Low-noise disturbance suppression method based on performance-oriented neural network estimator

Abstract

The invention discloses a low-noise disturbance suppression method based on a performance neural network estimator, and the method comprises the steps: constructing a reference trajectory tracking control system based on the PONN estimator, and the system comprises an internal model controller, a state observer, a controlled object, the PONN-based estimator, and a state feedback controller; the estimator based on the PONN is composed of a PONN neural network and a performance-oriented learning strategy module; the performance-oriented learning strategy module is used for updating the weight of the PONN; based on the constructed control system, obtaining a basic learning strategy of a performance-oriented learning strategy module by using a BP optimization algorithm; optimizing a basic learning strategy by adding a dynamic factor and an adjustable function; and on the basis of the optimized learning strategy, the weight of the PONN is updated, and an estimator of the PONN with the updated weight is used for controlling a controlled object to suppress low-noise disturbance.

Description

Technical Field

[0001] The present invention relates to an active disturbance rejection method in the field of control, and particularly to a low-noise disturbance rejection method based on a performance-oriented neural network estimator. Background Art

[0002] In the control of dynamic systems, the presence of unknown disturbances (such as model uncertainties, external disturbances, and nonlinear effects) can significantly affect the performance and stability of the closed-loop system. To address this issue, the equivalent input disturbance (EID) method has been widely applied in the field of disturbance rejection due to its characteristic of not requiring prior knowledge of the disturbance input matrix. However, traditional EID methods rely on linear gain adjustment for performance, and high gains are prone to noise sensitivity problems. On the other hand, neural networks, with their powerful nonlinear approximation ability and self-adaptability, have gradually been combined with feedback control to improve the disturbance rejection effect. However, existing neural network-based controllers have limitations in weight update strategies: the backpropagation (BP) algorithm based on gradient descent can optimize performance but lacks closed-loop stability guarantees; while the method based on the Lyapunov stability theorem ensures stability but is difficult to quantify learning performance.

[0003] In addition, existing methods have deficiencies in the balance between disturbance rejection and noise attenuation. The GEID method has a simple structure, but the disturbance estimation accuracy is limited by the linear gain and it is difficult to adapt to complex dynamic environments. The radial basis function (RBF) neural network can approximate any nonlinear function, but its sensitivity to changes near the origin is low and the dynamic response speed is insufficient. At the same time, traditional weight update strategies (such as the BP algorithm with an e correction term) lack an adaptive adjustment mechanism and cannot dynamically optimize the learning rate and damping term according to the disturbance intensity, resulting in performance degradation in strong disturbance or high-frequency noise scenarios.

[0004] Therefore, how to combine neural networks under the original EID framework for more effective unknown disturbance rejection is a problem to be solved by the present invention. Summary of the Invention

[0005] To address the deficiencies in the prior art, the present application proposes a low-noise disturbance rejection method based on a performance-oriented neural network estimator, which can quickly and accurately estimate unknown disturbances, thereby effectively suppressing the influence of disturbances on the system output and significantly improving the anti-disturbance ability of dynamic systems.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A low-noise disturbance rejection method based on a performance neural network estimator, comprising the following steps:

[0008] Step 1: Construct a reference trajectory tracking control system based on a PONN estimator. The system includes an internal model controller, a state observer, a controlled object, a PONN-based estimator, and a state feedback controller. The PONN-based estimator consists of a PONN neural network and a performance-oriented learning strategy module. The performance-oriented learning strategy module is used to update the weights of the PONN neural network.

[0009] Step 2: Based on the constructed control system, use the BP optimization algorithm to obtain the basic learning strategy of the performance-oriented learning strategy module.

[0010] Step 3: Optimize the basic learning strategy by adding dynamic factors and adjustable functions.

[0011] Step 4: Based on the optimized learning strategy, update the weights of the PONN neural network, and use the estimator of the PONN with updated weights for the control of the controlled object to suppress low-noise disturbances.

[0012] Furthermore, the basic learning strategy of the learning strategy module is denoted as:

[0013]

[0014] where, are the estimated values of the ideal weights of the second layer and the first layer of the neural network respectively, represents the derivative of, γ1 and γ2 are both learning rates, C α is a static estimate, y δ is the input of the neural network, is a dynamic function with respect to h is a set composed of the outputs of the first layer of p neural networks.

[0015] Furthermore, the optimized learning strategy is denoted as:

[0016]

[0017] where, τ1 and τ2 are both positive damping coefficients; ξ1 is a small positive constant; ||y δ || is a dynamic factor; Ψ(·) is a generalized adjustable function.

[0018] Furthermore, the adjustable function satisfies:

[0019]

[0020] where, x and y are arbitrary variables in the real number field.

