Variable step size FxLMS regulation and control system and method based on collaborative coupling of double nonlinear functions

Abstract

The invention discloses a variable step size FxLMS self-adaptive control method based on double nonlinear function collaborative coupling, which belongs to the technical field of hydraulic systems, and utilizes the combined arrangement of a reference / error sensor, a primary / secondary channel, a self-adaptive filter and a controller and the design of a step size adjustment function comprising a rational fraction item and an exponential item. And the hydraulic pulsation active control requirements under different hydraulic working conditions can be met. According to the system and the method, based on the synergistic effect of the rational fraction item and the exponential item, the step length can be accurately and dynamically adjusted according to the size of the error, the low steady-state error is maintained while rapid convergence is guaranteed, the remarkable performance advantage is shown in practical application, and the method is suitable for large-scale popularization and application. A new technical approach is provided for active control of pressure pulsation of the hydraulic system, and the method has excellent application prospects and economic value.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of hydraulic systems, and can be applied to application scenarios such as hydraulic system pressure pulsation control, mechanical vibration active control, noise active control, and specifically relates to a variable step size FxLMS regulation system and method based on double nonlinear function cooperative coupling. BACKGROUND

[0002] In the fields of engineering machinery, aerospace, ships and the like, there is a great application demand for active noise and vibration control technology, especially the technology related to low-frequency suppression capability and high-precision control characteristics. Among them, the hydraulic system is widely used in the power and transmission systems of the above-mentioned fields due to its high power density and flexible layout, and the effective suppression of the pressure pulsation of the hydraulic system becomes a typical challenge for active control.

[0003] The adaptive filtering algorithm is the core of active control, among which the least mean square (LMS) algorithm and its filtered-x version (Filtered-x Least Mean Square with Variable Step Size, referred to as FxLMS) are widely used due to their simple structure, efficient calculation and good stability. However, the traditional fixed step size LMS / FxLMS algorithm often faces an inherent contradiction, that is, a large step size can accelerate convergence but leads to an increase in steady-state error and even a risk of divergence; a small step size can reduce the steady-state error but significantly slows down the convergence speed. This contradiction is particularly prominent when dealing with signals such as hydraulic system pressure pulsation, which are fast-changing and have color characteristics. The color characteristics of the signal cause the input correlation matrix to have a large eigenvalue spread (the "stiffness" problem), forcing the fixed step size algorithm to make an unfavorable trade-off between convergence speed and stability, making it difficult to meet the dynamic control requirements.

[0004] To overcome the limitations of fixed step size, variable step size (VSS) LMS / FxLMS algorithm emerged as the times require, which is an important improvement of the classic FxLMS algorithm in active noise control (ANC), aiming to solve the core contradiction faced by the fixed step size FxLMS algorithm, that is, the trade-off between convergence speed and steady-state error. For the variable step size FxLMS algorithm, the core idea is to dynamically adjust the step size: a larger step size is used in the early stage of convergence to speed up the convergence, and the step size is reduced to reduce the steady-state error when approaching the steady state. For this purpose, researchers have proposed a variety of step size updating strategies based on nonlinear functions (such as logarithmic function, exponential function, swallow line function, Sigmoid function, hyperbolic tangent function, inverse tangent function, etc.), trying to establish a more optimal error-step size mapping relationship, deriving a series of improved schemes such as VSSFxLMS-1 algorithm, VSSFxLMS-2 algorithm, VSSFxLMS-3 algorithm, which can improve the problems existing in the fixed step size FxLMS algorithm to some extent. However, the existing improved algorithms still have the following shortcomings: (1) Performance trade-off difficulty: Most algorithms based on single or simple combination of nonlinear functions are difficult to balance high convergence speed and low steady-state error. Some strategies are not responsive enough in the early stage of convergence, and others are not fine enough in the steady-state region.

[0005] (2) Insufficient dynamic adaptability: The tracking ability and robustness of existing algorithms are often not ideal when facing complex dynamic environments such as system parameter mutation, load disturbance or non-stationary random changes.

[0006] (3) Design limitations: Some algorithms rely on manual adjustment of multiple internal parameters, lack of adaptive ability, and limit the flexibility and universality of engineering applications; some algorithms may lack sufficient smoothness in the step size adjustment process, causing fluctuations in the control process.

