disturbance rejection control scheme.

[0118] Example 2:

[0119] A time-delay control system based on an error-compensated extended state observer, such as Figure 7 As shown, it includes a first module 100, a second module 200, a third module 300, and a fourth module 400;

[0120] The first module 100 is configured to: acquire the input signal and track the various output states of the differentiator, and output the first control signal;

[0121] The second module 200 is used to construct an estimation error model of the extended state observer for the output displacement. Based on the first control signal, the total disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into an integrator series form, and the output displacement signal is based on the controlled object.

[0122] The third module 300 is used to input the displacement signal into the tracking differentiator to obtain real-time estimates of each state of the nano-positioning stage.

[0123] The fourth module 400 is used to feed back the real-time estimated values ​​of each state to the delay controller.

[0124] Based on the same inventive concept, this application also provides an electronic device that can realize the aforementioned time delay control function based on an error-compensated extended state observer. The electronic device includes:

[0125] At least one processor and a memory 82 connected to at least one processor 81. In this embodiment, the specific connection medium between the processor 81 and the memory 82 is not limited. Figure 8 The example shown is the connection between processor 81 and memory 82 via bus 80. Bus 80 is... Figure 8 The connections between other components are indicated by thick lines and are for illustrative purposes only, not as limiting information. Bus 80 can be divided into address bus, data bus, control bus, etc., for ease of representation. Figure 8 The term is represented by a single thick line, but this does not imply that there is only one bus or one type of bus. Alternatively, the processor 81 can also be called a controller; there is no restriction on the name.

[0126] In this embodiment, memory 82 stores instructions executable by at least one processor 81. By executing the instructions stored in memory 82, at least one processor 81 can perform the EGR control method described above. Processor 81 can implement... Figure 7 The functions of each module in the device shown.

[0127] The processor 81 is the control center of the device. It can connect to various parts of the control device through various interfaces and lines. By running or executing instructions stored in memory 82 and calling data stored in memory 82, the processor can perform various functions and process data, thereby monitoring the device as a whole.

[0128] In one possible design, processor 81 may include one or more processing units. Processor 81 may integrate an application processor and a modem processor, wherein the application processor mainly handles the operating system, user interface, and applications, and the modem processor mainly handles wireless communication. It is understood that the modem processor may also not be integrated into processor 81. In some embodiments, processor 81 and memory 82 may be implemented on the same chip; in some embodiments, they may also be implemented on separate chips.

[0129] Processor 81 can be a general-purpose processor, such as a central processing unit (CPU), digital signal processor, application-specific integrated circuit, field-programmable gate array or other programmable logic device, discrete gate or transistor logic device, or discrete hardware component, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the EGR control method disclosed in the embodiments of this application can be directly manifested as being executed by a hardware processor, or executed by a combination of hardware and software modules within the processor.

[0130] Memory 82, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. Memory 82 may include at least one type of storage medium, such as flash memory, hard disk, multimedia card, card-type memory, random access memory (RAM), static random access memory (SRAM), programmable read-only memory (PROM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), magnetic storage, magnetic disk, optical disk, etc. Memory 82 can be any other medium capable of carrying or storing desired program code in the form of instructions or data structures that can be accessed by a computer, but is not limited thereto. In the embodiments of this application, memory 82 can also be a circuit or any other device capable of implementing storage functions for storing program instructions and / or data.

[0131] By designing and programming the processor 81, the code corresponding to the EGR control method described in the foregoing embodiments can be embedded into the chip, enabling the chip to execute the code during operation. Figure 4The steps of the EGR control method in the illustrated embodiment are as follows. How to design and program the processor 81 is a technique well-known to those skilled in the art and will not be described further here.

[0132] Based on the same inventive concept, embodiments of this application also provide a storage medium storing computer instructions that, when executed on a computer, cause the computer to perform the EGR control method described above.

[0133] In some possible implementations, various aspects of the EGR control method provided in this application may also be implemented as a program product comprising program code that, when the program product is run on a device, causes the control device to perform the steps in the EGR control method according to the various exemplary embodiments of this application described above.

[0134] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0135] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0136] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0137] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0138] Furthermore, it should be noted that the shapes and names of the parts and components described in the specific embodiments described in this specification may differ. All equivalent or simple variations made to the structure, features, and principles described in this patent concept are included within the protection scope of this patent. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to replace them, as long as they do not depart from the structure of this invention or exceed the scope defined in these claims, they should all fall within the protection scope of this invention.

