An Improved Model-Free Control Method for Extended State Observer under Stochastic Disturbance Conditions

Abstract

This invention discloses an improved extended state observer model-free control method for random load disturbance conditions, relating to the field of speed control technology under nonlinear loads and disturbance conditions. The method includes: establishing the mechanical motion equations of a coal unloading crawler device; the coal unloading crawler device consists of a chain system, a scraper bucket, a tensioning mechanism, a drive motor, and a main frame; establishing a hyperlocal model of the coal unloading crawler device based on model-free control theory and rewriting the extended state equations; addressing the limitations of the finite difference method by introducing an extended state observer to estimate all unknown dynamics in real time; and introducing a compensation function to construct an improved extended state observer, correcting estimation errors, thereby designing a model-free controller. This invention proposes an improved extended state observer structure, which suppresses high-frequency noise interference in disturbance estimation by introducing a filtering compensation mechanism, improving the observer's frequency domain performance and the system's dynamic response speed.

Description

Technical Field

[0001] This invention relates to the field of speed control technology under nonlinear loads and disturbances, and in particular to an improved extended state observer model-free control method under random load and disturbance conditions. Background Technology

[0002] Bulk cargoes (such as coal, ore, and grain) play a vital role in national energy supply, industrial production, and transportation, serving as indispensable raw material support for basic industries like power, steel, metallurgy, and grain processing. With rapid global economic development and continuous optimization of industrial structures, the demand for transporting bulk cargoes continues to grow, and the stability and efficiency of their supply chains directly impact the smooth operation of the national economy. Railway transportation, as the core mode of bulk cargo transport, has become a crucial link in national energy transportation and industrial logistics due to its advantages such as large capacity, low cost, minimal weather impact, and high transport stability, undertaking the long-distance, high-efficiency transport of bulk materials. In railway transportation, the efficiency of unloading operations directly determines the operational efficiency of the entire logistics chain. The unloading process of bulk cargoes typically involves continuous, high-intensity, and large-scale material transfer. The level of unloading efficiency not only affects the release of railway freight capacity but also determines the supply efficiency of energy materials and the operational rhythm of its industrial chain. For example, in high-demand industries such as coal and ore, insufficient unloading efficiency can lead to obstructed railway freight yard turnover, increased transportation costs, and decreased overall supply chain efficiency, thereby affecting the normal operation of the national economy. Therefore, improving the unloading efficiency of bulk cargo and optimizing the automation and intelligence level of unloading equipment have become key factors in enhancing railway transportation capacity and ensuring the efficient operation of the industrial chain.

[0003] Faced with complex coal pile shapes, high compaction, frozen coal, and special track conditions, existing coal unloading equipment struggles to meet the demands for efficient, intelligent, and environmentally friendly unloading. The crawler-type coal unloading device, as a new type of intelligent coal unloading equipment, can autonomously crawl, precisely adjust speed, and adapt to different coal pile shapes. It overcomes the limitations of traditional equipment, such as large operational restrictions, excessive manual intervention, and incomplete unloading, providing a more flexible, efficient, and environmentally friendly solution for unloading bulk cargo on railways. In practical engineering applications, the crawler-type coal unloading device is a direct-drive motor system. The motor's operating environment is typically highly uncertain, especially under strong disturbances and non-stationary conditions, such as those experienced by the crawler-type device. System parameters dynamically change with factors such as load, temperature, and wear, making it difficult for controllers based on precise models to maintain stable performance over long periods. Typical examples include changes in motor stator resistance with temperature rise, shifts in d / q-axis inductance due to magnetic saturation, and rotor flux drift due to operating conditions. These parameter changes not only alter the system's transient response characteristics but can also cause significant errors in control components such as decoupling, observation, or feedforward compensation, thereby affecting the stability and energy efficiency of the entire speed control system. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides an improved extended state observer model-free control method for random load disturbance conditions to address the problem of researching a control mechanism with adaptive capabilities that does not rely on high-precision modeling in the context of motor parameter drift or difficulty in accurately obtaining the model.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] This invention provides an improved extended state observer model-free control method for random load disturbance conditions, comprising: establishing the mechanical motion equations of a coal unloading crawler device; the coal unloading crawler device is composed of a chain system, a scraper bucket, a tensioning mechanism, a drive motor, and a main frame; establishing a hyperlocal model of the coal unloading crawler device based on model-free control theory and rewriting the extended state equations; addressing the limitations of the finite difference method by introducing an extended state observer to estimate all unknown dynamics in real time; and introducing a compensation function to construct an improved extended state observer to correct estimation errors, thereby designing a model-free controller.

