Signal gain adaptive control method based on dynamic feedback

Abstract

The invention provides a signal gain self-adaptive control method based on dynamic feedback, which relates to the technical field of self-adaptive control, and comprises the following steps: carrying out initial gain control on an input signal to obtain a system output signal; the feedback quantity of the system output signal is collected, and the filtered actual output signal is obtained through filtering processing; based on the expected output signal and the actual output signal, calculating multi-order errors, including an amplitude error, a first-order derivative error and a second-order derivative error; calculating a collaborative weighting function according to the multi-order error; constructing a comprehensive error cost function based on the multi-order error and the collaborative weighting function; according to gradient information of the comprehensive error cost function and a product term of a second derivative error and a collaborative weighting function, updating a gain parameter by adopting a dynamic step length; and performing gain control on the input signal by using the updated gain parameter to obtain a new system output signal. According to the invention, dynamic self-adaptive adjustment of signal gain parameters can be realized, so that the response capability of the system to rapid dynamic change is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of adaptive control, and particularly to a signal gain adaptive control method based on dynamic feedback. Background Art

[0002] A signal gain amplifier is a key component in a signal processing system, mainly used to amplify an input signal by a certain ratio to meet the requirements of subsequent processing circuits. In practical applications, the signal gain amplifier not only needs to ensure linear amplification of the signal, but also needs to have anti-interference ability and dynamic adjustment ability to adapt to changes in different working environments and signal characteristics.

[0003] With the development of industrial control and signal processing technologies, signal gain control technology has gradually evolved from simple fixed gain control to adaptive gain control. Traditional adaptive gain control is mainly based on the error feedback principle, adjusts the gain parameters by calculating the output error in real time, and uses optimization methods such as gradient descent to achieve automatic adjustment of system parameters to improve control accuracy and system stability.

[0004] However, existing signal gain control technologies still have some deficiencies in dealing with complex industrial processes: First, traditional single error feedback is difficult to cope with the rapid dynamic changes of the system; second, fixed control parameters cannot adapt to frequent changes in the operating point; finally, in the presence of high-frequency disturbances and nonlinear characteristics, conventional control methods are difficult to ensure ideal control effects. These problems severely restrict the application of signal gain control technology in the field of high-precision control. Summary of the Invention

[0005] In view of this, the present invention proposes a signal gain adaptive control method based on dynamic feedback. By constructing a multi-order error system and a collaborative weight function, combined with a predictive control strategy, it realizes dynamic adaptive adjustment of signal gain parameters to improve the system's response ability to rapid dynamic changes, enhance the adaptability of the control system in the presence of high-frequency disturbances and nonlinear characteristics, and at the same time ensure the stability and control accuracy of the system under large disturbance conditions.

[0006] The technical solution of the present invention is implemented as follows:

[0007] The present invention provides a signal gain adaptive control method based on dynamic feedback, including:

[0008] S1. Perform initial gain control on the input signal to obtain a system output signal;

[0009] S2. Collect the feedback amount of the system output signal and obtain the filtered actual output signal through filtering processing;

[0010] S3. Calculate multi - order errors based on the expected output signal and the actual output signal, where the multi - order errors include amplitude error, first - derivative error, and second - derivative error;

[0011] S4. Calculate a collaborative weight function according to the multi - order errors, and the collaborative weight function is dynamically adjusted with the change of the multi - order errors;

[0012] S5. Construct a comprehensive error cost function based on the multi - order errors and the collaborative weight function;

[0013] S6. Update the gain parameter with a dynamic step size according to the gradient information of the comprehensive error cost function and the product term of the second - derivative error and the collaborative weight function;

[0014] S7. Perform gain control on the input signal using the updated gain parameter to obtain a new system output signal.

[0015] Based on the above - mentioned solution, preferably, the filtering process in step S2 uses an extended Kalman filter for noise and interference suppression.

[0016] Based on the above - mentioned solution, preferably, in step S3:

[0017] The amplitude error is the difference between the expected output signal and the actual output signal;

[0018] The first - derivative error is the first - order derivative with respect to time of the difference between the expected output signal and the actual output signal;

[0019] The second - derivative error is the second - order derivative with respect to time of the difference between the expected output signal and the actual output signal.