[0021] Furthermore, dynamic factors are added in the static estimation, expressed as:

[0022]

[0023] wherein, is the state of the observation error system after equivalent input disturbance, is the output of the estimator based on PONN, y δ is the input of the neural network, ||y δ || is the dynamic factor; is the inverse of A-LC, A is the controlled object system matrix, L is the observer gain, C is the controlled object output matrix, B is the controlled object input matrix, and J is the cost function of the performance index.

[0024] Furthermore, the mathematical model of the state observer is expressed as:

[0025]

[0026] wherein, L is the observer gain, u F (t), are respectively the state, input, and output of the observer, is, A, B, C are the system matrices with dimensions in each item, and y(t) is the system output of the controlled object.

[0027] Furthermore, the mathematical model of the internal model controller is expressed as:

[0028]

[0029] wherein, x R (t) is the state of the internal model, A R , B R are the internal model constant matrices with appropriate dimensions, r(t) is the reference input, and y(t) is the system output of the controlled object.

[0030] Furthermore, the mathematical model of the state feedback controller is expressed as:

[0031]

[0032] wherein, u F (t) is the output of the state feedback controller, K p and K R are the control gains to be determined in each item, is the state of the observer, x R (t) is the state of the internal model. The beneficial effects of the present invention:

[0033] (1) The present invention uses a PONN-based estimator, which can quickly and accurately estimate unknown interference, thereby effectively suppressing the impact of interference on the system output and significantly improving the anti-interference ability of the dynamic system;

[0034] (2) By introducing an adjustable function into the learning strategy, the present invention achieves a dynamic balance between interference suppression and noise attenuation performance. Under different interference intensities and noise levels, the system can maintain stable performance, avoiding system performance degradation or instability caused by excessive interference or noise. Experimental results show that the response stability of the present invention in a high-noise environment is significantly better than that of the prior art;

[0035] (3) The present invention designs a PONN-based estimator only using the system output, avoiding the need for direct measurement of the internal state of the system, and greatly reducing the complexity and cost of the system. This design enables the present invention to be applicable to a wider range of dynamic systems, especially those complex systems that are difficult to directly measure the internal state, and has high practicality and economy;

[0036] (4) Through an improved BP algorithm and a weight update strategy with stability guarantee, the present invention ensures the stability of the closed-loop system. Compared with traditional neural network control methods based on the BP algorithm, the present invention avoids the problem of system divergence caused by unstable weight updates while ensuring control performance, and improves the reliability and safety of the system;

[0037] (5) By optimizing the control strategy and system configuration, the present invention simplifies the structure of the control system and reduces the complexity of system design and maintenance. Description of the Drawings

[0038] Figure 1 It is a block diagram of a reference trajectory tracking control system incorporating a PONN-based estimator.

[0039] Figure 2 It is equivalent to Figure 1 The equivalent system structure block diagram.

[0040] Figure 3 It is a technical flow chart of the inventive method.

[0041] Figure 4 Schematic diagram of simulation and experimental results.

[0042] Figure 5 It is a comparison chart of the simulation effects of the present invention and other existing methods. Detailed Embodiments

[0043] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0044] The present invention proposes a low-noise disturbance suppression method based on a performance neural network estimator, comprising the following steps:

[0045] Step 1: Construct a reference trajectory tracking control system based on the PONN estimator. The control system block diagram is as follows: Figure 1 、 2 As shown in Figure 1, it includes an internal model controller, a state observer, a controlled object, a PONN-based estimator, and a state feedback controller; the details are as follows:

[0046] (1) Mathematical modeling of the controlled object. In this embodiment, a motor-to-drag experimental platform is used as the controlled object, and the mathematical model of the motor-to-drag experimental platform is constructed as an example for introduction.

[0047] The mathematical model of the controlled object is as follows:

[0048]

[0049] in, and are the state, control input and system output of the system respectively; A, B and C are the system matrices with dimensions respectively; is the aggregate disturbance, which may include external disturbances, unmodeled dynamics, uncertainties, etc.; B g is the unknown input matrix of g(t).

[0050] Assume that the controlled object (A, B, C) can be controlled and observed, and the disturbance is bounded and satisfies ||g(t)||≤g max , g max is an unknown constant.

[0051] (2) The state observer is used to reconstruct the system. The mathematical model of the state observer is expressed as follows:

[0052]

[0053] Where L is the observer gain, u F (t), are the state, input, and output of the observer respectively.

[0054] (3) In order to effectively track the trajectory, the control system also designs an internal model controller, whose mathematical model is expressed as:

[0055]

[0056] where x R (t) is the state of the internal model, A R , B R are internal model constant matrices of appropriate dimensions, and r(t) is the reference input.