[0007] Because of the existence of the above shortcomings, the existing variable step size FxLMS algorithm cannot fully meet the needs of engineering applications, and has certain limitations. The current technology urgently needs a new type of variable step size FxLMS algorithm. The algorithm should be able to. SUMMARY

[0008] In view of one or more of the above defects or improvement needs of the prior art, the present application provides a variable step size FxLMS regulation system and method based on double nonlinear function cooperative coupling, which can break through the traditional trade-off between convergence speed and steady-state error, and realize fast convergence and extremely low steady-state error in complex dynamic environment, has excellent dynamic tracking ability and robustness, and meets the needs of high-demand engineering applications.

[0009] To achieve the above object, one aspect of the present application provides a variable step size FxLMS control system based on double nonlinear function cooperative coupling, comprising: a reference sensor, which can be installed at the vibration source position, for collecting pressure pulsation reference signals of the vibration source and transmitting the signals in real time to the adaptive filter and the controller; an error sensor, which can be arranged at the target position where pressure pulsation suppression is needed, and is arranged at intervals with the reference sensor on the hydraulic pipeline, for detecting error signals of the target position and feeding the signals back to the controller to form a closed-loop control; a primary channel, which is used to represent the natural propagation path of pressure pulsation from the vibration source position to the target position; a secondary channel, which includes the signal propagation path from the output end of the controller to the target position, including the actuator and the pipeline from the actuator to the error sensor, for converting the control signals into actual pressure pulsation suppression signals ; an adaptive filter, which is arranged on the secondary channel, for generating control signals according to the reference signals ; a controller, which is connected with the reference sensor, the error sensor and the actuator respectively, for dynamically adjusting the step size according to the error signals , generating and outputting the control signals to the actuator, while monitoring the system state in real time; and the function of the step size is:

[0010] wherein, is a rational fraction term; is an exponential term; is the maximum step size, is an exponential parameter, is a rational fraction parameter; is the error signal, and wherein, is the reference signal after propagation through the primary channel, is the control signal after propagation through the secondary channel.

[0011] As a further improvement of the present application, the adaptive filter is an FIR transverse filter.

[0012] Another aspect of the present application also provides a variable step size FxLMS control method based on the cooperative coupling of double nonlinear functions, which can be used to control the pressure pulsation of a hydraulic system by using the variable step size FxLMS control system based on the cooperative coupling of double nonlinear functions. The method comprises the following steps: (1) setting the order of the adaptive filter L , and setting the adjustment parameters of the double nonlinear functions , and ; (2) determining the reference signal vector; (3) initializing the control system and obtaining the control signal by passing the reference signal vector through the adaptive filter; (4) superimposing the output signal of the control signal after propagating through the secondary channel with the expected signal to obtain the error signal , and feeding back the error signal to the controller; (5) updating the weight vector at the next time point according to the error signal ; (6) updating the step size of the adaptive filter based on the function of the step size; (7) repeating steps (2)-(6) until the control system reaches a steady state. As a further improvement of the present application, in step (1), the initialized weight vector of the adaptive filter is set as

[0013] ; and / or satisfies ; in the formula, is the maximum eigenvalue of the autocorrelation matrix of the reference signal. As a further improvement of the present application, in step (2), the reference signal vector of the component is:

[0014] . As a further improvement of the present application, in step (3), the control signal

[0015] is:

[0016] in the formula, is the control signal obtained by passing the reference signal vector through the adaptive filter; is the reference signal collected by the reference sensor; is​ transpose, for n The adaptive filter weight vector at time t, and .

[0017] As a further improvement of the present invention, in step (4), the output signal for:

[0018] In the formula, This is the impulse response of the secondary channel; This represents the convolution operation.

[0019] As a further improvement of the present invention, in step (4), the desired signal The following formula represents:

[0020] In the formula, This is the pressure pulsation signal passing through the primary channel; This is the random white noise introduced.

[0021] As a further improvement of the present invention, in step (5), the calculation is updated. n The adaptive filter weight vector at time +1 is:

[0022] In the formula, for n The step size factor of the time-adaptive filter; for n The adaptive filter weight vector at time step; For the estimation model via secondary channels The filtered reference signal vector, which passes through the reference signal Through estimated secondary channels The result after filtering is as follows, and .

[0023] As a further improvement of the present invention, in steps (1) and (6), the values ​​of each adjustment parameter are derived from empirical values ​​obtained from a large number of simulation experiments.

[0024] The aforementioned improved technical features can be combined with each other as long as they do not conflict with each other.

