Online iterative learning control method and device based on bidirectional frequency binary search

Abstract

The invention discloses an online iterative learning control method and device based on bidirectional frequency binary search, and belongs to the technical field of tracking control, and the method comprises the steps: building a piezoelectric positioning system, and enabling the piezoelectric positioning system to have a certain low-frequency disturbance suppression capability while keeping stable through adjusting the parameters of a proportional-integral controller; constructing a control structure combining a YK parameterization method and iterative learning control; constructing a robust filter in iterative learning control by adopting a filter design method of a parallel cascade composite structure; a differential parameter constraint space is set for each filter based on a bidirectional frequency binary search method, and iterative updating of filter parameters is driven in a time domain by taking norm minimization of system errors as an optimization target, so that continuous optimization of online disturbance suppression performance is realized. According to the method, YK parameterization and an iterative learning control structure are combined, and the stability of the piezoelectric positioning system in the whole frequency domain can be ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of tracking control, and in particular relates to an online iterative learning control method and device based on bidirectional frequency binary search. Background Art

[0002] Precision positioning systems based on piezoelectric actuators have been widely used in space telescopes, hard disk drives, photolithography, and other fields. To achieve micrometer- or even nanometer-level positioning accuracy, closed-loop precision control of the piezoelectric positioning system is required based on the position error signal. However, in practical applications, limited bandwidth and inevitable complex time-varying interference severely degrade control performance and may undermine the stability of the piezoelectric positioning system. Furthermore, the inherent hysteresis of feedback control and the model dependence of traditional feedforward methods can further exacerbate these challenges. To address these limitations, control strategies based on iterative learning have become a key approach.

[0003] Iterative learning control (ILC) has been demonstrated to offer extremely high control accuracy in repetitive operations. It is a data-driven feedforward compensation method that gradually improves control performance over multiple iterations using a predefined learning law. However, its effectiveness relies heavily on ideal initial conditions and highly reproducible operating trajectories, often requiring offline iterations even when the data variance is minimal. To enhance the online robustness of ILC, existing technologies have proposed various improvement strategies, such as the introduction of moving averages, parameter updates, adaptive nonlinear learning mechanisms, and integration with predictive models to improve adaptability to changing trajectories. In ILC, the key to improving disturbance rejection lies in the design of robust filters. Theoretical studies have shown that an ideal filter should effectively suppress random disturbances while retaining repetitive errors for learning. Existing ILC technologies typically design robust filters as low-pass filters. However, fixed-structure low-pass filters have poor adaptability in complex environments. To this end, existing technologies have proposed time-varying filters, adaptive cutoff frequency adjustment mechanisms, and design methods based on energy distribution and optimization algorithms to improve the system's tracking capability and convergence speed under variable trajectories. However, existing technologies still have shortcomings in handling high-frequency disturbances outside the bandwidth range and complex coupled disturbances. The technical problems faced are as follows:

[0004] Technical Problem 1: Since traditional iterative learning control methods usually design robust filters as low-pass forms, stability cannot be effectively guaranteed when there are high-frequency disturbances in the control system.

[0005] Technical Issue 2: When a piezoelectric positioning system experiences multiple spike disturbances, traditional control methods typically require a higher filter order. However, high-order filters are difficult to implement in practical systems. Furthermore, time delays exist in piezoelectric positioning systems, severely impacting the performance of the control algorithm.

[0006] Technical Problem 3: Traditional iterative learning control may fail when multiple disturbance frequencies in the piezoelectric positioning system change.

[0007] Technical Problem 4: Traditional iterative learning control usually involves a lot of calculations and needs to be performed offline. Summary of the Invention

[0008] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0009] An online iterative learning control method based on bidirectional frequency binary search, comprising:

[0010] Step 1: Build a piezoelectric positioning system. By adjusting the parameters of the proportional-integral controller in the basic feedback control, the piezoelectric positioning system can maintain stability while also having a certain ability to suppress low-frequency disturbances.

