Automatic parameter tuning method for controllers based on differential evolution algorithm

Abstract

This disclosure provides an automatic parameter tuning method for a controller based on a differential evolution algorithm, comprising: before starting an ultra-precision motion system, determining a first optimization objective for the controller of the ultra-precision motion system under the current application environment; optimizing the controller's control parameters based on an offline differential evolution algorithm according to the first optimization objective, so that the controller controls the ultra-precision motion system based on the control parameters; when the application environment changes or the control effect degrades, determining a second optimization objective for the controller; and optimizing the controller's control parameters based on an online differential evolution algorithm according to the second optimization objective, so that the controller adjusts the ultra-precision motion system based on the control parameters, wherein the initial population of the online differential evolution algorithm is the elite population obtained after optimization by the offline differential evolution algorithm. This method can improve the parameter tuning efficiency and accuracy of precision equipment.

Description

Technical Field

[0001] This disclosure relates to the field of ultra-precision motion control technology, and in particular to an automatic parameter tuning method for controllers based on differential evolution algorithm. Background Technology

[0002] Ultra-precision motion systems are a crucial component of precision manufacturing and processing equipment, with significant applications in aerospace, laser technology, and the semiconductor industry. To ensure high productivity and precision in precision equipment, the controller must not only rapidly converge the tracking error of the controlled object to the nanometer or even sub-nanometer level after high acceleration and deceleration, but also maintain high precision under various complex operating conditions.

[0003] Currently, the control method for ultra-precision motion systems in engineering typically employs classic PID control, with control parameters manually tuned. However, manual tuning has the following problems: First, this method requires a significant amount of time for online trial and error, leading to reduced efficiency of the motion system and consequently affecting equipment productivity. Second, this method lacks adaptive parameter tuning capabilities; when the equipment operates for extended periods or the operating environment changes, it is usually necessary to readjust the control parameters according to the current operating conditions to meet the high precision requirements of ultra-precision equipment. Summary of the Invention

[0004] In view of the above problems, the present invention provides an automatic parameter tuning method for controllers based on differential evolution algorithm to solve the above technical problems.

[0005] One aspect of this disclosure provides an automatic parameter tuning method for a controller based on a differential evolution algorithm, comprising: before starting an ultra-precision motion system, determining a first optimization objective for the controller of the ultra-precision motion system under the current application environment, the first optimization objective including multiple sub-performance evaluation indicators of the ultra-precision motion system; optimizing the control parameters of the controller based on an offline differential evolution algorithm according to the first optimization objective, so that the controller controls the ultra-precision motion system based on the control parameters; when the application environment changes or the control effect degrades, determining a second optimization objective for the controller, the second optimization objective including one of the sub-performance indicators of the first optimization objective; optimizing the control parameters of the controller based on an online differential evolution algorithm according to the second optimization objective, so that the controller adjusts the ultra-precision motion system based on the control parameters, wherein the initial population of the online differential evolution algorithm is an elite population obtained after optimization by the offline differential evolution algorithm.

[0006] Optionally, optimizing the controller's control parameters based on an offline differential evolution algorithm according to the first optimization objective, so that the controller controls the ultra-precision motion system based on the control parameters, includes: generating an initial population for the offline differential evolution algorithm; selecting at least one individual from the initial population to generate the elite population, wherein at least one sub-performance index of the at least one individual is the smallest in the initial population; performing a non-repeating roulette wheel selection on the individuals in the initial population according to each sub-performance evaluation index, selecting a preset number of individuals for each sub-performance evaluation index to form a first evolutionary population; performing a mutation operation on the individuals in the first evolutionary population, and selecting individuals from the first evolutionary population and the elite population for a crossover operation to obtain a first crossover population; selecting a dominant individual or an individual with greater crowding from the first crossover population, and selecting the individual with greater crowding to update the corresponding individuals in the first evolutionary population and the elite population; iteratively updating the first evolutionary population and the elite population until the iteration ends, selecting the optimal individual from the elite population, and applying the control parameters corresponding to the optimal individual to control the ultra-precision motion system.

[0007] Optionally, generating the initial population for the offline differential evolution algorithm includes: substituting individuals from the initial population as control parameters into the controller and evaluating the stability index of the ultra-precision motion system; when the stability index of an individual is unqualified, generating a new individual to replace it.