[0025] In summary, the beneficial effects of the above-described technical solutions conceived by this invention compared with the prior art include: The variable step size FxLMS regulation system and method based on the cooperative coupling of double nonlinear functions can meet the active control requirements of hydraulic pulsation under different hydraulic working conditions, can accurately dynamically adjust the step size according to the error size based on the cooperative action of the rational fraction term and the exponential term, can maintain a lower steady-state error while ensuring rapid convergence, and has excellent application prospect and economic value. BRIEF DESCRIPTION OF DRAWINGS

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative effort on the basis of these drawings.

[0027] Figure 1 is a flow chart of the variable step size FxLMS regulation method based on the cooperative coupling of double nonlinear functions of the present application; Figure 2 is a system principle diagram of the variable step size FxLMS regulation system based on the cooperative coupling of double nonlinear functions of the present application; Figure 3 is a performance comparison diagram of the variable step size FxLMS regulation method applied to the system mutation scene in the embodiments of the present application and other FxLMS algorithms; Figure 4 is a performance comparison diagram of the variable step size FxLMS regulation method applied to the load periodic change scene in the embodiments of the present application and other FxLMS algorithms; Figure 5 is a performance comparison diagram of the variable step size FxLMS regulation method applied to the load non-stable random change scene in the embodiments of the present application and other FxLMS algorithms; DETAILED DESCRIPTION In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0028] In the description of the present application, it is to be understood that the orientations or positional relationships indicated by the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential" and the like are based on the orientations or positional relationships shown in the drawings, and are merely for the convenience of describing the present application and simplifying the description, and are not intended to indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be construed as limiting the present application.

[0029] In addition, unless explicitly defined otherwise, the terms "first", "second", etc. are used only for descriptive purposes and cannot be construed as indicating or implying relative importance or an implied indication of the number of technical features indicated. Therefore, the features defined as "first", "second" can explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "a plurality of" is at least two, for example, two, three, etc., unless explicitly defined otherwise.

[0030] In the present application, unless explicitly defined otherwise, the terms "mounting", "connecting", "connecting", "fixing" and the like should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or it can be integrated; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the internal communication of two elements or the interaction relationship between two elements, unless explicitly defined otherwise. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0031] In the present application, unless explicitly defined otherwise, the first feature "on" or "under" the second feature can be that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. Moreover, the first feature "above", "over" and "on" the second feature can be that the first feature is directly above or obliquely above the second feature, or it can only mean that the horizontal height of the first feature is higher than that of the second feature. The first feature "below", "under" and "under" the second feature can be that the first feature is directly below or obliquely below the second feature, or it can only mean that the horizontal height of the first feature is less than that of the second feature.

[0032] In the following, with reference to Figures 1-5 The variable step size FxLMS control system and method based on the cooperative coupling of double nonlinear functions according to the preferred embodiment of the present application are described.

[0033] For the variable step size FxLMS control system in the preferred embodiment, the system composition is as follows Figure 2As shown, it includes a reference sensor, an error sensor, a primary channel, a secondary channel, an adaptive filter, and a controller.

[0034] The reference sensor can be installed at the vibration source location (such as the outlet of a hydraulic pump or other vibration source location) to collect reference signals of pump pressure pulsation. And transmit it to the adaptive filter and controller in real time; An error sensor can be positioned at the target location where pressure pulsation suppression is required. It maintains an appropriate distance from the reference sensor on the hydraulic line to detect residual pressure pulsation signals at the target location. The error signal is fed back to the controller in real time to form a closed-loop control. Primary Channel The hydraulic lines and related hydraulic components between the reference sensor and the error sensor are used to characterize the natural propagation path of pressure pulsations from the vibration source to the target position.

[0035] Secondary channel This includes the signal propagation path from the controller output to the error sensor location, including the actuator (such as a piezoelectric actuator, servo valve, etc.) and the piping from the actuator to the error sensor, used to transmit the control signal. Converted into actual pressure pulsation suppression signal .

[0036] In a preferred embodiment, the secondary channel It characterizes the transmission characteristics from the controller output to the error sensor, which includes the combined effects of power amplifier, actuator, pipeline impedance and other components. Accurate modeling of the secondary channel is a key factor to ensure the stable convergence of the FxLMS algorithm.

[0037] More specifically, in the preferred embodiment, an FIR filter is preferably used to model the secondary channel, and an estimated model of the secondary channel model is obtained through offline identification or online adaptive methods. .