[0020] Based on the above - mentioned solution, preferably, the collaborative weight function is obtained by multiplying the absolute values of the amplitude error, the first - derivative error, and the second - derivative error by their corresponding coupling coefficients respectively, then summing them up and performing an exponential operation. Its calculation formula is as follows:

[0021]

[0022] In the formula, S(t) is the collaborative weight function, which varies with time; e(t) is the amplitude error; is the first - derivative error; is the second - derivative error; μ1, μ2, μ3 are coupling coefficients; exp represents the exponential operation; t represents the current moment.

[0023] Based on the above - mentioned solution, preferably, the coupling coefficients μ1, μ2, μ3 are used to measure the coupling degree of each - order error to the system dynamics. When the second - derivative error is large or the first - derivative error surges, the collaborative weight function increases accordingly.

[0024] Based on the above solution, preferably, the comprehensive error cost function is:

[0025]

[0026] In the formula, J total (t) is the comprehensive error cost function; e(t) is the amplitude error; is the first derivative error; is the second derivative error; S(t) is the collaborative weight function, which varies with time; γ1 and γ2 are basic weight coefficients; t represents the current moment.

[0027] Based on the above solution, preferably, the method further includes:

[0028] After step S2 and before step S3, use an autoregressive model or a recurrent neural network to perform short-term prediction on the actual output signal to obtain a predicted output signal, and calculate the prediction error between the predicted output signal and the desired output signal;

[0029] In step S5, add the square term of the prediction error as an additional calculation term to the comprehensive error cost function.

[0030] Based on the above solution, preferably, the update formula for the gain parameter in step S6 is:

[0031]

[0032] In the formula, ΔK(t) is the gain parameter update amount; η(t) is the dynamic step size; is the collaborative compensation term; ρ is the compensation coefficient, used to amplify the influence of the second-order error; J total (t) is the comprehensive error cost function; is the second derivative error; is the gradient operator; is the gradient of the comprehensive error cost function with respect to the gain parameter; t is the current moment.

[0033] Based on the above solution, preferably, the update rule for the dynamic step size η(t) is:

[0034]

[0035] In the formula, η(t + 1) is the dynamic step size at the next moment; η(t) represents the dynamic step size at the current moment; δ is the step size adjustment coefficient, used to control the sensitivity of the step size change; sign(·) is the sign function, which outputs 1 when the input is positive, -1 when the input is negative, and 0 when the input is zero; clip[·] represents the clipping function to ensure η(t) + δ· The value is restricted to η min and η max ; η min represents the minimum allowable step size; η max represents the maximum allowable step size.

[0036] Based on the above solution, preferably, the method further includes a system stability analysis step:

[0037] Construct an extended Lyapunov function considering the influence of the cooperative compensation term to evaluate the overall energy change of the system. The extended Lyapunov function includes a quadratic term of the system state and a constraint term related to the comprehensive error function;

[0038] Based on the time derivative of the extended Lyapunov function and combined with the constraint conditions of the dynamic step size and cooperative compensation, derive the system stability criterion;

[0039] By verifying whether the stability criterion satisfies the negative definite condition, ensure the asymptotic stability of the system under large disturbances and non-linear working conditions.

[0040] The present invention has the following beneficial effects compared with the prior art:

[0041] (1) By constructing a multi-order error system and a cooperative weight function, and combining a predictive control strategy and a dynamic step size update mechanism, the present invention realizes the adaptive adjustment of the signal gain parameter, significantly improves the response ability of the system to rapid dynamic changes, and at the same time ensures the control accuracy, enabling the system to still operate stably under large disturbances and non-linear working conditions;

[0042] (2) Using a multi-order error system (including amplitude error, first derivative error, and second derivative error) for control can more comprehensively reflect the dynamic characteristics of the system compared with traditional single error feedback, and effectively improve the tracking ability of the system to high-order dynamic changes;

[0043] (3) Introducing the cooperative weight function S(t) and dynamically adjusting the weights of each order of error in an exponential form enables the control system to adaptively adjust the control strategy according to the error characteristics, effectively balancing the requirements of the system for fast response and stability;

[0044] (4) Introducing a prediction error term into the comprehensive error cost function and using an autoregressive model or a recurrent neural network for short-term prediction enhances the forward-looking control ability of the system, reduces the lag effect of the system, and improves the real-time performance of control;