[0011] Step 2: Construct a control structure that combines the YK parameterization method with iterative learning control, transforming the complex disturbance suppression problem into an iterative design problem of multiple sets of parallel optimal robust filters;

[0012] Step 3: A filter design method of a parallel-cascade composite structure is used to construct a robust filter in iterative learning control, wherein the order of the overall filter is reduced by parallel filtering, and system delay is compensated by cascade filtering;

[0013] In step 4, a differentiated parameter constraint space is set for each filter based on the bidirectional frequency binary search method. The norm of the system error is minimized as the optimization goal, and the filter parameters are iteratively updated in the time domain to achieve continuous optimization of the online disturbance suppression performance.

[0014] An online iterative learning control device based on bidirectional frequency binary search, comprising:

[0015] System building module, build a piezoelectric positioning system, and by adjusting the parameters of the proportional-integral controller in the basic feedback control, make the piezoelectric positioning system have a certain low-frequency disturbance suppression ability while maintaining stability;

[0016] The control structure building module constructs a control structure that combines the YK parameterization method with iterative learning control, transforming the complex disturbance suppression problem into an iterative design problem of multiple sets of parallel optimal robust filters;

[0017] The supplementary module uses a filter design method with a parallel and cascaded composite structure to construct a robust filter for iterative learning control. The order of the overall filter is reduced through parallel filtering, and system delay is compensated through cascade filtering.

[0018] The optimization module sets differentiated parameter constraint spaces for each filter based on a bidirectional frequency binary search method. Taking the minimum norm of the system error as the optimization goal, it drives the iterative update of the filter parameters in the time domain to achieve continuous optimization of the online disturbance suppression performance.

[0019] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the online iterative learning control method based on bidirectional frequency binary search are implemented.

[0020] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the online iterative learning control method based on bidirectional frequency binary search.

[0021] The present invention has the following beneficial effects:

[0022] The present invention adopts a method based on the YK (Youla-Kucera) parameterization method (a parameterization method named after a person) combined with iterative learning control to transform the complex disturbance suppression task into an iterative design process of multiple groups of parallel optimal robust filters, thereby effectively suppressing system disturbances.

[0023] (1) The present invention combines YK parameterization and iterative learning control structure to ensure the stability of the piezoelectric positioning system in the full frequency domain;

[0024] (2) The present invention uses a composite filter design, wherein parallel filtering is used to reduce the filter order, and cascade filtering is used to achieve delay compensation; this improves the realizability of the filter and effectively solves the performance degradation problem caused by system delay;

[0025] (3) The present invention applies a bidirectional frequency domain binary search method to segment the frequency range, assigning different parameter constraint spaces to each filter, and simultaneously uses the root mean square error value as a gradient to drive the time domain iterative optimization of the filter parameters to achieve the best disturbance suppression effect;

[0026] (4) The control structure of the present invention is simple, the computational complexity is low, and it is easy to implement online. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Flowchart of the online iterative learning control method based on bidirectional frequency binary search of the present invention;

[0028] Figure 2 It is a structural diagram of the parallel cascade composite filter of the present invention;

[0029] Figure 3 Schematic diagram of the bidirectional frequency domain binary search method of the present invention;

[0030] Figure 4 The figures compare the suppression effects of basic feedback control and the present invention after adding time-varying multi-spike disturbances; wherein, (a) is a time domain comparison figure of the suppression effects of basic feedback control and the present invention, and (b) is a frequency domain comparison figure of the suppression effects of basic feedback control and the present invention. DETAILED DESCRIPTION

[0031] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate 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 may be combined with each other as long as they do not conflict with each other.

[0032] like Figure 1 As shown, the piezoelectric positioning system includes a laser, a tilt mirror, a reflector, a lens, an image sensor, and a digital signal processing control unit based on a YK parameterized ILC module.