[0038] Adaptive Filter According to the reference signal Generate optimal control signal Through weight coefficients The adaptive adjustment achieves active suppression of pressure pulsations. In a preferred embodiment, the adaptive filter preferably uses a length of... L The FIR transverse filter structure.

[0039] The controller preferably includes DSP Processor or digital signal processing unit (e.g.) FPGAIt is bidirectionally connected to the reference sensor and the error sensor, and unidirectionally connected to the actuator. It executes the DNVSS-FxLMS algorithm to achieve adaptive updating of the weight vector based on the error signal. Dynamically adjust step size It generates and outputs control signals to the actuator, while monitoring the system status in real time to ensure control stability.

[0040] In the preferred embodiment, the controller transmits signals to the reference sensor, the error sensor, and the actuator. The two sensors are responsible for inputting pipeline signals to the controller in real time. After processing, the controller generates a control signal, which is then transmitted to the actuator to perform the corresponding action. Therefore, the controller in the preferred embodiment can be understood as a signal processing unit, while the LMS and corresponding algorithms are the software components. DSP The processor is a hardware component; in practical applications, the software code is burned into it. DSP In the hardware, this is used to complete the functional settings of the controller.

[0041] When the system is working, the reference signal Control signals are generated after processing by an adaptive filter. control signals The output signal passes through the secondary channel. ,Will Compared with the original pulsating signal (desired signal) The error signal is obtained by superimposing the signals. The error signal is detected by an error sensor. Subsequently, the error signal Feedback is sent to the controller to update the weighting coefficients and step size, and then passed to the adaptive filter to form closed-loop control, thereby achieving efficient suppression of pressure pulsation in the hydraulic system.

[0042] Based on the aforementioned variable step-size FxLMS control system, a preferred embodiment further designs a variable step-size FxLMS control method (i.e., the DNVSS-FxLMS algorithm) based on the cooperative coupling of two nonlinear functions. Its preferred computational flow is as follows: Figure 1 As shown, and preferably includes the following steps: (1) Set the length (order) of the adaptive filter. L Given the adjustment parameters of the double nonlinear function , , ;in, For the maximum step size, For exponential parameters, is the parameter of the rational fraction.

[0043] The values ​​of the aforementioned adjustment parameters can preferably be empirical values ​​derived from extensive simulation experiments. Control the upper bound of the step size; Adjust the sensitivity of the small error step size; the smaller the value, the lower the steady-state error. Control the step size transition rate; the larger the value, the longer the step size is maintained in the early stages of convergence.

[0044] It is understandable that the values ​​of the aforementioned parameters can be adjusted as needed for different systems or different experimental conditions of the same system.

[0045] Furthermore, based on the determination of the aforementioned adjustment parameter values, the initial weight vector of the adaptive filter is further preferably set as follows: .

[0046] More preferably, in the preferred embodiment satisfy In the formula, This is the largest eigenvalue of the autocorrelation matrix of the reference signal. (2) Determine the reference signal vector; Specifically, reference signals are acquired through a reference sensor. And construct a reference signal vector:

[0047] In the formula, n Referring to different moments; for n The reference sensor's sampled value is constantly monitored. This signal reflects the propagation characteristics of pump source pulsations in the pipeline.

[0048] (3) Initialize the control system and obtain the control signal by passing the reference signal vector through an adaptive filter:

[0049] In the formula, The control signal is obtained after the reference signal vector is passed through an adaptive filter. The reference signal is acquired by the reference sensor; for transpose, for n The adaptive filter weight vector at time t, and .

[0050] (4) Control signal via secondary passage After propagation and the expected signal Superimpose to obtain the error signal and the error signal Feedback is sent to the controller; whereby the error signal is:

[0051] wherein, is a control signal propagated through the secondary channel the output signal after propagation; is a reference signal x (n) the output signal after propagation through the primary channel.

[0052] In actual control, the output signal after propagation through the secondary channel is converted into :

[0053] wherein, is a secondary channel impulse response; denotes a convolution operation.