[0008] As a preferred embodiment of the improved extended state observer model-free control method under random disturbance conditions described in this invention, the mechanical motion equation of the coal unloading crawler device is:

[0009]

[0010] Where J is the moment of inertia, ω m T is the mechanical angular velocity of the rotor. e Where T is the electromagnetic torque, T1 is the load torque, and f is the coefficient of friction. This indicates the angular acceleration of the coal unloading crawler device;

[0011] Set the d-axis current i d =0, at this time the electromagnetic torque simplifies to:

[0012]

[0013] Where P is the number of pole pairs of the motor, φ f Let i be the electromotive force constant. d Let i be the stator current component along the d-axis. q The stator current component in the q-axis direction;

[0014] Substituting the electromagnetic torque equation into the mechanical motion equation of the coal unloading crawler device, we get:

[0015]

[0016] As a preferred embodiment of the improved extended state observer model-free control method for random load disturbance conditions described in this invention, the model-free control theory includes the following steps:

[0017] Consider a class of single-input, single-output systems whose dynamic characteristics are described by the following ordinary differential equations:

[0018]

[0019] Where y(t) is the system output and u(t) is the system input, y (v) (t) and u (y) (t) represent the higher-order derivatives of the output and input, respectively, M. p () represents the unknown dynamic model of the system;

[0020] In most cases, the input-output relationship of the system can be explicitly expressed as:

[0021]

[0022] in, Represents the inherent dynamic characteristics of the system. d(t) represents the input gain, and d(t) represents the external disturbance.

[0023] Taking further consideration of the system's uncertainties, the system model is revised as follows:

[0024]

[0025] in, This represents the unmodeled dynamics and parameter uncertainties of the system.

[0026] If the system's input gain If we set the constant α, then it simplifies to:

[0027] y (v) (t)=F(t)+ξu(t);

[0028] Where F(t) represents all unknown dynamics, and ξ is the control gain of the experiment.

[0029] As a preferred embodiment of the improved extended state observer model-free control method under random load disturbance conditions described in this invention, the establishment of the hyperlocal model of the coal unloading crawler device refers to rewriting the mechanical motion equations of the coal unloading crawler device into the hyperlocal model of the coal unloading crawler device based on model-free control theory, with the expression being:

[0030]

[0031] in, As a control output, u = i qAs a control input It is the control gain coefficient;

[0032] The extended state equation is:

[0033]

[0034] Where x1 = y is the system output, and x2 = F(t) is the unmodeled dynamics. Let F(t) be the rate of change of the disturbance.

[0035] As a preferred embodiment of the improved extended state observer model-free control method for random disturbance conditions described in this invention, the extended state observer is:

[0036]

[0037] in, It is an estimate of x1 = y. It is an estimate of x2=F(t), and β1 and β2 are the observation gains of the extended state observer.

[0038] As a preferred embodiment of the improved extended state observer model-free control method for random disturbance conditions described in this invention, wherein: the improved extended state observer refers to the introduction of a compensation function Correcting the estimation error of F(t), we obtain the improved extended state observer as follows:

[0039]

[0040] in, The first derivative of the compensation function, It is the compensation function, and λ is the filter factor.

[0041] As a preferred embodiment of the improved extended state observer model-free control method under random load disturbance conditions described in this invention, the model-free controller refers to a feedback linearized control designed based on the estimated F(t), with the following control law:

[0042]

[0043] in, It is the v-th derivative of the expected output; e(t) is the tracking error, g c (e(t)) is the error feedback term.