[0008] Optionally, the step of selecting a dominant individual or an individual with greater crowding from the first crossover population to update the corresponding individuals in the first evolutionary population and the elite population includes: randomly selecting two individuals from the first crossover population, and selecting a dominant individual from the two individuals to update the first evolutionary population, wherein the dominant individual is the individual among the two individuals whose sub-performance indicators are all better than the other individual; if the two individuals are not dominant to each other, selecting the individual with greater crowding to update the first evolutionary population and the elite population; the crowding is the sum of the distances to adjacent individuals in the normalized space after normalization of the sub-performance indicator function; after each update of the first evolutionary population, deleting the individual that updated the first evolutionary population from the first crossover population; repeating the above steps until the first evolutionary population is completely updated; selecting the individual with the smallest sub-performance indicators from the updated first evolutionary population to add to the elite population, and updating the elite population.

[0009] Optionally, the step of selecting the optimal individual from the generated elite population and applying the control parameters corresponding to the optimal individual to control the ultra-precision motion system includes: normalizing all individuals in the elite population as parameter vectors; selecting the individual with the smallest distance between the normalized parameter vector and the zero vector as the optimal individual; and applying the control parameters corresponding to the optimal individual to control the ultra-precision motion system.

[0010] Optionally, optimizing the control parameters of the controller based on an online differential evolution algorithm according to the second optimization objective, so that the controller adjusts the ultra-precision motion system based on the control parameters, includes: initializing a second evolutionary population; when the number of individuals in the elite population does not meet the preset number of individuals in the second evolutionary population, performing Gaussian distribution expansion or random subtraction operations on the elite population to bring the second evolutionary population to the preset number of individuals; selecting M individuals with the smallest sub-performance index corresponding to the second optimization objective from the second evolutionary population and adding them to the elite population; performing mutation operations on the individuals in the second evolutionary population and crossover operations with the individuals in the elite population to obtain a second crossover population; selecting dominant individuals from the second crossover population to update the corresponding individuals in the second evolutionary population and the elite population; iteratively updating the second evolutionary population and the elite population; stopping the iteration when the second optimization objective is reached; selecting the optimal individual from the elite population and applying the control parameters corresponding to the optimal individual to control the ultra-precision motion system.

[0011] Optionally, the step of selecting a dominant individual from the second crossover population to update the individuals corresponding to the second evolutionary population and the elite population includes: randomly selecting two individuals from the second crossover population, and selecting a dominant individual from the two individuals to update the second evolutionary population, wherein the dominant individual is the individual among the two individuals whose sub-performance indicators are all better than the other individual; if the two individuals are not dominant to each other, randomly selecting one individual to update the second evolutionary population; after each update of the second evolutionary population, deleting the individual that updated the second evolutionary population from the second crossover population; repeating the above steps until the second evolutionary population is updated; and selecting the individual with the smallest sub-performance indicators from the updated second evolutionary population to add to the elite population, thereby updating the elite population.

[0012] Optionally, the method includes: when updating the elite population, determining whether the capacity of the elite population exceeds the rated capacity; if it exceeds the rated capacity, deleting the individual with the lowest crowding in the elite population.

[0013] Optionally, the first optimization objective includes:

[0014] minJ = {f1, f2, f3};

[0015]

[0016] Wherein, minJ represents the first optimization objective, f1, f2, and f3 represent sub-performance evaluation metrics, and t start t represents the start time of motion of the ultra-precision motion system in a single motion cycle. end Let represent the end time of motion of the ultra-precision motion system in a single motion cycle, and let e(t) represent the tracking error of the controller on the reference trajectory of the ultra-precision motion system during the motion process. t represents the rate of change of the control quantity during the motion of the ultra-precision motion system. settling This indicates the time it takes for the controller to converge the tracking error to within the threshold.

[0017] Optionally, the second optimization objective includes:

[0018]

[0019] Where min K represents the second optimization objective, t start t represents the start time of motion of the ultra-precision motion system in a single motion cycle. end The value represents the end time of motion of the ultra-precision motion system in a single motion cycle, and e(t) represents the tracking error of the controller on the reference trajectory of the ultra-precision motion system during the motion process.