[0054] In more detail, the desired signal is preferably characterized by the following equation:

[0055] wherein, is a pressure pulsation signal through the primary channel ; is a random white noise introduced for identification of the secondary channel. In the preferred embodiment,

[0056] is a residual signal after suppression of the pressure pulsation, and is also a feedback signal for the next time step adjustment and weight update. The size of the error signal directly determines the value of the step factor, and thus affects the convergence characteristics of the algorithm. (5) The controller updates the weight vector of the next time step according to the error signal

[0057] ; wherein the reference signal is filtered through the estimated secondary channel , and the filtered reference signal is obtained therefrom, i.e. . For the above filtering process, it compensates for the phase and amplitude influence of the secondary channel on the control signal. The update calculation of the adaptive filter weight vector at time step

[0058] +1 is: n

[0059] wherein, is n ​​a step factor of the time-adaptive filter; for estimating the model of the secondary path a filtered reference signal vector.

[0060] (6) dynamically updating the step of the adaptive filter based on a double non-linear function cooperative coupling mechanism; wherein the double non-linear step function is:

[0061] wherein, is a rational fraction term, used to provide smooth step transition characteristics and avoid step mutations; is an exponential term, used to enhance the sensitivity to small errors and achieve fine control.

[0062] For the aforementioned double non-linear step function, the cooperative coupling mechanism is that the rational fraction term dominates the fast response in the large error region, the exponential term dominates the fine tuning in the small error region, and the product of the two achieves the balance between convergence speed and steady-state error.

[0063] (7) repeating steps (2) to (6) until the control system reaches a steady state.

[0064] In the entire iteration process, the step factor adaptively adjusts according to the size of the error signal: When the error is large, the step function provides a large step value to speed up the convergence; when the error approaches zero, the step function automatically switches to a small step to reduce the steady-state error. Through this double non-linear function cooperative coupling mechanism, the algorithm achieves the optimal balance between convergence speed and steady-state accuracy, and continuously uses the iteration process until the preset convergence condition is met or a steady state is reached.

[0065] In the preferred embodiment, by designing the above implementation steps, a complete hydraulic system pressure pulsation active control process is constructed, and the double non-linear function cooperative coupling variable step mechanism makes the algorithm adaptively adjust the convergence process, ensuring fast response while achieving excellent steady-state control accuracy, and is particularly suitable for complex and variable hydraulic system working conditions.

[0066] As follows, the aforementioned double non-linear function cooperative coupling variable step FxLMS control method is applied to three specific embodiments to demonstrate the scheme in the preferred embodiment.

[0067] It should be noted that in the following three embodiments, in order to make the description clearer and more concise, only some key steps in each embodiment are described, and the detailed implementation steps can be operated according to the description in the aforementioned embodiments, which will not be repeated here.

[0068] Embodiment 1: Active control of pressure fluctuation under sudden change of working condition of hydraulic system In this embodiment, the variable step size FxLMS control system and method based on double nonlinear function cooperative coupling are used to control the pressure fluctuation of the hydraulic system under sudden change of working condition, and the working condition is further preferably the typical industrial application of switching from the excavating condition to the rotating condition of the hydraulic excavator, switching from the idle state to the machining state of the hydraulic machine tool, etc.

[0069] The specific implementation steps are as follows: (1) System parameter initialization; Set the order of the adaptive filter L =64; and set the adjustment parameters according to the characteristics of the hydraulic system , , , , , . The selection of these parameters takes into account the frequency range (usually 10-500Hz) and amplitude characteristics of the pressure fluctuation of the hydraulic system.

[0070] (2) Reference signal preprocessing; The signal collected by the reference sensor is filtered by a 32-order low-pass FIR filter, and the cutoff frequency is set to 1000Hz to filter out high-frequency noise interference.

[0071] After normalization processing, a colored signal with frequency correlation is obtained, which simulates the phenomenon of non-uniform frequency spectrum distribution caused by pipeline transmission characteristics and pump fluctuation characteristics in the hydraulic system.

[0072] (3) Initial system modeling; In the system startup stage (iteration number from n =0 to n =5000), the initial system characteristics are simulated by using a bell-shaped weight distribution, and the weight coefficient is set according to the following formula:

[0073] In the formula, M is the order of the adaptive filter, rand is a random number function.

[0074] (4) System sudden change simulation; At the 5000th iteration, the working condition of the hydraulic system is simulated, and the system weight is changed to an oscillating distribution: .

[0075] (5) Algorithm execution and performance monitoring.

[0076] Steps (1)-(7) of the aforementioned algorithm (DNVSS-FxLMS algorithm) are run, the mean square error (MSE) is calculated and recorded in real time, and finally the mean square error change curve as shown in Figure 3 is obtained.