[0045] (5) Through the introduction of a dynamic step size update mechanism and a cooperative compensation term, the system can adaptively adjust the control parameters according to the error gradient information, which not only ensures fast convergence when there is a large error but also ensures the control accuracy when there is a small error, improving the adaptive ability of the system. Brief Description of the Drawings

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0047] Figure 1 It is the flowchart of the method of the present invention;

[0048] Figure 2 It is the technical implementation diagram of the present invention. Detailed Embodiments

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0050] As Figure 1 shown, the present invention provides a signal gain adaptive control method based on dynamic feedback, including:

[0051] S1. Perform initial gain control on the input signal to obtain a system output signal;

[0052] S2. Collect the feedback amount of the system output signal and obtain the filtered actual output signal through filtering processing;

[0053] S3. Calculate multi-order errors based on the desired output signal and the actual output signal, where the multi-order errors include amplitude error, first-order derivative error, and second-order derivative error;

[0054] S4. Calculate a collaborative weight function according to the multi-order errors, and the collaborative weight function is dynamically adjusted according to the change of the multi-order errors;

[0055] S5. Construct a comprehensive error cost function based on the multi-order errors and the collaborative weight function;

[0056] S6. Update the gain parameter with a dynamic step according to the gradient information of the comprehensive error cost function and the product term of the second-order derivative error and the collaborative weight function;

[0057] S7. Use the updated gain parameter to perform gain control on the input signal to obtain a new system output signal.

[0058] Please refer to Figure 2 , the present invention provides a signal gain adaptive control method based on dynamic feedback. The core technical idea is as follows: By constructing a multi-order error system including amplitude error, first derivative error, and second derivative error, introducing a collaborative weight function S(t) based on exponential operation to dynamically weight each order of error, and combining the prediction error to construct a comprehensive error cost function; when updating the gain parameter, a dynamic step size mechanism is adopted and a collaborative compensation term (the product of the second derivative error and the collaborative weight function) is introduced to achieve accurate tracking of fast dynamic changes by the system and effective suppression of nonlinear disturbances; at the same time, through the stability analysis of the extended Lyapunov function, the asymptotic stability of the system under large disturbance conditions is ensured.

[0059] Specifically, in an embodiment of the present invention, step S1 includes:

[0060] First, set the initial gain parameter K0 of the system. The selection of this initial gain parameter needs to consider the actual working conditions of the system. Usually, it can be set according to the rated working range of the system, and the recommended value range is a positive number between 0.1 and 10. A larger initial gain value is suitable for the case where the amplitude of the input signal is small, and a smaller initial gain value is suitable for the case where the amplitude of the input signal is large.

[0061] Let u(t) be the system input or desired trajectory reference signal, and the system simply amplifies / attenuates it initially.

[0062] For the input signal u(t), the system output signal y(t) is obtained through the following calculation:

[0063] y(t) = u(t)·K0

[0064] where, u(t) is the system input signal, which can be an analog signal (such as voltage, current, etc.) or a sampled discrete signal; K0 is the initial gain parameter; y(t) is the system output signal.

[0065] Specifically, in an embodiment of the present invention, step S2 includes:

[0066] First, collect the system output signal y(t) output by step S1. During the collection process, the selection of the sampling frequency needs to satisfy the Nyquist sampling theorem, that is, the sampling frequency should not be lower than 2 times the highest frequency component of the signal. In practical applications, the sampling frequency is set to 5 - 10 times the highest frequency of the signal to ensure the sampling quality. The collected feedback quantity is denoted as y m (t).

[0067] Next, use the extended Kalman filter (EKF) to filter the collected signal. The specific implementation of the EKF includes the following steps:

[0068] 1. State prediction:

[0069]

[0070] P(t|t - 1) = F(t)P(t - 1|t - 1)F'(t) + Q(t)

[0071] Wherein, is the state estimation value, is the state prediction value at time t based on the information at time t - 1, is the state estimation value at time t - 1, P(t|t - 1) is the prediction error covariance matrix, F(t) is the Jacobian matrix of the state transition matrix, Q(t) is the process noise covariance matrix, F'(t) is the transpose matrix of F(t), and f(·) is the state prediction function for predicting the state at the next moment.