[0020] The above-described at least one technical solution adopted in the embodiments of this disclosure can achieve the following beneficial effects:

[0021] This disclosure provides a method for self-tuning controller parameters for ultra-precision motion systems. Addressing the inefficiency of manual parameter tuning, it employs an offline differential evolution algorithm to tune the control parameters, automatically adjusting them according to a preset control objective, thereby improving tuning efficiency. Furthermore, addressing the issue that manually tuned control parameters cannot adaptively adjust to changes in the working environment, it uses an online fast differential evolution algorithm to tune the control parameters, enabling rapid adjustment of control parameters when the environment changes or control performance degrades, thus improving system efficiency. Attached Figure Description

[0022] To gain a more complete understanding of this disclosure and its advantages, reference will now be made to the following description taken in conjunction with the accompanying drawings, wherein:

[0023] Figure 1 This illustration schematically shows a control architecture diagram of an ultra-precision motion system provided in an embodiment of the present disclosure;

[0024] Figure 2The flowchart illustrates an automatic parameter tuning method for a controller based on the differential evolution algorithm provided in an embodiment of this disclosure.

[0025] Figure 3 The flowchart illustrating the automatic tuning of control parameters for the offline differential evolution algorithm in an embodiment of this disclosure is shown in the schematic diagram.

[0026] Figure 4 The flowchart illustrating the automatic tuning of control parameters for the online differential evolution algorithm in an embodiment of this disclosure is shown. Detailed Implementation

[0027] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0028] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0029] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0030] The accompanying drawings show some block diagrams and / or flowcharts. It should be understood that some blocks or combinations thereof in the block diagrams and / or flowcharts can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that when executed by the processor, these instructions can create means for implementing the functions / operations described in these block diagrams and / or flowcharts.

[0031] Therefore, the technology disclosed herein can be implemented in hardware and / or software (including firmware, microcode, etc.). Additionally, the technology disclosed herein can take the form of a computer program product stored on a computer-readable medium, which can be used by or in conjunction with an instruction execution system. In the context of this disclosure, a computer-readable medium can be any medium capable of containing, storing, transmitting, propagating, or transmitting instructions. For example, a computer-readable medium can include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, apparatuses, or propagation media. Specific examples of computer-readable media include: magnetic storage devices, such as magnetic tape or hard disk drives (HDDs); optical storage devices, such as optical discs (CD-ROMs); memory, such as random access memory (RAM) or flash memory; and / or wired / wireless communication links.

[0032] Figure 1 The schematic diagram illustrates a control architecture of an ultra-precision motion system provided in an embodiment of this disclosure.

[0033] like Figure 1 As shown, 001 is the trajectory planning system of the ultra-precision motion system, and its output is the reference trajectory of the motion system; 002 is the controller of the ultra-precision motion system; 003 is the controlled object of the ultra-precision motion system, i.e., the simplified mathematical model of the equipment; 004 is the position measuring device of the ultra-precision motion system, and its output is the actual position of the controlled object. The controller 002 generates control parameters based on the reference trajectory planned by the trajectory planning system 001, and controls the motion of the ultra-precision motion system 003; the position measuring device 004 monitors the position of the ultra-precision motion system 003 in real time and feeds back the measurement data to the controller 002; the controller 002 adjusts the control parameters based on the feedback information to converge the tracking error of the reference trajectory to within a threshold.

[0034] This disclosure provides an automatic parameter tuning method for a controller based on a differential evolution algorithm. The method presets the optimization target of the controller according to the current scenario and application requirements, and automatically tunes the control parameters using an offline differential algorithm. When the system application environment changes or the control effect degrades, the control parameters are quickly adjusted using an online differential evolution algorithm.

[0035] Figure 2 The flowchart illustrates an automatic parameter tuning method for a controller based on a differential evolution algorithm provided in an embodiment of this disclosure.

[0036] like Figure 2 As shown in the figure, the automatic parameter tuning method for a controller based on the differential evolution algorithm provided in this disclosure includes steps S210 to S240.

[0037] S210, before starting the ultra-precision motion system, determine the first optimization objective of the controller of the ultra-precision motion system under the current application environment. The first optimization objective includes multiple sub-performance evaluation indicators of the ultra-precision motion system.