[0077] According to the result curve as shown in Figure 3 , it can be seen that: In the initial stage, the DNVSS-FxLMS algorithm completes convergence after 1167 iterations, and the steady-state MSE reaches -24.7 dB; after the system mutates at the 5000th iteration, the algorithm only needs 894 iterations to re-converge to the steady state, and the steady-state MSE is -20.3 dB.

[0078] At the same time, by comparing the aforementioned mean square error change curve with the results of the traditional fixed step size FxLMS algorithm, the existing variable step size algorithm VSSFxLMS1 / 2 / 3, it can be seen that: the traditional fixed step size FxLMS algorithm needs 4172 iterations to complete the initial convergence, and needs 4223 iterations to re-stabilize after mutation; the existing variable step size algorithm VSSFxLMS-1 needs 2605 and 2557 iterations; the existing variable step size algorithm VSSFxLMS-2 needs 2600 and 1894 iterations; the existing variable step size algorithm VSSFxLMS-3 needs 2206 and 1293 iterations.

[0079] According to the above comparison results, it is not difficult to find that the DNVSS-FxLMS algorithm in the preferred embodiment has superior performance in the hydraulic system working condition mutation scene, and through the cooperative adjustment of the step size by the double nonlinear function, it can quickly respond and re-converge when the system mutates. The fast convergence characteristics and low steady-state error of the DNVSS-FxLMS algorithm make it particularly suitable for hydraulic equipment that needs to frequently switch working conditions, such as engineering machinery, injection molding machines, hydraulic machine tools, etc.

[0080] Example 2: Pressure pulsation control under periodic load change condition In this embodiment, the variable step size FxLMS regulation system and method based on the cooperative coupling of double nonlinear functions are used to regulate the pressure pulsation of the hydraulic system under the periodic load change condition, and the above condition is further preferably the typical industrial applications such as the cyclic injection process of an injection molding machine, the periodic excitation of a hydraulic vibration table, and the reciprocating motion of a hydraulic punch.

[0081] In this embodiment, the periodic change of the load is simulated by modulating the system weight by a sine function, and two different change periods are set: the slow change mode with period T1=5000 is used for the first 5000 iterations to simulate the normal working state; and the fast change mode with period T2=2500 is used for the subsequent period to simulate the high-frequency working state.

[0082] The specific implementation steps are as follows: (1) Construct a periodic load model; Specifically, the system weight is based on an oscillation distribution and is time-varying modulated by a sine function.

[0083] (2) Set the working condition switching point; Specifically, at the 5000th iteration, the system period is switched from T1=5000 to T2=2500, and the weight change amplitude is increased from 0.3 to 0.5, simulating the case of increasing load change.

[0084] (3) Track performance evaluation using DNVSS-FxLMS algorithm.

[0085] Specifically, the tracking speed of the algorithm at the peak point of the weight change rate is observed, and the tracking speed is defined as the number of iterations from the peak of the weight change rate to the re-convergence of the algorithm, and finally the performance comparison of different FxLMS algorithms under periodic load change is obtained as shown in Figure 4 .

[0086] According to Figure 4 , it can be seen that: (a) In the first stage (T1=5000), when the weight change rate reaches the peak at T=2639, the DNVSS-FxLMS algorithm only needs 35 iterations to complete tracking, and the steady-state MSE is -18.1dB; among existing algorithms, the VSSFxLMS-3 algorithm with better performance also needs 225 iterations, and the fixed step FxLMS needs 582 iterations. n n (b) In the second stage (T2=2500), when the weight change rate reaches the peak at T=6329, the DNVSS-FxLMS algorithm needs 87 iterations to complete tracking, and the steady-state MSE is -15.8dB; among existing algorithms, the VSSFxLMS-3 algorithm with better performance still needs 155 iterations.

[0087] (c) During the entire working condition switching process, the MSE fluctuation amplitude of the DNVSS-FxLMS algorithm is the smallest, showing excellent robustness. n n According to the comparison of the present embodiment, the superior tracking performance of the DNVSS-FxLMS algorithm under periodic load change environment is verified. The synergistic effect of the double nonlinear functions enables the algorithm to maintain low steady-state error while quickly responding to periodic changes in system parameters, ensuring reliable application in hydraulic equipment with regular actions.