[0072] 2. Measurement update:

[0073] K(t) = P(t|t - 1)H'(t)[H(t)P(t|t - 1)H'(t) + R(t)] -1

[0074]

[0075] P(t|t) = [I - K(t)H(t)]P(t|t - 1)

[0076] Wherein, K(t) is the Kalman gain matrix for weighing the credibility of the predicted value and the measured value; H(t) is the Jacobian matrix of the observation matrix describing the relationship between the state and the measurement; H'(t) is the transpose matrix of H(t); R(t) is the measurement noise covariance matrix characterizing the uncertainty of the measurement; is the state estimation value at time t; h(·) is the observation function mapping the state space to the observation space; P(t|t) is the updated error covariance matrix; I is the identity matrix.

[0077] Specifically, the parameter settings of the EKF are as follows:

[0078] Initial state estimation value can be set as the first measured value; the initial error covariance matrix P(0|0) can be set as the identity matrix multiplied by a large positive number (such as 100); the process noise covariance matrix Q(t) and the measurement noise covariance matrix R(t) can be calibrated offline according to the actual system noise characteristics.

[0079] Meanwhile, the operating point perception is also required during the filtering process. The specific method is:

[0080] Monitor the rate of change of the amplitude of the output signal. When the rate of change exceeds a preset threshold, it is considered that the operating point of the system has changed significantly; record the characteristic parameters of the current operating point (such as signal amplitude, frequency, etc.) to provide a reference for subsequent gain parameter updates. After the above processing, the filtered actual output signal y(t) is obtained, and this signal will be used as the input of step S3 for the calculation of multi-order errors. The filtered signal has the following characteristics: effectively suppressing measurement noise and external interference; maintaining the dynamic characteristics of the signal; providing reliable operating point information.

[0081] Specifically, in an embodiment of the present invention, step S3 includes:

[0082] Based on the desired output signal y d (t) and the actual output signal y(t), calculate the multi-order errors. Specifically, it includes:

[0083] Amplitude error, where the amplitude error is the difference between the desired output signal and the actual output signal:

[0084]

[0085] First derivative error, where the first derivative error is the first derivative with respect to time of the difference between the desired output signal and the actual output signal:

[0086]

[0087] Second derivative error, where the second derivative error is the second derivative with respect to time of the difference between the desired output signal and the actual output signal:

[0088]

[0089] In engineering implementation, numerical differentiation methods can be used to calculate the derivative errors. For the first derivative error, a backward difference format can be used:

[0090]

[0091] where Ts is the sampling period. For the second derivative error, a central difference format can be used:

[0092]

[0093] Correspondingly, step S4 includes:

[0094] Calculate the collaborative weight function S(t) according to the multi-order errors. The collaborative weight function is obtained by multiplying the absolute value of the amplitude error, the absolute value of the first derivative error, and the absolute value of the second derivative error by the corresponding coupling coefficients respectively, summing them up, and then performing an exponential operation. Its calculation formula is as follows:

[0095]

[0096] Wherein, S(t) is the collaborative weight function, which varies with time; e(t) is the amplitude error; is the first derivative error; is the second derivative error; μ1, μ2, and μ3 are coupling coefficients; exp represents the exponential operation; t represents the current time.

[0097] The coupling coefficients μ1, μ2, and μ3 are used to measure the coupling degree of each order of error to the system dynamics. When the second derivative error is large or the first derivative error surges, the collaborative weight function increases accordingly. Specifically, μ1: 0.1 - 1.0, mainly reflecting the influence of the steady-state error; μ2: 0.05 - 0.5, reflecting the dynamic response characteristics of the system; μ3: 0.01 - 0.1, reflecting the influence of the system acceleration change.

[0098] Correspondingly, step S5 includes:

[0099] Constructing an integrated error cost function based on the multi-order error and the collaborative weight function:

[0100]

[0101] Wherein, J total (t) is the integrated error cost function; e(t) is the amplitude error; is the first derivative error; is the second derivative error; S(t) is the collaborative weight function, which varies with time; γ1, γ2 are basic weight coefficients; t represents the current time.

[0102] Specifically, in another embodiment of the present invention, after step S2 and before step S3, a short-term prediction is performed on the actual output signal by using an autoregressive model or a recurrent neural network to obtain a predicted output signal, and the prediction error between the predicted output signal and the desired output signal is calculated;

[0103] In step S5, the square term of the prediction error is added as an additional calculation term to the integrated error cost function.