[0033] Among them, the laser is used to simulate the light beam emitted by the observed target; the tilt mirror and the reflector are used to simulate the vibration caused by the carrier platform and the interference during the transmission of the light beam respectively; the lens is used to converge the light; the image sensor is used to provide the error signal required for closed-loop control; the digital signal processing control unit based on the YK parameterized ILC module is used to generate a control signal to control the deflection of the tilt mirror. The light beam emitted by the laser passes through the tilt mirror, reflector and lens driven by piezoelectric ceramics in sequence, and is finally projected onto the image sensor. The control algorithm proposed in the present invention is implemented in the digital signal processing control unit, and the control signal generated by the digital signal processing control unit controls the deflection of the tilt mirror through the driving amplifier, thereby reducing the light beam jitter. The implementation steps of the online iterative learning control method based on bidirectional frequency binary search proposed in the present invention are as follows:

[0034] Step 1: Build a piezoelectric positioning system (hereinafter referred to as the system). By adjusting the parameters of the proportional-integral (PI) controller in the basic feedback control (the proportional-integral controller is the basic feedback controller of the piezoelectric positioning system and is implemented in the digital signal processing control unit), the piezoelectric positioning system can maintain stability while also having a certain ability to suppress low-frequency disturbances.

[0035] Step 2: Construct a control structure that combines the Youla-Kucera (YK) parameterization method with iterative learning control (ILC) (an ILC module based on YK parameterization) to transform the complex disturbance suppression problem into an iterative design problem of multiple sets of parallel optimal robust filters.

[0036] Step 3: A filter design method of a parallel-cascade composite structure is used to construct a robust filter in iterative learning control, wherein the order of the overall filter is reduced by parallel filtering, and compensation for system delay is achieved by cascade filtering.

[0037] In step 4, a differentiated parameter constraint space is set for each filter based on the bidirectional frequency binary search method. The norm of the system error is minimized as the optimization goal, and the filter parameters are iteratively updated in the time domain to achieve continuous optimization of the online disturbance suppression performance.

[0038] In step 2, the control structure diagram combining the Youla-Kucera (YK) parameterization method with iterative learning control (ILC) is shown in the figure below: Figure 1 As shown. Since the piezoelectric positioning system is a discrete system, the analysis is based on the Z domain. This means that there is a Z-transform domain. MEM represents the memory module, which stores data information from the previous iteration process. and Represent the control input and measurement error of the system respectively. The subscripts and Indicates the number of iterations. and are the tracking error and disturbance signal. and are learning filters and robust filters respectively, Represents the proportional-integral (PI) controller in feedback-based control, On behalf of the accused, Represents the presence of piezoelectric positioning system Frame delay, similarly, Represents the need for YK parametric design Frame delay. represents pure ILC output. The ILC law defined in the Z domain is:

[0039] (1)

[0040] (2)

[0041] (3)

[0042] When the number of iterations approaches infinity, the performance of ILC depends on the asymptotic value of the error :

[0043] (4)

[0044] In order to meet the stability requirements, The design of the filter needs to be carried out under certain constraints, namely:

[0045] (5)

[0046] in, is an infinite norm.

[0047] As the frequency increases, The magnitude response of Designed as the inverse of the nominal model of the system , and set , at this time, the robust filter in the low frequency range The design can easily meet the stability conditions. In the high frequency range, and There is a deviation , but if satisfied , the system is still stable. Among them, is the nominal model, .

[0048] When the system satisfies the stability condition, the performance of the method of the present invention depends on The filter is designed by optimizing Filter parameter matrix To achieve multi-peak disturbance suppression, the performance of the disturbance suppression algorithm is usually measured by the system error. The norm is a quantitative criterion, that is, the optimization criterion can be designed for:

[0049] (6)

[0050] in, For the feasible solution set The filter that minimizes the objective function , represents a set of filters with real coefficients, causal and stable, represents the objective function, Represents the optimal parameter matrix that satisfies the objective function. For the The system tracking error vector in the iteration, , the numbers in brackets represents the sampling time, Indicates the total number of sampling points in one iteration. is the square of the 2-norm, which is used to measure the error energy.

[0051] Traditional IIR filter , and are the orders of the filter numerator and denominator, respectively. , Respectively represent the filter The coefficients corresponding to the numerator and denominator of the order. Then, the filter parameter matrix The corresponding specific form is:

[0052] (7)

[0053] in, , , , , , , , . is the total number of sampling points in one iteration (same as above).