[0088] According to the comparison of the present embodiment, the superior tracking performance of the DNVSS-FxLMS algorithm under periodic load change environment is verified. The synergistic effect of the double nonlinear functions enables the algorithm to maintain low steady-state error while quickly responding to periodic changes in system parameters, ensuring reliable application in hydraulic equipment with regular actions.

[0089] According to the comparison of the present embodiment, the superior tracking performance of the DNVSS-FxLMS algorithm under periodic load change environment is verified. The synergistic effect of the double nonlinear functions enables the algorithm to maintain low steady-state error while quickly responding to periodic changes in system parameters, ensuring reliable application in hydraulic equipment with regular actions.

[0090] ​​Example 3: Pressure fluctuation control under non-stationary random load In this example, the variable step size FxLMS control system and method based on double non-linear function cooperative coupling are used to regulate the pressure fluctuation of the hydraulic system under non-stationary random load conditions. These conditions are usually complex industrial environments, and further preferred are actual conditions such as multi-load coupling of hydraulic pump stations, multi-actuator cooperative operation, and random external disturbances.

[0091] In this example, a non-stationary random change model is preferably constructed by superimposing sine waves of three different frequency components to simulate the combined effects of various disturbance factors in actual hydraulic systems. The three frequency components are: f 1 = 1 / 3500, f 2 = 1 / 2500, f 3 = 1 / 1000.

[0092] The specific implementation steps are as follows: (1) Construct a complex disturbance model.

[0093] Specifically, the system weight is based on the bell-shaped distribution modulated by three different component sine waves (periods T1 = 3500, T2 = 2500, T3 = 1000, amplitudes A1 = 0.40, A2 = 0.25, A3 = 0.15).

[0094] (2) Algorithm parameter setting.

[0095] Specifically, considering the complexity of the system, the system parameters of the DNVSS-FxLMS algorithm are preferably set as: ; ; At the same time, the order of the adaptive filter L = 64.

[0096] (3) Performance evaluation index.

[0097] In addition to the conventional MSE index, the tracking performance of each algorithm at the peak value point of the weight change rate and the stability during the entire running process are also evaluated in this example, and the comparison results are shown in Figure 5

[0098] According to the MSE curve of Figure 5 , the convergence performance differences of different algorithms in this environment are intuitively displayed. Specifically: (a) At the first peak point of the weight change rate ( n ​=4456), DNVSS-FxLMS algorithm only needs 44 iterations to complete tracking, and MSE is-13.6dB; in the prior art, VSSFxLMS-3 with better performance still needs 95 iterations, and fixed step FxLMS needs 264 iterations.

[0099] (b) at the second peak of the weight change rate (t=0.5s) n =7415), DNVSS-FxLMS algorithm needs 60 iterations to complete tracking, and MSE is-16.4dB; in the prior art, VSSFxLMS-3 with better performance needs 101 iterations.

[0100] (c) During the entire simulation process, the convergence speed of the DNVSS-FxLMS algorithm is at least doubled compared with other algorithms, and the steady-state error is reduced by 2-5dB.

[0101] (d) In the face of irregular weight changes, the DNVSS-FxLMS algorithm shows stable control performance, and the MSE curve fluctuates less, reflecting the strong robustness of the algorithm.

[0102] Through the test of the present embodiment, the superior performance of the DNVSS-FxLMS algorithm in complex non-stationary random environment is fully verified. Through the synergistic effect of the rational fraction term and the exponential term, the algorithm can accurately dynamically adjust the step size according to the error size, ensuring fast convergence while maintaining a low steady-state error. This feature enables the algorithm to effectively adapt to the complex time-varying process of the hydraulic system, providing an efficient and robust solution for active control of hydraulic system pressure pulsation that requires real-time tracking control.

[0103] As can be seen from the foregoing embodiments, the variable step FxLMS regulation system and method based on the synergistic coupling of double nonlinear functions (DNVSS-FxLMS algorithm) in the preferred embodiments can meet the demand for active control of hydraulic pulsation under different hydraulic working conditions. Based on the synergistic effect of the rational fraction term and the exponential term, the algorithm can accurately dynamically adjust the step size according to the error size, ensuring fast convergence while maintaining a low steady-state error. In practical applications, it exhibits significant performance advantages, providing a new technical approach for active control of hydraulic system pressure pulsation, and has excellent application prospects and economic value.