[0104] Specifically, in this embodiment, first, a short-term prediction is performed on the actual output signal by using an autoregressive model or a recurrent neural network. The specific prediction method is as follows:

[0105] Autoregressive model prediction:

[0106] Using a p-order autoregressive model AR(p), the predicted output signal can be expressed as:

[0107]

[0108] Wherein, a iis the autoregressive coefficient, which can be calibrated offline by the least squares method; p is the model order, usually taken as 3 - 5; Ts is the sampling period.

[0109] Recurrent neural network prediction:

[0110] Adopt a simple recurrent neural network (RNN) structure. The input is the output sequence of the most recent n sampling points, and the output is the predicted value. The number of hidden layer nodes of the RNN is 10 - 20, and the tanh activation function is adopted.

[0111] Prediction error calculation:

[0112]

[0113] After calculating the prediction error, combine the multi - order error with the collaborative weight function and introduce the prediction error term. At this time, the comprehensive error cost function is defined as follows:

[0114]

[0115] In the formula, S(t): collaborative weight function, which varies with time / state; γ1, γ2: basic weight coefficients; e p (t + Δt): prediction error, balanced by the coefficient λ, and the value range of λ is 0.1 - 1.0. A larger λ value is suitable for occasions where the system has obvious lag characteristics, and a smaller λ value is suitable for occasions where the system has a fast dynamic response.

[0116] When implementing in engineering, the selection of the prediction time interval Δt needs to consider the characteristic time constant of the system, usually taken as 3 - 5 times the sampling period. At the same time, to ensure the real - time performance of the prediction, it is recommended to adopt the sliding time window method to update the parameters of the prediction model regularly.

[0117] Specifically, in an embodiment of the present invention, a system stability analysis step is added before step S6:

[0118] Construct an extended Lyapunov function considering the influence of the collaborative compensation term to evaluate the overall energy change of the system. The extended Lyapunov function includes the quadratic form term of the system state and the constraint term related to the comprehensive error function;

[0119] Based on the time derivative of the extended Lyapunov function, combined with the constraint conditions of the dynamic step size and collaborative compensation, deduce the system stability criterion;

[0120] By verifying whether the stability criterion satisfies the negative definite condition, ensure the asymptotic stability of the system under large disturbances and nonlinear working conditions.

[0121] In a specific example, the process of stability analysis includes:

[0122] 1. Construct an extended Lyapunov function:

[0123]

[0124] where: x is the system state vector, including the error e(t) and its derivative terms; P is a symmetric positive definite matrix, which can be obtained by solving the Lyapunov equation; Γ(J total ) is a constraint term related to the comprehensive error cost function; J total is the comprehensive error cost function constructed in step S5.

[0125] 2. Derive the stability criterion:

[0126] Based on the time derivative of the above extended Lyapunov function:

[0127]

[0128] Combined with the constraint conditions of the dynamic step size η(t) and the cooperative compensation term :

[0129] The value range of η(t): η min ≤ η(t) ≤ η max ; The constraint of the compensation coefficient ρ: 0 < ρ < ρ max ; The boundedness of the cooperative weight function S(t): 1 ≤ S(t) ≤ S max .

[0130] Derive the stability criterion:

[0131]

[0132] where λ > 0 represents the final convergence speed factor. ||e|| represents the norm of the error vector, and e includes the amplitude error, the first derivative error, and the second derivative error.

[0133] 3. Verify the stability conditions:

[0134] To ensure the asymptotic stability of the system under large disturbances and non - linear conditions, the following conditions need to be verified:

[0135] (1) Dynamic step size constraint:

[0136]

[0137] Satisfy: 0 < η min ≤ η(t) ≤ η max .

[0138] (2) Cooperative compensation constraint:

[0139]

[0140] where M is a positive upper bound constant.

[0141] (3) Comprehensive stability condition:

[0142]

[0143] When the above conditions are satisfied simultaneously, the asymptotic stability of the system can be guaranteed.

[0144] Specifically, in an embodiment of the present invention, the specific implementation of step S6 is as follows:

[0145] First, according to the comprehensive error cost function J total (t) obtained in step S5, calculate its gradient with respect to the gain parameter This gradient information reflects the direction and magnitude of the adjustment required for the gain parameter.