[0044] The beneficial effects of this invention are as follows: Under the framework of a hyperlocal model, the system dynamics are reconstructed into a combination of control gain and unknown disturbance. The system disturbance is estimated using the online response of the input and output signals, and a feedback linearized control law is designed to achieve precise tracking control of the output state. To improve the stability of model-free control methods under high-frequency disturbances and dynamic environments, an improved extended state observer structure is proposed. A filtering compensation mechanism is introduced to suppress high-frequency noise interference in disturbance estimation, thereby improving the observer's frequency domain performance and the system's dynamic response speed. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is an overall flowchart of an improved extended state observer model-free control method under random load disturbance conditions according to an embodiment of the present invention.

[0047] Figure 2 The load characteristics of the coal unloading crawler device under the coal unloading condition are described in an embodiment of the present invention, which is based on the improved extended state observer model-free control method under random load disturbance conditions.

[0048] Figure 3 The load condition simulation curves are for an improved extended state observer model-free control method under random load disturbance conditions according to an embodiment of the present invention.

[0049] Figure 4 The simulation curves show the dynamic response of different control strategies under complex disturbance conditions for the improved extended state observer model-free control method under random disturbance conditions, according to an embodiment of the present invention.

[0050] Figure 5 This is a magnified view of the initial state of the simulation curves of the dynamic response of different control strategies under complex disturbance conditions using the improved extended state observer model-free control method under random disturbance conditions, according to an embodiment of the present invention.

[0051] Figure 6 This is a magnified view of the dynamic response simulation curves of different control strategies under complex disturbance conditions using the improved extended state observer model-free control method under random disturbance conditions, according to an embodiment of the present invention, at the moment of the first impact.

[0052] Figure 7 This is a magnified view of the dynamic response simulation curves of different control strategies under complex disturbance conditions using the improved extended state observer model-free control method under random disturbance conditions, according to an embodiment of the present invention, at the second impact moment.

[0053] Figure 8 This is the current signal of the improved extended state observer model-free control method under random load disturbance conditions according to an embodiment of the present invention.

[0054] Figure 9 The current signal is used to compare the improved extended state observer model-free control method with the PID method under random load disturbance conditions according to an embodiment of the present invention.

[0055] Figure 10 The image shows the dynamic simulation curves of the load tracking performance of the improved extended state observer model-free control method under random load disturbance conditions according to an embodiment of the present invention. Detailed Implementation

[0056] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0057] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0058] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0059] Example 1, referring to Figure 1 This embodiment provides an improved model-free control method for extended state observers under random load conditions, including the following steps:

[0060] S1. Establish the mechanical motion equations of the coal unloading crawler device.

[0061] Specifically, the coal unloading crawler device consists of a chain system, a scraper bucket, a tensioning mechanism, a drive motor, and a main frame. It relies on the drive motor as a power source, and transmits the rotational kinetic energy of the motor to the high-strength chain through the sprocket system, so that the chain moves in a cycle along a set trajectory, thereby driving the scraper bucket to complete the process of grabbing, conveying and unloading coal.

[0062] The mechanical motion equations of the coal unloading crawler device are as follows:

[0063]

[0064] Where J is the moment of inertia, ωm T is the mechanical angular velocity of the rotor. e Where T is the electromagnetic torque, T1 is the load torque, and f is the coefficient of friction. This indicates the angular acceleration of the coal unloading crawler device.

[0065] This equation shows the angular acceleration of the coal unloading crawler device. It depends on three factors: electromagnetic torque As the primary driving force, the electromagnetic force generated by the internal windings of the motor acts on the rotor, forming the driving torque; the load torque T1 represents the external resistance experienced by the motor when driving the load; increasing the load will reduce the motor speed; the frictional torque fω m As the rotational speed increases, the frictional resistance gradually increases, which inhibits the motor speed.