Claims

1. A time-delay control method based on an error-compensated extended state observer, characterized in that, Includes the following steps: The time delay controller acquires the input signal and tracks the various output states of the differentiator, and outputs the first control signal; Acquire the first control signal and the full disturbance signal to determine the output displacement of the nanopositioning stage; Based on the output displacement, system order, and third control signal, a corresponding extended state observer is constructed, and the relevant parameters and bandwidth of the extended state observer are obtained. The output displacement of the nanostation is combined with the first estimated state of the extended state observer to obtain the estimation error of the extended state observer about the first state. The first state estimation error is combined with the first control signal to obtain the second control signal; The second control signal is combined with the full disturbance signal to obtain the third control signal; By performing a Laplace transform on the error equations of the extended state observer with respect to all states, a frequency domain expression for the estimation error of the extended state observer with respect to the first state is obtained, and an estimation error model of the extended state observer for the output displacement is constructed. Based on the estimation error of the first control signal, the full disturbance signal and the extended state observer, the controlled object is transformed into an integrator series form, and a displacement signal is output based on the controlled object; The displacement signal is input into the tracking differentiator to obtain real-time estimates of each state of the nanopositioning stage; The real-time estimates of each state are fed back to the delay controller; The state-space model of the nanopositioning stage is represented as follows: in, This represents the known part of the state-space model. Represents the control signal distribution matrix. This represents the full perturbation information. C Represents the system's output matrix. y Indicates the system output displacement. u This indicates the output of the delay controller. ƒ This indicates unknown disturbance information. n Indicates the system order; Regarding the parameters of the nanopositioning stage b The estimated value of the control signal gain is a known quantity, defining the system state. x p The output displacement and its derivatives are, i.e. , to enhance the state The corresponding extended state observer is represented as: in, For each output state of the extended state observer, The parameters represent the extended state observer. ω o This represents the bandwidth of the extended state observer. u Indicates the first control signal, when ω o When the output states of the extended state observer approach the preset threshold, they closely approximate the actual states of the linear active disturbance rejection controller. ; Assume the first control signal is represented as: The first output displacement is obtained by combining the output displacement model, and the first output displacement is expressed as: The error of the first extended state observer corresponding to the output displacement is expressed as: Applying a Laplace transform to the first-state estimation error of the extended state observer yields the observation error of the extended state observer: in, E 1( s )and D 1( s They are respectively e 1 and d Laplace transform of 1, l n e 1 is the residual disturbance d The low-frequency approximation of 1; The mathematical model of the nanostation with an error-type extended state observer can be expressed as: in, x This indicates the system state after introducing an error-type extended state observer. ， This represents the system matrix of the state-space model at this point; This indicates that the input distribution matrix is ​​being used at this point; d r This indicates residual disturbances that were not completely eliminated; If the time delay control uses the disturbance value from the previous sampling time as the disturbance estimate for the current time, then: in, t Indicates the current moment. L Indicates a sampling period; The control law model given by time delay control is: in, , and These are the system matrix and input matrix of the desired model, respectively. r For the desired trajectory, t Indicates the current moment. L Indicates the sampling time interval. x This represents the system state after introducing an error-type extended state observer. express The pseudo-inverse matrix; To obtain the states and their derivatives in the control law model, a tracking differentiator is introduced. The state-space model of the tracking differentiator is expressed as: in, The system matrix represents the tracking differentiator. This represents the input distribution matrix of the tracking differentiator. This represents the state vector of the differentiator; y This indicates the output displacement of the nanostage. ω td Indicates the bandwidth of the tracking differentiator; After obtaining the estimated values ​​of each state of the system using the aforementioned tracking differentiator, the controlled object is represented as follows: in, express The pseudo-inverse matrix, t Indicates the current moment. L Indicates the sampling time interval. x This represents the system state after introducing the error state observer. A This represents the system matrix after introducing the error state observer. B This represents the control input distribution matrix after introducing the error state observer. v This represents the estimated value of the tracking differentiator for each state. u Indicates the control input signal. and These are the system matrix and input matrix of the desired model, respectively. r The desired trajectory.