[0146] Secondly, use a dynamic step size η(t) to update the gain parameter. The update rule for the dynamic step size is:

[0147]

[0148] where η(t + 1) is the dynamic step size at the next moment; η(t) represents the dynamic step size at the current moment; δ represents the step size adjustment coefficient, which is used to control the sensitivity of the step size change; sign(·) is the sign function, which outputs 1 when the input is positive, -1 when the input is negative, and 0 when the input is zero; clip[·] represents the clipping function to ensure that the value of is restricted between η min and η max ; η min represents the minimum allowable step size; η max represents the maximum allowable step size.

[0149] Then, combine the product term of the second derivative error and the collaborative weight function S(t) to construct an update formula for the gain parameter:

[0150]

[0151] where ΔK(t) is the gain parameter update amount; η(t) is the dynamic step size; is the collaborative compensation term; ρ is the compensation coefficient, which is used to amplify the influence of the second-order error; J total (t) is the comprehensive error cost function; is the second derivative error; is the gradient operator; is the gradient of the comprehensive error cost function with respect to the gain parameter; t is the current moment.

[0152] This update formula consists of two parts:

[0153] Gradient descent term Based on the gradient information of the comprehensive error cost function, a basic adjustment is made; the collaborative compensation term If is very large and S(t) is relatively high, it indicates that the system error acceleration and coupling degree are extremely strong, and strong compensation is required; if is small or S(t) is close to 1, the system is in a stable or normal state, and no additional strong compensation is necessary.

[0154] Finally, update the gain parameter:

[0155] K(t + 1) = K(t) + Δk(t)

[0156] In the specific implementation, the following measures are taken: perform amplitude limiting processing on the gain parameter K(t + 1) to ensure that it is within the range allowed by the system; when the system tends to a stable state (both the error and its derivative are very small), the step size can be appropriately reduced to avoid parameter jitter.

[0157] The output gain parameter K(t + 1) of this step will be used in step S7 to perform gain control on the input signal. Through the cooperation of the dynamic step size and collaborative compensation, both the fast response ability of the system to large disturbances and the stability in the small error region are ensured.

[0158] Specifically, in a specific embodiment of the present invention, step S6 can also utilize the segmented idea and adopt different update strategies for error signals in different ranges, so as to reduce the response time in the large error region and suppress the oscillation caused by high gain in the small error region. The implementation process is as follows:

[0159] Classify according to the amplitude error |e(t)| or the system operating point, and define multiple working intervals, such as:

[0160] Large error interval Ω1: |e(t)| > θ1, medium error interval Ω2: θ2 ≤ |e(t)| ≤ θ1, small error interval Ω3: |e(t)| < θ2; where θ1 > θ2 > 0 are error thresholds.

[0161] Then, adopt a dynamic step size update mechanism to update the dynamic step size η(t) according to the above update rules:

[0162]

[0163] Among them, the step size adjustment coefficient δ takes different values in different error intervals. For example, in the large error interval Ω1: δ = 0.01, in the medium error interval Ω2: δ = 0.005, and in the small error interval Ω3: δ = 0.001.

[0164] Next, calculate the update amount ΔK(t) of the gain parameter:

[0165]

[0166] Among them, the compensation coefficient ρ takes different values in different error intervals. For example, in the large error interval Ω1: ρ = 0.1, in the medium error interval Ω2: ρ = 0.05, and in the small error interval Ω3: ρ = 0.01.

[0167] Finally, update the gain parameter K(t + 1) = K(t) + ΔK(t).

[0168] Specifically in implementation, when the system continuously operates in the Ω3 interval for more than a preset time (such as 10 sampling periods), the step size adjustment coefficient δ can be appropriately reduced to avoid parameter jitter; when the system suddenly changes from the Ω3 interval to the Ω1 interval, the compensation coefficient ρ is temporarily increased (such as doubled) to provide a stronger correction effect.

[0169] Specifically, in an embodiment of the present invention, the specific implementation of step S7 is as follows:

[0170] First, obtain the gain parameter K(t + 1) updated in step S6 and perform gain control on the input signal u(t). The calculation formula for the new system output signal y(t + 1) is:

[0171] y(t + 1) = k(t + 1)·u(t)

[0172] In engineering implementation, the following measures are taken:

[0173] Gain parameter limit protection:

[0174] Before applying the updated gain parameter K(t + 1), perform limit processing:

[0175] K(t + 1) = clip[K(t + 1), K min , K max

[0176] Among them: K min is the allowable minimum gain value; K max is the allowable maximum gain value; clip[·] represents the limit function.