[0038] In this embodiment, the first optimization objective includes:

[0039] minJ = {f1, f2, f3};

[0040]

[0041] Where minJ represents the first optimization objective, f1, f2, and f3 represent sub-performance evaluation metrics, and t start t represents the start time of motion of an ultra-precision motion system in a single motion cycle. end Let represent the end time of motion in a single motion cycle of the ultra-precision motion system, and e(t) represent the tracking error of the controller on the reference trajectory of the ultra-precision motion system during the motion process. t represents the rate of change of the control quantity during the motion of an ultra-precision motion system. settling This indicates the time it takes for the controller to converge the tracking error to within the threshold.

[0042] S220, based on the first optimization objective, optimizes the controller's control parameters using an offline differential evolution algorithm, enabling the controller to control the ultra-precision motion system based on the control parameters.

[0043] S230, when the application environment changes or the control effect degrades, determine the second optimization objective of the controller. The second optimization objective includes one of the sub-performance indicators of the first optimization objective.

[0044] In this embodiment, the second optimization objective includes:

[0045]

[0046] Where min K represents the second optimization objective, t start t represents the start time of motion of an ultra-precision motion system in a single motion cycle. end e(t) represents the end time of motion of the ultra-precision motion system in a single motion cycle, and e(t) represents the tracking error of the controller on the reference trajectory of the ultra-precision motion system during the motion process.

[0047] S240, based on the second optimization objective, optimize the control parameters of the controller using an online differential evolution algorithm, so that the controller adjusts the ultra-precision motion system based on the control parameters. The initial population of the online differential evolution algorithm is the elite population obtained after optimization by the offline differential evolution algorithm.

[0048] Figure 3The flowchart illustrating the automatic tuning of control parameters for the offline differential evolution algorithm in an embodiment of this disclosure is shown in the illustration.

[0049] like Figure 3 As shown in this embodiment, S220 optimizes the control parameters of the controller based on the offline differential evolution algorithm according to the first optimization objective, including S310 to S360.

[0050] S310 generates the initial population for the offline differential evolution algorithm.

[0051] In this embodiment, the population is initialized by randomly generating N0 individuals X within a given range of control parameters. i =[P i I i D i ]. Individual X from the initial population i The parameters are substituted into the controller, and the stability index of the ultra-precision motion system is evaluated. If the corresponding control system is unstable (the system is considered unstable when the control bandwidth is less than 50Hz or the phase margin is less than 30°), that is, when the stability index of the individual is unqualified, a new individual is generated to replace it.

[0052] S320, at least one individual is selected from the initial population to generate an elite population, wherein at least one sub-performance index of the at least one individual is the smallest in the initial population.

[0053] It should be noted that if an individual has two or more component function performance indicators that have reached the minimum value, this individual will only be selected once, and the selection will not be repeated.

[0054] S330, based on various performance evaluation indicators f j A roulette wheel selection process without repetition is performed on individuals in the initial population. For each sub-performance evaluation index f... j A predetermined number of individuals were selected to form the first evolutionary population.

[0055] Specifically, assuming the screening ratio is β, for each f i Filter out Each individual ultimately yields the population size participating in the differential evolution algorithm.

[0056] S340, perform mutation operations on individuals in the first evolutionary population, and select individuals from the first evolutionary population and the elite population for crossover operations to obtain the first crossover population.

[0057] In this process, adaptive mutation and adaptive crossover factors are added to individuals in the first evolutionary population. Individuals in the first evolutionary population are mutated, and an adaptive mutation strategy is used to mutate individuals in the populations participating in differential evolution. An adaptive crossover strategy is then used to perform crossover operations on the mutated population.

[0058] S350: Select dominant individuals or individuals with higher crowding from the first crossover population, and update the corresponding individuals in the first evolutionary population and the elite population.

[0059] S350 includes S351 to S355.

[0060] S351. Randomly select two individuals from the first crossover population, calculate the sub-performance indices of the two individuals, and select the dominant individual from the two individuals to update the first evolutionary population. The dominant individual is the individual among the two individuals whose sub-performance indices are better than the other individual.

[0061] S352, if two individuals are not dominant to each other, select the individual with the greater crowding to update the first evolutionary population. The crowding is the sum of the distances to the adjacent individuals in the normalized space after normalization of the performance index function.

[0062] S351~S352 can be represented as:

[0063]

[0064] Among them, X i，G+1 This represents the G+1 generation of individual i. Individual dominance means that the individual has better performance in all sub-indicators, max{dX} i，G，U dX i，G，V} represents the individual with greater crowding between individuals U and V in the first crossover population of generation G. Crowding degree d refers to the sum of distances to neighboring individuals in the normalized space after normalization of the performance index function.