[0104] Those skilled in the art will readily understand that the above description is only of the preferred embodiments of the present application and is not intended to limit the present application, and any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A variable step size FxLMS control system based on dual nonlinear function synergistic coupling, characterized in that, Comprising: a reference sensor, which can be installed at the vibration source position, for collecting a pressure pulsation reference signal of the vibration source and transmitting it in real time to the adaptive filter and the controller; An error sensor is arranged at a target position where pressure pulsation needs to be suppressed, and is arranged at a position spaced apart from the reference sensor on the hydraulic pipeline to detect an error signal of the target position and feeds back the error signal to the controller in real time to form a closed-loop control a primary path for characterizing a natural propagation path of pressure pulsations from a source location to a target location; a secondary channel comprising a signal propagation path from a controller output to said target location, including an actuator and a conduit from the actuator to an error sensor for converting a control signal into an actual pressure pulsation suppression signal ; An adaptive filter is provided on the secondary path for generating a control signal based on a reference signal generating a control signal ; a controller connected with the reference sensor, the error sensor and the actuator respectively, for generating and outputting a control signal to the actuator according to the error signal dynamically adjusting the step size , generating and outputting a control signal to the actuator while monitoring the system state in real time; and the function of the step size is: wherein is a rational fraction term; is an exponential term; is a maximum step size, is an exponential parameter, is a rational fraction parameter; is an error signal, and wherein is a reference signal is an output signal after propagation through a primary channel, is a control signal is an output signal after propagation through a secondary channel.

2. The variable step size FxLMS control system based on the cooperative coupling of dual nonlinear functions according to claim 1, characterized in that, The adaptive filter is a FIR transversal filter.

3. A variable step size FxLMS control method based on the cooperative coupling of double nonlinear functions, which can be used for the control of pressure pulsation in a hydraulic system by using the variable step size FxLMS control system based on the cooperative coupling of double nonlinear functions according to claim 1 or 2; characterized in that, The method comprises the following steps: (1) setting the order of the adaptive filter L , given the adjustment parameters of the double nonlinear function , and ; (2) determining a reference signal vector; (3) The control system is initialized, and the reference signal vector is passed through an adaptive filter to obtain a control signal : (4) the control signal the output signal after propagation through the secondary channel is superimposed with the desired signal to obtain an error signal and the error signal is fed back to the controller (5) the controller updates the weight vector based on the error signal updates the weight vector for the next time instant; (6) updating the step size of the adaptive filter based on a function of the step size; (7) repeating steps (2)-(6) until the control system reaches a steady state.

4. The variable step-size FxLMS control method based on the cooperative coupling of dual nonlinear functions according to claim 3, characterized in that, In step (1), the initial weight vector of the adaptive filter is set to ; And / or satisfies ; where is the maximum eigenvalue of the reference signal autocorrelation matrix.

5. The variable step-size FxLMS control method based on the cooperative coupling of dual nonlinear functions according to claim 3, characterized in that, In step (2), the reference signal vector of the component is: 。 6. The variable step size FxLMS control method based on the cooperative coupling of dual nonlinear functions according to any one of claims 3-5, characterized in that, In step (3), the control signal is: In the formula, is a control signal obtained after the reference signal vector passes through the adaptive filter; is a reference signal collected by a reference sensor; is a transpose of is a transpose of is a transpose of n is an adaptive filter weight vector at the moment, and .

7. The variable step size FxLMS control method based on the cooperative coupling of dual nonlinear functions according to any one of claims 3-5, characterized in that, In step (4), the output signal is: wherein is the secondary channel impulse response; denotes a convolution operation.

8. The variable step size FxLMS control method based on the cooperative coupling of dual nonlinear functions according to any one of claims 3-5, characterized in that, In step (4), the desired signal The following formula is represented: wherein is the pressure pulsation signal through the primary channel; is the introduced random white noise.

9. The variable step size FxLMS control method based on the cooperative coupling of dual nonlinear functions according to any one of claims 3-5, characterized in that, In step (5), the update calculation n The adaptive filter weight vector at time +1 is: wherein is n a step factor of the adaptive filter at time instant is n an adaptive filter weight vector at time instant is a secondary path estimate model a filtered reference signal vector, obtained by filtering a reference signal by the estimated secondary path is filtered and .

10. The variable step size FxLMS control method based on the cooperative coupling of dual nonlinear functions according to any one of claims 3-5, characterized in that, In steps (1) and (6), the values of the respective adjustment parameters are derived from empirical values obtained from simulation experiments.

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