[0054] make , then the objective function Pair Matrix The derivative gradient is:

[0055] (8)

[0056] in, It is an intermediate quantity and has no physical meaning; and are the matrix forms corresponding to the learning filter and PI controller, Delay for the system The matrix representation of the frame, Delay for the system The matrix representation of the frame, yes The input vector of the filter. As the number of disturbances in the system increases, more and more parameters need to be identified. Existing research shows that When the filter is designed as a notch filter, its key parameters are The rest of the parameters are the same as There is a linear relationship. This characteristic can greatly simplify the amount of calculation, but when the number of disturbances is large, high-order filters are difficult to implement in the system, so disturbance decoupling design is required.

[0057] In step 3, the cascade composite filter structure is as follows: Figure 2 As shown, when there is When there are multiple frequency disturbances, the expression of the parallel design of robust filter is:

[0058] (9)

[0059] is the z-domain expression of the robust filter, For the corresponding A bandpass filter designed with a perturbation frequency, The value range is 1 to Since there is a delay in the system, in order to compensate for the delay, it is necessary to design an advance link (For the delay phase The reciprocal of ), if this part is taken out separately, then For the corresponding first A bandpass filter designed for each disturbance frequency.

[0060] However, time delay in the system may not only amplify the disturbance, but also damage the stability of the system. Therefore, a cascade structure can be used for compensation:

[0061] (10)

[0062] in, for Frame delay.

[0063] The combination of equations (9) and (10) realizes a cascaded composite filter structure. This design method can extend each filter independently, reduce the filter order and compensate for the system delay. The structure of the filter cascade is as follows Figure 2 As shown in the figure, this design approach can extend each filter independently, enhance the robustness of the system, and improve the rationality and engineering feasibility of the filter design.

[0064] In step 4, according to the above analysis, when the system has multi-frequency disturbance, The filter is split into multiple filters and iterated independently to minimize the overall system error. The optimization objective can be expressed as:

[0065] (11)

[0066] in, Indicates the indivual The error component corresponding to the filter, Any one of Indicates the indivual The parameter matrix corresponding to the filter, is a positive integer, , is the total number of disturbances in the piezoelectric positioning system. For multiple filter parameters The parameter combination that minimizes the objective function is searched in the joint feasible region. It is an objective function about multiple filter parameters, usually a weighted energy measure of the tracking error (or disturbance response), used to measure the quality of control performance.

[0067] Furthermore, for a single filter The optimization can be expressed as:

[0068] (12)

[0069] Where, is the weight coefficient of each error component. If all satisfy Equation (12), the overall error is also minimized. In fact, since the structures of all filters are the same and the parameter iteration rules are consistent, using the same initial value will cause all filters to converge to the same steady-state value, and it is impossible to achieve parallel search of multiple perturbation frequency points. To this end, a two-way frequency domain binary search method is proposed. By combining it with time domain parameter optimization, the search space is gradually refined, such as Figure 3 shown. Figure 3 In the equation, the horizontal axis is the disturbance frequency and the vertical axis is the disturbance amplitude. Figure 3 The distribution of disturbances in is shown as a schematic diagram. is the Nyquist frequency.

[0070] First level search: The parameter range of the filter is divided into two equal-width sub-intervals:

[0071] , .

[0072] in, is the first subinterval, is the second subinterval, is the filter pole radius. A parallel filter bank is configured at the parameter boundary point set, and its core parameters adopt the following complementary iteration strategy, which is essentially the iteration of two filter parameters belonging to the same interval in different directions, namely:

[0073] (13)

[0074] Where, express The iterative gradient symbol, Indicates the corresponding number of filters, For the The key parameters of the filter are: there are two filters in each subinterval. In order to speed up the convergence speed, the root mean square (RMS) value of the error is introduced. As the gradient, its calculation formula is:

[0075] (14)

[0076] in, is the total number of sampling points in one iteration (same as above), For the The square of the error value at each sampling moment.