[0177] Soft start strategy:

[0178] When it is detected that the gain parameter changes greatly (such as |K(t + 1) - K(t)| > ΔK th ), adopt a progressive transition:

[0179] K'(t + 1) = K(t) + α·[K(t + 1) - K(t)]

[0180] ​Where: ΔK th is the gain change threshold, with a value of 10% - 20% of the current gain; α is the smoothing coefficient, with a value range of 0.1 - 0.5; K'(t + 1) is the gain value actually applied.

[0181] Output signal protection:

[0182] Perform amplitude limiting and slope limiting on the system output signal:

[0183] Amplitude limiting: Ensure that the output signal y(t + 1) does not exceed the system - allowed range [y min , y max .

[0184] Rate - of - change limiting: |y(t + 1)-y(t)|≤Δy max , where Δy max is the maximum allowable rate of change.

[0185] Steady - state judgment and processing:

[0186] Set the steady - state judgment conditions:

[0187] Amplitude error |e(t)|<ε s ; first - order derivative error second - order derivative error where ε s , ε d , ε a are the corresponding steady - state thresholds.

[0188] When the system meets the steady - state conditions for a preset time Ts (such as 10 sampling periods): The gain parameters can be fixed, the update can be paused; the sampling frequency can be reduced to reduce the computational burden; the current operating - point parameters can be recorded for subsequent rapid recovery.

[0189] Abnormal - handling mechanism: When the output signal exceeds the amplitude - limiting range, the gain parameters are automatically reduced; when severe oscillation of the output is detected, a soft - start strategy is triggered; when the system cannot converge for a long time, it automatically reverts to a conservative gain setting.

[0190] Through the above implementation method, step S7 not only ensures the stable and controllable output of the system but also provides a reliable initial state for the next round of iteration. The new system output signal y(t + 1) output by this step will be used as the feedback quantity for the next - round control, and the processing of step S2 will continue, thus forming a complete adaptive - control closed - loop.

[0191] Specifically, the adaptive - control method of the present invention can be implemented based on the following hardware system:

[0192] 1. Signal acquisition unit: A high-precision ADC (such as a 16-bit or 24-bit ADC) is used to acquire the input signal u(t); a multi-channel sampling circuit with a sampling frequency not less than 10 kHz; anti-interference design: a signal conditioning circuit including a low-pass filter and an isolation amplifier.

[0193] 2. Core processing unit: A main controller implemented by a monolithic integrated digital circuit; integrated with a 32-bit fixed-point arithmetic unit and a hardware multiplier array; on-chip dual-port RAM for data caching and intermediate result storage; a clock frequency of 100 MHz to achieve the optimal area and power consumption of the system.

[0194] 3. Control output unit: A high-precision DAC (such as a 16-bit DAC) is used to output the control signal; a PWM output circuit (with adjustable frequency and resolution ≥ 12 bits); an output protection circuit.

[0195] In a specific example, taking the signal amplitude control system as an example, the digital-analog circuit is monolithically integrated; the sampling circuit integrates a 16-bit synchronous sampling ADC; the output driver integrates a 16-bit DAC. The signal processing flow is as follows: (1) Acquire feedback signals such as signal voltage and frequency; (2) Execute the adaptive gain control algorithm of the present invention; (3) Modulate and output the control signal through a high-speed integrated DAC circuit; (4) Achieve signal amplitude and eye diagram control.

[0196] Through the above hardware implementation method, the adaptive gain control method of the present invention can achieve high-precision, low-latency real-time control, and has good system integration and cost-effectiveness.