[0065] S353: After each update of the first evolutionary population, the individuals that updated the first evolutionary population will be removed from the first crossover population.

[0066] S354, Repeat the above steps until the first evolutionary population is updated.

[0067] S355: Select individuals with the lowest performance indicators across all sub-indicators from the updated first evolutionary population and add them to the elite population, thus updating the elite population.

[0068] In this embodiment, when adding an individual to the elite population, it is necessary to determine whether the capacity of the elite population exceeds the rated capacity; if it exceeds the rated capacity, the individual with the lowest crowding in the elite population is deleted.

[0069] S360 iteratively updates the first evolutionary population and the elite population until the iteration ends. It selects the best individual from the elite population and applies the control parameters corresponding to the best individual to control the ultra-precision motion system.

[0070] When the algorithm ends, the elite population That is, the optimal solution set. (Yes / No) All individuals in the vector [P] are used as parameter vectors. i I i D i Normalize the vector and select the individual that is closest to the zero vector [0, 0, 0] after normalization as X. best The control parameters corresponding to the optimal individual are applied to control the ultra-precision motion system.

[0071] In this embodiment, according to S230, when the application environment changes or the control effect degrades, the controller needs to determine the controller's second optimization objective and re-optimize the control parameters. The change in environment is defined as: the system's reference trajectory (module 0001) changes, or the controller's tracking error e(t) in the operating range is greater than ε (ε is generally in the nanometer or even sub-nanometer range).

[0072] When the environment changes, the controller's optimization objective becomes... Where t start t represents the start time of motion in a single motion cycle. end e(t) represents the end time of motion in a single motion cycle; e(t) represents the tracking error of the controller on the reference trajectory during the motion process.

[0073] According to S240, in this embodiment, the control parameters are automatically tuned using an online differential evolution algorithm.

[0074] Figure 4 The flowchart illustrating the automatic tuning of control parameters for the online differential evolution algorithm in an embodiment of this disclosure is shown.

[0075] like Figure 4 As shown in this embodiment, the control parameters of the controller are optimized based on the online differential evolution algorithm according to the second optimization objective, specifically including S410 to S450.

[0076] S410, Initialize the second evolutionary population. When the number of individuals in the elite population does not meet the preset number of individuals in the second evolutionary population, perform Gaussian distribution expansion or random subtraction on the elite population to make the second evolutionary population reach the preset number of individuals.

[0077] Specifically, if If the number of individuals exceeds the initial population size set by the online evolutionary algorithm, then... n0 individuals are randomly selected as the initial population; if If the number of individuals in X is less than the initial population size set by the online evolutionary algorithm, then for X... best The initial population was obtained by expanding the population according to the Gaussian distribution.

[0078] S420: Select M individuals from the second evolutionary population that have the smallest sub-performance index corresponding to the second optimization objective and add them to the elite population. For example, select the two individuals corresponding to the smallest evaluation index of the second optimization objective and add them to the elite population.

[0079] S430 involves performing mutation operations on individuals in the second evolutionary population and crossover operations with individuals in the elite population to obtain the second crossover population.

[0080] S440: Select dominant individuals from the second crossover population to update the corresponding individuals in the second evolutionary population and the elite population.

[0081] S440 includes S441 to S445.

[0082] S441, randomly select two individuals from the second crossover population, and select the dominant individual from the two individuals to update the second evolutionary population. The dominant individual is the individual whose performance indicators are better than the other individual.

[0083] S442, when two individuals are not dominant to each other, randomly select one of them to update the second evolutionary population.

[0084] S441~S442 can be represented as:

[0085]

[0086] Where, x i，G+1 This represents the G+1 generation of individual i. Individual dominance means that the individual has better performance in all sub-indicators. (randvu) i，G，U x i，G，V} indicates that in the Gth generation, an individual is randomly selected from individuals U and V in the second crossover population.

[0087] S443: After each update of the second evolutionary population, the individuals that updated the second evolutionary population will be removed from the second crossover population.

[0088] S444, repeat the above steps until the second evolutionary population is updated.

[0089] S445: Select the individual with the lowest performance index in each sub-indicator from the updated second evolutionary population and add it to the elite population, thus updating the elite population.