[0077] Based on the gradient information, the update formula is as follows:

[0078] (15)

[0079] in, for Moment indivual The key parameter values ​​of the filter, for Moment indivual Key parameter values ​​of the filter; is the learning rate, which is used to control the rate of parameter update.

[0080] Since the number of disturbances in the system is uncertain, it is necessary to make a comprehensive judgment based on the parameter range and the iteration stop condition (see formula (12)), which can be divided into the following three cases:

[0081] No disturbance: When the parameters belonging to the same interval are iterated from the initial value to the boundary of another interval and none of them satisfy Equation (12), there is no disturbance signal in the interval and the binary search of the interval can be terminated.

[0082] Single perturbation: If the parameters belonging to the same interval iterate to the same value and all satisfy Equation (12), it means that there is only one main perturbation frequency in the interval and the search can be terminated.

[0083] Multiple perturbations: Parameters belonging to the same interval are iterated to different values, all satisfying Equation (12). Since only two filters are placed in one interval, a maximum of two perturbations can be suppressed. If the number of perturbations is greater than two, the next level of search is required.

[0084] Since the first level iteration divides the full frequency parameter interval of the filter into two equal width sub-intervals and , these two equal-width subintervals have the same iterative process and are independent of each other. Therefore, in the subsequent description, only optimization process. The iterative process follows The same operations will not be repeated later.

[0085] Second level search: After the first level search is completed, the frequency interval that has not been searched is The filter bank is set up and the parameters are iterated according to the same iterative strategy as the first-level search. is the key parameter value of the first filter found in the first stage search. The key parameter value of the second filter found in the first stage search.

[0086] No. Level search: After the level search is completed, the frequency interval that has not been searched is , iterate according to the same iterative strategy as the first-level search until the entire frequency range is traversed.

[0087] If the disturbance signal in the system is time-varying, the iterative stopping condition of the existing filter may be destroyed in a certain level of search, such as Figure 3 in At this point, it is necessary to relocate the interval to which the parameter belongs and reset it to the endpoint of the interval, and then update the parameter according to the original iterative strategy to adapt to the change of disturbance.

[0088] In order to demonstrate the effect of the online iterative learning control method based on bidirectional frequency binary search in the present invention on the ability to improve the disturbance suppression capability of time-varying multi-frequency in the piezoelectric positioning system, a corresponding controller was designed and implemented using a digital signal processing unit, and an experiment was conducted. In the experiment, the disturbance lasted for ,exist and At the moment, the disturbance has changed. Figure 4 As shown, Figure 4 (a) is a time domain comparison diagram of the suppression effect of basic feedback control and the present invention (the horizontal axis is the duration of the experiment, and the vertical axis is the amplitude of the error). Figure 4 (b) is a frequency domain comparison diagram of the suppression effect of basic feedback control and the present invention (the horizontal axis is the frequency of the error, and the vertical axis is the amplitude of the error). Figure 4 In (a), trajectory C3 shows the experimental results of the proposed control method, while trajectory C1 shows the experimental results of basic feedback control in a piezoelectric positioning system. During the disturbance phases at different time intervals, the root mean square error (RMS) achieved by C3 was approximately 80% lower than that achieved by C1. The frequency domain disturbance was attenuated by at least 8dB and up to 15dB, demonstrating the proposed method's enhanced adaptability and interference rejection under complex operating conditions.

[0089] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROMs, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention may be implemented using various computer languages.

[0090] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts 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, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0091] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0092] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0093] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0094] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

[0095] The above descriptions are merely embodiments of the present invention and are not intended to limit the scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention description and drawings, or directly or indirectly applied to other related system fields, are also included in the scope of protection of the present invention.

[0096] The contents not described in detail in the specification of the present invention belong to the prior art known to those skilled in the art.