[0057] (4) The mathematical model of the state feedback controller is usually designed as:

[0058]

[0059] where K p and K R are control gains to be determined for each item.

[0060] (5) Construct an estimator based on PONN. The estimator based on PONN consists of a PONN neural network and a performance-oriented learning strategy module, and is specifically described as follows:

[0061] The PONN neural network consists of multiple layers, and the structure of each layer is as follows:

[0062] Define the first layer of the neural network as:

[0063]

[0064] where y δ is the input of the neural network, denoted as y is the output of the controlled object, is the output of the state observer; c i is the center vector of the i-th neuron, denoted as, N y is the number of neurons in the center vector; d i is the width of the i-th neuron, and p is the number of neurons in each layer.

[0065] Define the second layer of the neural network as:

[0066]

[0067] where is the output of the i-th neuron in the first layer of the neural network.

[0068] Then each element of the network output can be expressed as:

[0069]

[0070] where is the element in the i-th row and j-th column of, is the estimated value of the ideal weight matrix of the second layer of the neural network.

[0071] The output of the PONN neural network is finally denoted as:

[0072]

[0073] where is a set composed of p and is denoted as is a set composed of p and is denoted as is the estimated value of the ideal weight matrix of the first layer of the neural network, and h is a set of activation functions of the first layer of p neural networks, denoted as [h1,...,h i ,...,h p .

[0074] The performance-oriented learning strategy module is used to update the weights of the PONN neural network, so that the output of the PONN neural network after updating the weights has a better noise disturbance suppression effect.

[0075] To reduce the influence of the lumped disturbance g(t), according to the output of the estimator based on PONN the input of the controlled object is designed as:

[0076]

[0077] where u F (t) is the output of the state feedback controller.

[0078] Step 2: Based on the constructed control system, use the BP optimization algorithm to obtain the basic learning strategy of the performance-oriented learning strategy module. The method is as follows:

[0079] Define the cost function of the performance index as:

[0080]

[0081] There is the following optimization problem:

[0082]

[0083] where V and W are the ideal weights of the second layer and the ideal weights of the first layer in the neural network respectively, sup is the upper bound, and g e (t) is the equivalent input disturbance of the controlled object.

[0084] Applying the backpropagation algorithm based on gradient descent to train the neural network, we can obtain:

[0085]

[0086] Among them, is the state of the observation error system after equivalent input interference.

[0087] Applying the static gradient approximation, that is, assuming we have:

[0088]

[0089] Among them, is the inverse of A-LC.

[0090] Therefore, the basic learning strategy of the performance-oriented learning strategy module is denoted as:

[0091]

[0092] Among them, both γ1 and γ2 are learning rates, γ1, γ2 > 0, C α is a static estimate, denoted as is a dynamic function with respect to denoted as Π(h) is an extended diagonal matrix of vector h (each element of the vector is on the main diagonal of the diagonal matrix, and other elements are 0), I is the identity matrix, and h is a set composed of the outputs of the first layer of p neural networks.

[0093] Step 3: Since the basic learning strategy of the above-mentioned performance-oriented learning strategy module lacks stability guarantee, the present invention adds dynamic factors and adjustable functions to optimize the basic learning strategy; to accelerate the control process and enable the control performance of the system to be adaptively adjusted, balancing disturbance suppression and noise performance.

[0094] Next, the process of optimizing the basic learning strategy by the present invention is introduced:

[0095] Based on the basic learning strategy recorded in Equation (20), the optimized learning strategy of the present invention is denoted as:

[0096]

[0097] Among them, both τ1 and τ2 are positive damping coefficients; ξ1 is a small positive quantity; ||y δ || is a dynamic factor; Ψ(·) is a generalized adjustable function. The addition of Ψ(||y δ ||) enables the control performance of the system to be adaptively adjusted.

[0098] More specifically, the adjustable function satisfies:

[0099]

[0100] Among them, x and y are arbitrary variables in the real number field.

[0101] More specifically, compared with (13), a dynamic factor is added to the static estimation in the present invention, which is expressed as:

[0102]

[0103] Step 4: Based on the above-optimized learning strategy, update the weights of the PONN neural network, and use the estimator of the PONN with updated weights for the control of the controlled object.

[0104] Simulation results and analysis:

[0105] (1) Simulation results of the proposed method

[0106] In the simulation, a band-limited white noise environment is considered, with a signal-to-noise ratio of approximately 12 dB and a sampling time of 0.001 s. Figure 4 The simulation results show that the designed control system has fast and robust response characteristics. When a disturbance is applied in the time period of (10 s - 24 s), the estimator based on PONN can quickly learn according to the performance index y δ to effectively suppress the disturbance; when the disturbance is removed, the adjustable function adjusts the damping term in the learning strategy, enabling the system to maintain a stable response while remaining less sensitive to noise.