[0090] S450 iteratively updates the second evolutionary population and the elite population. When the second optimization goal is reached, the iteration stops, the best individual is selected from the elite population, and the control parameters corresponding to the best individual are applied to control the ultra-precision motion system.

[0091] When selecting dominant individuals to update the elite population, it is determined whether the capacity of the elite population exceeds the rated capacity; if it exceeds the rated capacity, the individual with the lowest crowding in the elite population is deleted.

[0092] In this embodiment, when the optimal individual (K) in the elite population min The iteration stops when the tracking error e(t) ≤ ε within the working interval.

[0093] Elite population at the end of the selection algorithm iteration The optimal individual in the population can be used as a new control parameter to find the optimal individual (K) in the elite population. min If K min If there are multiple individuals, one is randomly selected. The selected individual's [P] i I i D i It is used as a new control parameter in ultra-precision motion systems.

[0094] This disclosure provides a method for self-tuning controller parameters for ultra-precision motion systems. Addressing the inefficiency of manual parameter tuning, it employs an offline differential evolution algorithm to tune the control parameters, automatically adjusting them according to a preset control objective, thereby improving tuning efficiency. Furthermore, addressing the issue that manually tuned control parameters cannot adaptively adjust to changes in the working environment, it uses an online fast differential evolution algorithm to tune the control parameters, enabling rapid adjustment of control parameters when the environment changes or control performance degrades, thus improving system efficiency.

[0095] It is understood that at least one of the method steps provided in the embodiments of this disclosure can be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), a programmable logic array (PLA), a system-on-a-chip, a system-on-a-substrate, a system-on-package, an application-specific integrated circuit (ASIC), or can be implemented in hardware or firmware in any other reasonable manner of integrating or packaging the circuit, or in a suitable combination of software, hardware, and firmware implementations. Alternatively, at least one of the method steps can be at least partially implemented as a computer program module, which, when run by a computer, can perform the functions of the corresponding module.

[0096] Those skilled in the art will understand that the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. In particular, the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways without departing from the spirit and teachings of this disclosure. All such combinations and / or combinations fall within the scope of this disclosure.

[0097] Although this disclosure has been shown and described with reference to specific exemplary embodiments thereof, those skilled in the art will understand that various changes in form and detail may be made to this disclosure without departing from the spirit and scope of the disclosure as defined by the appended claims and their equivalents. Therefore, the scope of this disclosure should not be limited to the above embodiments, but should be defined not only by the appended claims, but also by their equivalents.

Claims

1. A method for automatic parameter tuning of a controller based on differential evolution algorithm, characterized in that, include: Before starting the ultra-precision motion system, a first optimization objective for the controller of the ultra-precision motion system in the current application environment is determined. The first optimization objective includes multiple sub-performance evaluation indicators of the ultra-precision motion system. Based on the first optimization objective, the control parameters of the controller are optimized using an offline differential evolution algorithm, so that the controller controls the ultra-precision motion system based on the control parameters. When the application environment changes or the control effect degrades, a second optimization objective of the controller is determined, and the second optimization objective includes one of the sub-performance indicators of the first optimization objective. According to the second optimization objective, the control parameters of the controller are optimized based on the online differential evolution algorithm, so that the controller adjusts the ultra-precision motion system based on the control parameters. The initial population of the online differential evolution algorithm is the elite population obtained after optimization by the offline differential evolution algorithm. The step of optimizing the control parameters of the controller based on the first optimization objective using an offline differential evolution algorithm, so that the controller controls the ultra-precision motion system based on the control parameters, includes: Generate the initial population for the offline differential evolution algorithm; At least one individual is selected from the initial population to generate the elite population, wherein at least one sub-performance index of the at least one individual is the smallest in the initial population; Based on each sub-performance evaluation index, individuals in the initial population are selected using a roulette wheel selection process without repetition. A preset number of individuals are selected for each sub-performance evaluation index to form the first evolutionary population. Mutation operations are performed on individuals in the first evolutionary population, and individuals are selected from the first evolutionary population and the elite population for crossover operations to obtain the first crossover population. Select dominant individuals or individuals with greater crowding from the first crossover population, and update the first evolutionary population and the elite population; The first evolutionary population and the elite population are iteratively updated until the iteration ends. The best individual is selected from the elite population, and the control parameters corresponding to the best individual are applied to control the ultra-precision motion system. The step of optimizing the control parameters of the controller based on an online differential evolution algorithm according to the second optimization objective, so that the controller adjusts the ultra-precision motion system based on the control parameters, includes: Initialize the second evolutionary population. When the number of individuals in the elite population does not meet the preset number of individuals in the second evolutionary population, perform Gaussian distribution expansion or random subtraction operations on the elite population to make the second evolutionary population reach the preset number of individuals. From the second evolutionary population, select the M individuals with the smallest sub-performance index corresponding to the second optimization objective and add them to the elite population; Mutation operations are performed on individuals in the second evolutionary population, and crossover operations are performed with individuals in the elite population to obtain a second crossover population; Select dominant individuals from the second crossover population to update the second evolutionary population and the elite population; The second evolutionary population and the elite population are iteratively updated. When the second optimization objective is reached, the iteration is stopped, the best individual is selected from the elite population, and the control parameters corresponding to the best individual are applied to control the ultra-precision motion system.