Claims

1. An online iterative learning control method based on bidirectional frequency binary search, characterized in that: include: Step 1: Build a piezoelectric positioning system. By adjusting the parameters of the proportional-integral controller in the basic feedback control, the piezoelectric positioning system can maintain stability while also having a certain ability to suppress low-frequency disturbances. Step 2: Construct a control structure that combines the YK parameterization method with iterative learning control, transforming the complex disturbance suppression problem into an iterative design problem of multiple sets of parallel optimal robust filters; Step 3: A filter design method of a parallel-cascade composite structure is used to construct a robust filter in iterative learning control, wherein the order of the overall filter is reduced by parallel filtering, and system delay is compensated by cascade filtering; In step 4, a differentiated parameter constraint space is set for each filter based on the bidirectional frequency binary search method. The norm of the system error is minimized as the optimization goal, and the filter parameters are iteratively updated in the time domain to achieve continuous optimization of the online disturbance suppression performance.

2. The online iterative learning control method based on bidirectional frequency binary search according to claim 1 is characterized in that: In step 1, the piezoelectric positioning system includes a laser, a tilt mirror, a reflector, a lens, an image sensor, and a digital signal processing control unit based on a YK parameterized ILC module; Among them, the laser is used to simulate the light beam emitted by the observed target; the tilt mirror and the reflector are used to simulate the vibration caused by the carrier platform and the interference in the light beam transmission process respectively; the lens is used to converge the light; the image sensor is used to provide the error signal required for closed-loop control; the digital signal processing control unit based on the YK parameterized ILC module is used to generate a control signal to control the deflection of the tilt mirror; the light beam emitted by the laser passes through the tilt mirror, the reflector and the lens in sequence, and is finally projected onto the image sensor; the online iterative learning control method based on bidirectional frequency binary search is implemented in the digital signal processing control unit based on the YK parameterized ILC module, and the control signal generated by the digital signal processing control unit based on the YK parameterized ILC module controls the deflection of the tilt mirror through the drive amplifier.

3. The online iterative learning control method based on bidirectional frequency binary search according to claim 2 is characterized in that: In step 2, the control structure combining the YK parameterization method with iterative learning control is: and are the control input and measurement error of the system, respectively. and Indicates the number of iterations; and is the tracking error and disturbance signal; and are learning filters and robust filters respectively, is a proportional-integral controller based on feedback control, For the accused, Represents the presence of piezoelectric positioning system Frame delay, Needed for YK parameterized design Frame delay; is a pure ILC output; the ILC law defined in the Z domain is: （1） （2） （3） When the number of iterations approaches infinity, the performance of ILC depends on the asymptotic value of the error : （4） The filter constraints are: （5） in, is the infinite norm; When the system satisfies the stability condition, the performance of the method depends on The filter is designed by optimizing Filter parameter matrix To achieve multi-peak disturbance suppression, the performance of the disturbance suppression algorithm is usually measured by the system error. Norm is a quantitative criterion and a design optimization criterion for: （6） in, For the feasible solution set The filter that minimizes the objective function , represents a set of filters with real coefficients, causal and stable, represents the objective function, Represents the optimal parameter matrix that satisfies the objective function; For the The system tracking error vector in the iteration, , the numbers in brackets represents the sampling time, Indicates the total number of sampling points in one iteration; is the square of the 2-norm, which is used to measure the error energy; make , then the objective function Pair Matrix The derivative gradient is: （8） in, and are the matrix forms corresponding to the learning filter and PI controller, Delay for the system The matrix representation of the frame, Delay for the system The matrix representation of the frame, yes Input vector to the filter.

4. The online iterative learning control method based on bidirectional frequency binary search according to claim 3 is characterized in that: Step 3 includes: when there is When there are multiple frequency disturbances, the expression of the parallel design of robust filter is: （9） is a robust filter, For the corresponding A bandpass filter designed with a perturbation frequency, The value range is 1 to ; Advanced link For the delay phase The reciprocal of For the corresponding first The bandpass filter designed for each disturbance frequency is compensated using a cascade structure: （10） in, for Frame delay; are the constant terms and Term coefficient, The denominator polynomial of the bandpass filter is and Term coefficient.