[0107] (2) Comparative simulation results

[0108] To compare with the developed method, two other control strategies are adopted: the first uses a Generalized Extended Disturbance Observer (GEID) for disturbance estimation; the second uses a basic learning strategy with an e-modification term on the premise that the neural network estimator structure is the same as that of the developed method. To ensure a fair comparison, the parameters (K p , K R ) and L of both methods are kept the same. The parameters of the GEID observer are selected as A e = 0, C e = 1, and L e = 0.9 through a trial-and-error method; the parameter settings of the basic learning strategy with an e-modification term are γ1 = 0.1, ρ1 = 3.5, γ2 = 0.1, and ρ2 = 1.

[0109] For comparison, Figure 5The response curves of the developed method were compared and analyzed with those of the other two methods. Although the structure of the Generalized Extended Interference Observer (GEID) is simpler, the developed method shows significant advantages in both disturbance rejection and noise attenuation. In addition, under the condition of the same estimator structure, due to the improved gradient approximation strategy and the design of the adjustable damping function, the control performance of the developed method is significantly better than that of the comparative method using the original learning strategy.

[0110] The above embodiments are only used to illustrate the design concept and characteristics of the present invention, and the purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made according to the principles and design concepts disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A low-noise disturbance suppression method based on a performance neural network estimator, characterized in that, It includes the following steps: Step 1: Construct a reference trajectory tracking control system based on a PONN estimator. The system includes an internal model controller, a state observer, a controlled object, a PONN-based estimator, and a state feedback controller. The PONN-based estimator is composed of a PONN neural network and a performance-oriented learning strategy module. The performance-oriented learning strategy module is used to update the weights of the PONN neural network; Step 2: Based on the constructed control system, use the BP optimization algorithm to obtain the basic learning strategy of the performance-oriented learning strategy module; Step 3: Optimize the basic learning strategy by adding dynamic factors and adjustable functions; Step 4: Based on the optimized learning strategy, update the weights of the PONN neural network, and use the estimator of the PONN with updated weights to control the controlled object to suppress low-noise disturbances.

2. The low-noise disturbance suppression method based on a performance neural network estimator according to claim 1, wherein, The basic learning strategy of the learning strategy module is denoted as: Among them, are the estimated values of the ideal weights of the second layer of the neural network and the estimated values of the ideal weights of the first layer, represents the derivative of, γ1 and γ2 are both learning rates, C α is a static estimate, y δ is the input of the neural network, is a dynamic function with respect to h is a set composed of the outputs of the first layer of p neural networks.

3. A low-noise disturbance suppression method based on a performance neural network estimator according to claim 2, characterized in that, The optimized learning strategy is denoted as: where τ1 and τ2 are both positive damping coefficients; ξ1 is a small positive constant; ||y δ || is a dynamic factor; Ψ(·) is a generalized adjustable function.

4. A low-noise disturbance suppression method based on a performance neural network estimator according to claim 3, wherein The adjustable function satisfies: where x and y are arbitrary variables in the real number domain.

5. A low-noise disturbance suppression method based on a performance neural network estimator according to claim 3, characterized in that Dynamic factors are added in static estimation, expressed as: Among them, is the state of the observation error system after equivalent input interference, is the output of the estimator based on PONN, y δ is the input of the neural network, ||y δ || is a dynamic factor; is the inverse of A-LC, where A is the controlled object system matrix, L is the observer gain, C is the controlled object output matrix, B is the controlled object input matrix, and J is the cost function of the performance index.

6. A low-noise disturbance suppression method based on a performance neural network estimator according to claim 1, characterized in that, The mathematical model of the state observer is expressed as: where L is the observer gain, u F (t), are the state, input, and output of the observer respectively, and A, B, C are system matrices with dimensions in each term, and y(t) is the system output of the controlled plant.

7. A low-noise disturbance suppression method based on a performance neural network estimator according to claim 1, characterized in that The mathematical model of the internal model controller is expressed as: where, x R (t) is the state of the internal model, A R , B R are internal model constant matrices of appropriate dimensions, r(t) is the reference input, and y(t) is the system output of the controlled plant.

8. A low-noise perturbation suppression method based on a performance neural network estimator according to claim 1, characterized in that The mathematical model of the state feedback controller is expressed as: where, u F (t) is the output of the state feedback controller, K p and K R are control gains to be determined, is the state of the observer, x R (t) is the state of the internal model.

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