2. The method according to claim 1, characterized in that, The initial population for generating the offline differential evolution algorithm includes: The individuals in the initial population are substituted into the controller as control parameters, and the stability index of the ultra-precision motion system is evaluated. When the stability index of an individual fails to meet the requirements, a new individual is generated to replace it.

3. The method according to claim 1, characterized in that, The step of selecting dominant individuals or individuals with greater crowding from the first crossover population to update the first evolutionary population and elite population includes: Two individuals are randomly selected from the first crossover population, and a dominant individual is selected from the two individuals to update the first evolutionary population. The dominant individual is the one of the two individuals whose performance indicators are all better than the other individual. If the two individuals are not dominant to each other, the individual with the greater crowding is selected to update the first evolutionary population. The crowding is the sum of the distances to the adjacent individuals in the normalized space after normalization of the performance index function. After each update of the first evolutionary population, the individuals that updated the first evolutionary population are removed from the first crossover population. Repeat the above steps until the first evolutionary population has been updated; From the updated first evolutionary population, select the individual with the smallest performance index in each sub-indicator to add to the elite population, and update the elite population.

4. The method according to claim 1, characterized in that, The step of selecting the optimal individual from the generated elite population and applying the control parameters corresponding to the optimal individual to control the ultra-precision motion system includes: The entire elite population was normalized as a parameter vector. The individual whose normalized parameter vector is closest to the zero vector is selected as the optimal individual, and the control parameters corresponding to the optimal individual are applied to control the ultra-precision motion system.

5. The method according to claim 1, characterized in that, The step of selecting dominant individuals from the second crossover population to update the second evolutionary population and the elite population includes: Two individuals are randomly selected from the second crossover population, and a dominant individual is selected from the two individuals to update the second evolutionary population. The dominant individual is the individual among the two individuals whose performance indicators are all better than the other individual. If the two individuals do not dominate each other, one individual is randomly selected to update the second evolutionary population; After each update of the second evolutionary population, the individuals that updated the second evolutionary population are removed from the second crossover population; Repeat the above steps until the second evolutionary population is completely updated; From the updated second evolutionary population, select the individual with the smallest performance index in each sub-indicator to add to the elite population, and update the elite population.

6. The method according to claim 1, characterized in that, include: When updating the elite population, determine whether the capacity of the elite population exceeds the rated capacity; If the population exceeds the rated capacity, the individual with the lowest crowding in the elite population will be removed.

7. The method according to claim 1, characterized in that, The first optimization objective includes: ； ； in, This represents the first optimization objective. This represents a sub-performance evaluation index. This indicates the start time of the motion of the ultra-precision motion system in a single motion cycle. This indicates the end time of the motion of the ultra-precision motion system in a single motion cycle. This represents the tracking error of the controller on the reference trajectory of the ultra-precision motion system during the motion process. This represents the rate of change of the control quantity during the motion of the ultra-precision motion system. This indicates the time it takes for the controller to converge the tracking error to within the threshold.

8. The method according to claim 1, characterized in that, The second optimization objective includes: ； in, This represents the second optimization objective. This indicates the start time of the motion of the ultra-precision motion system in a single motion cycle. This indicates the end time of the motion of the ultra-precision motion system in a single motion cycle. This indicates the tracking error of the controller on the reference trajectory of the ultra-precision motion system during the motion process.

Images