5. The online iterative learning control method based on bidirectional frequency binary search according to claim 4 is characterized in that: In step 4, The filter is split into multiple filters that are iterated independently, and the optimization objective is expressed as: （11） in, For the indivual The error component corresponding to the filter, Any one of For the indivual The parameter matrix corresponding to the filter, is a positive integer, , is the total number of disturbances in the piezoelectric positioning system; For multiple filter parameters Search for the parameter combination that minimizes the objective function in the joint feasible domain of is the objective function with respect to multiple filter parameters; For a single filter Optimization: （12） in, is the weight coefficient of each error component, if If both satisfy formula (12), the overall error will be minimized accordingly; A two-way frequency domain binary search method is proposed, which is combined with time domain parameter optimization to gradually refine the search space.

6. The online iterative learning control method based on bidirectional frequency binary search according to claim 5, characterized in that: In the two-way frequency domain binary search method of step 4, in the first level search, The parameter range of the filter is divided into two equal-width sub-intervals, and a parallel filter bank is configured at the parameter boundary point set. The core parameters adopt the following complementary iteration strategy, which essentially iterates the two filter parameters belonging to the same interval in different directions. Based on the gradient information, the update formula is: （15） in, for Moment indivual The key parameter values ​​of the filter, for Moment indivual Key parameter values ​​of the filter; is the learning rate, which is used to control the rate of parameter update; is the root mean square error; The number of disturbances in the system is uncertain. A comprehensive judgment based on the parameter range and the iteration stop condition is made, which can be divided into the following three cases: No disturbance: Parameters belonging to the same interval are iterated from the initial value to the boundary of another interval, and none of them satisfy Equation (12). Then there is no disturbance signal in the interval, and the binary search of the interval is terminated. Single perturbation: If the parameters in the same interval iterate to the same value and satisfy equation (12), it means that there is only one main perturbation frequency in the interval and the search is terminated. Multiple perturbations: Parameters belonging to the same interval are iterated to different values, and all satisfy Equation (12). Since only two filters are placed in one interval, at most two perturbations can be suppressed. If the number of perturbations is greater than two, the next level of search is required.

7. The online iterative learning control method based on bidirectional frequency binary search according to claim 6, characterized in that: In the two-way frequency domain binary search method of step 4, after the first level search is completed, the frequency interval that has not been searched is ; Set the filter bank and perform parameter iteration according to the same iterative strategy as the first-level search; is the key parameter value of the first filter found in the first stage search. The key parameter value of the second filter found in the first stage search; In the After the level search is completed, the frequency interval that has not been searched is , iterate according to the same iterative strategy as the first-level search until the entire frequency range is traversed; If the disturbance signal in the system is time-varying, the iterative stopping condition of the existing filter may be destroyed in a certain level of search; At this time, it is necessary to relocate the interval to which the parameter belongs and reset it to the endpoint of the interval. Then, the parameter is updated according to the original iterative strategy to adapt to the changes in the disturbance.

8. An online iterative learning control device based on bidirectional frequency binary search, characterized in that: include: System building module, build a piezoelectric positioning system, and by adjusting the parameters of the proportional-integral controller in the basic feedback control, make the piezoelectric positioning system have a certain low-frequency disturbance suppression ability while maintaining stability; The control structure building module constructs a control structure that combines the YK parameterization method with iterative learning control, transforming the complex disturbance suppression problem into an iterative design problem of multiple sets of parallel optimal robust filters; The supplementary module uses a filter design method with a parallel and cascaded composite structure to construct a robust filter for iterative learning control. The order of the overall filter is reduced through parallel filtering, and system delay is compensated through cascade filtering. The optimization module sets differentiated parameter constraint spaces for each filter based on a bidirectional frequency binary search method. Taking the minimum norm of the system error as the optimization goal, it drives the iterative update of the filter parameters in the time domain to achieve continuous optimization of the online disturbance suppression performance.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the online iterative learning control method based on bidirectional frequency binary search according to any one of claims 1 to 7 are implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the online iterative learning control method based on bidirectional frequency binary search as claimed in any one of claims 1 to 7 are implemented.

Images