[0197] The above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A signal gain adaptive control method based on dynamic feedback, characterized in that Including: S1. Perform initial gain control on the input signal to obtain the system output signal; S2. Collect the feedback amount of the system output signal and obtain the filtered actual output signal through filtering processing; S3. Calculate multi-order errors based on the desired output signal and the actual output signal, where the multi-order errors include amplitude error, first derivative error, and second derivative error; S4. Calculate the collaborative weight function according to the multi-order errors, and the collaborative weight function is dynamically adjusted with the change of the multi-order errors; S5. Construct an integrated error cost function based on the multi-order errors and the collaborative weight function; S6. Update the gain parameter with a dynamic step size according to the gradient information of the integrated error cost function and the product term of the second derivative error and the collaborative weight function; S7. Perform gain control on the input signal using the updated gain parameter to obtain a new system output signal.

2. The method for adaptively controlling signal gain based on dynamic feedback according to claim 1, wherein The filtering process in step S2 uses an extended Kalman filter for noise and interference suppression.

3. A signal gain adaptive control method based on dynamic feedback according to claim 1, characterized in that In step S3: The amplitude error is the difference between the desired output signal and the actual output signal; The first derivative error is the first derivative with respect to time of the difference between the desired output signal and the actual output signal; The second derivative error is the second derivative with respect to time of the difference between the desired output signal and the actual output signal.

4. A signal gain adaptive control method based on dynamic feedback according to claim 1, characterized in that The collaborative weight function is obtained by multiplying the absolute values of the amplitude error, the first derivative error, and the second derivative error by the corresponding coupling coefficients respectively, summing them up, and then performing an exponential operation. Its calculation formula is as follows: where \(S(t)\) is the collaborative weight function, which varies with time; \(e(t)\) is the amplitude error; is the first derivative error; is the second derivative error; \(\mu_1\), \(\mu_2\), \(\mu_3\) are coupling coefficients; exp represents the exponential operation; \(t\) represents the current time.

5. A signal gain adaptive control method based on dynamic feedback according to claim 4, characterized in that The coupling coefficients μ1, μ2, and μ3 are used to measure the coupling degree of each order of error to the system dynamics. When the second derivative error is large or the first derivative error surges, the collaborative weight function increases accordingly.

6. A signal gain adaptive control method based on dynamic feedback according to claim 3, characterized in that The integrated error cost function is: where J total (t) is the comprehensive error cost function; e(t) is the amplitude error; is the first derivative error; is the second derivative error; S(t) is the collaborative weight function, which varies with time; γ1 and γ2 are the basic weight coefficients; t represents the current time.

7. A method for adaptively controlling signal gain based on dynamic feedback according to claim 3, characterized in that, The method further includes: After step S2 and before step S3, use an autoregressive model or a recurrent neural network to perform short-term prediction on the actual output signal to obtain a predicted output signal, and calculate the prediction error between the predicted output signal and the desired output signal; In step S5, add the square term of the prediction error as an additional calculation term to the integrated error cost function.

8. A signal gain adaptive control method based on dynamic feedback according to claim 1, characterized in that, The gain parameter update formula in step S6 is: where ΔK(t) is the update amount of the gain parameter; η(t) is the dynamic step size; is the collaborative compensation term; ρ is the compensation coefficient for amplifying the influence of the second-order error; J total (t) is the comprehensive error cost function; is the second derivative error; is the gradient operator; is the gradient of the comprehensive error cost function with respect to the gain parameter; t is the current time.

9. A signal gain adaptive control method based on dynamic feedback according to claim 8, characterized in that The update rule of the dynamic step size η(T) is: In the formula, η(t + 1) is the dynamic step size at the next moment; η(t) represents the dynamic step size at the current moment; δ represents the step size adjustment coefficient, which is used to control the sensitivity of the step size change; sign(·) is the sign function, which outputs 1 when the input is positive, -1 when the input is negative, and 0 when the input is zero; clip[·] represents the clipping function to ensure that the value of is restricted to η min and η max ; η min represents the minimum allowable step size; η max represents the maximum allowable step size.

10. A signal gain adaptive control method based on dynamic feedback according to claim 1, characterized in that, The method further includes a system stability analysis step: Construct an extended Lyapunov function considering the influence of the collaborative compensation term to evaluate the overall energy change of the system. The extended Lyapunov function includes a system state quadratic term and a constraint term related to the integrated error function; Based on the time derivative of the extended Lyapunov function, combined with the constraint conditions of the dynamic step size and collaborative compensation, deduce the system stability criterion; Verify whether the stability criterion satisfies the negative definite condition to ensure the asymptotic stability of the system under large disturbances and nonlinear working conditions.

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