2. A time-delay control system based on an error-compensated extended state observer, characterized in that, It includes Module 1, Module 2, Module 3, and Module 4; The first module is configured to: acquire the input signal and track the various output states of the differentiator, and output the first control signal; The second module is used to acquire the first control signal and the full disturbance signal to determine the output displacement of the nano-positioning stage; Based on the output displacement, system order, and third control signal, a corresponding extended state observer is constructed, and the relevant parameters and bandwidth of the extended state observer are obtained. The output displacement of the nanostation is combined with the first estimated state of the extended state observer to obtain the estimation error of the extended state observer about the first state. The first state estimation error is combined with the first control signal to obtain the second control signal; The second control signal is combined with the full disturbance signal to obtain the third control signal; By performing a Laplace transform on the error equations of the extended state observer with respect to all states, a frequency domain expression for the estimation error of the extended state observer with respect to the first state is obtained, and an estimation error model of the extended state observer for the output displacement is constructed. Based on the estimation error of the first control signal, the full disturbance signal and the extended state observer, the controlled object is transformed into an integrator series form, and a displacement signal is output based on the controlled object; The third module is used to input the displacement signal into the tracking differentiator to obtain real-time estimates of each state of the nanopositioning stage. The fourth module is used to feed back the real-time estimated values ​​of each state to the delay controller; The state-space model of the nanopositioning stage is represented as follows: in, This represents the known part of the state-space model. Represents the control signal distribution matrix. This represents the full perturbation information. C Represents the system's output matrix. y Indicates the system output displacement. u This indicates the output of the delay controller. ƒ This indicates unknown disturbance information. n Indicates the system order; Regarding the parameters of the nanopositioning stage b The estimated value of the control signal gain is a known quantity, defining the system state. x p The output displacement and its derivatives are, i.e. , to enhance the state The corresponding extended state observer is represented as: in, For each output state of the extended state observer, The parameters represent the extended state observer. ω o This represents the bandwidth of the extended state observer. u Indicates the first control signal, when ω o When the output states of the extended state observer approach the preset threshold, they closely approximate the actual states of the linear active disturbance rejection controller. ; Assume the first control signal is represented as: The first output displacement is obtained by combining the output displacement model, and the first output displacement is expressed as: The error of the first extended state observer corresponding to the output displacement is expressed as: Applying a Laplace transform to the first-state estimation error of the extended state observer yields the observation error of the extended state observer: in, E 1( s )and D 1( s They are respectively e 1 and d Laplace transform of 1, l n e 1 is the residual disturbance d The low-frequency approximation of 1; The mathematical model of the nanostation with an error-type extended state observer can be expressed as: in, x This indicates the system state after introducing an error-type extended state observer. ， This represents the system matrix of the state-space model at this point; This indicates that the input distribution matrix is ​​being used at this point; d r This indicates residual disturbances that were not completely eliminated; If the time delay control uses the disturbance value from the previous sampling time as the disturbance estimate for the current time, then: in, t Indicates the current moment. L Indicates a sampling period; The control law model given by time delay control is: in, , and These are the system matrix and input matrix of the desired model, respectively. r For the desired trajectory, t Indicates the current moment. L Indicates the sampling time interval. x This represents the system state after introducing an error-type extended state observer. express The pseudo-inverse matrix; To obtain the states and their derivatives in the control law model, a tracking differentiator is introduced. The state-space model of the tracking differentiator is expressed as: in, The system matrix represents the tracking differentiator. This represents the input distribution matrix of the tracking differentiator. This represents the state vector of the differentiator; y This indicates the output displacement of the nanostage. ω td Indicates the bandwidth of the tracking differentiator; After obtaining the estimated values ​​of each state of the system using the aforementioned tracking differentiator, the controlled object is represented as follows: in, express The pseudo-inverse matrix, t Indicates the current moment. L Indicates the sampling time interval. x This represents the system state after introducing the error state observer. A This represents the system matrix after introducing the error state observer. B This represents the control input distribution matrix after introducing the error state observer. v This represents the estimated value of the tracking differentiator for each state. u Indicates the control input signal. and These are the system matrix and input matrix of the desired model, respectively. r The desired trajectory.

3. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in claim 1.

4. A time delay control device based on an error-compensated extended state observer, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in claim 1.

Images