[0066] The d-axis current i is typically set. d =0, to reduce reactive power loss and optimize efficiency, the electromagnetic torque simplifies to:

[0067]

[0068] Where P is the number of pole pairs of the motor, φ f Let i be the electromotive force constant. d Let i be the stator current component along the d-axis. q The stator current component in the q-axis direction;

[0069] Substituting the electromagnetic torque equation into the mechanical motion equation of the coal unloading crawler device, we get:

[0070]

[0071] The formula is the mechanical motion equation of the coal unloading crawler device, and the controller is designed based on this formula.

[0072] S2. Based on model-free control theory, establish a hyperlocal model of the coal unloading crawler device and rewrite the extended state equations.

[0073] Specifically, model-free control theory is as follows:

[0074] Consider a class of single-input, single-output systems whose dynamic characteristics are described by the following ordinary differential equations:

[0075]

[0076] Where y(t) is the system output and u(t) is the system input, y (v) (t) and u (y) (t) represent the higher-order derivatives of the output and input, respectively. M represents the first derivative of the system output and input, respectively. p() represents the unknown dynamic model of the system, which may be linear or nonlinear; undisclosed external disturbances may affect the dynamic behavior of the system.

[0077] In most cases, the input-output relationship of the system can be explicitly expressed as:

[0078]

[0079] in, Represents the inherent dynamic characteristics of the system. The input gain represents the input gain, which may be a nonlinear function, while d(t) represents the external disturbance, such as environmental noise or load disturbance.

[0080] Taking further consideration of the system's uncertainties, the system model is revised as follows:

[0081]

[0082] in, This represents the unmodeled dynamics and parameter uncertainties of the system, where d(t) still represents external disturbances or noise.

[0083] If the system's control gain If approximated by a constant α, then it simplifies to:

[0084] y (v) (t)=F(t)+ξu(t);

[0085] in, At this point, all unknown dynamic characteristics, unmodeled dynamics, and disturbances are reduced to F(t), which is the standard form of the hyperlocal model. v depends on the controlled object, usually taking v = 1 or v = 2, and ξ is the experimental control gain, such that ξu(t) and y (v) (t) have the same order of magnitude.

[0086] Based on model-free control theory, the mechanical motion equations of the coal unloading crawler device are rewritten as a hyperlocal model of the device, expressed as follows:

[0087]

[0088] in, As a control output, u = i q As a control input It is the control gain coefficient, which is adjusted during controller design. F(t) represents all unknown dynamics, including: load torque T1, viscous friction term fω. m Unmodeled dynamic Δf(t).

[0089] Furthermore, the extended state equation is:

[0090]

[0091] Where x1 = y is the system output, and x2 = F(t) is the unmodeled dynamics. Let F(t) be the rate of change of the disturbance.

[0092] S3. To address the limitations of the finite difference method, an extended state observer is introduced to estimate all unknown dynamics in real time.

[0093] Specifically, the limitations of the finite difference method are:

[0094] Since F(t) directly affects system behavior, its accurate estimation is crucial for the effectiveness of model-free control. In model-free control, the disturbance F(t) is estimated online using input-output data. Assuming u(t) is time-continuous, F(t) can be approximated using the finite-difference method:

[0095]

[0096] in, T is the estimated disturbance value; s i is the sampling period; q (tT s () represents the input from the previous time step to avoid algebraic loops. Ideally, when T... s When →0, we have: Even if the system model is unknown, F(t) can still be estimated online using input and output data, and a controller can then be designed to compensate for its effects. However, in practical applications, T... s The choice of T is constrained by hardware sampling rate, computing power, noise impact, and stability issues, resulting in flaws in the controller design: In digital implementation, T s >>0 is unavoidable, which makes it difficult for the finite difference method to accurately estimate F(t) under high-frequency dynamic changes.

[0097] Furthermore, the extended state observer is:

[0098]

[0099] in, It is an estimate of x1 = y. It is an estimate of x2 = F(t), that is, the unmodeled dynamics of the system. Let x1 be the first derivative of the estimated value. Let β1 and β2 be the first derivative of the estimated value of x2, and let β1 and β2 be the observation gains of the extended state observer, which are usually chosen appropriately to ensure good convergence. When the observation gains β1 and β2 are chosen appropriately, It can accurately track F(t), thereby improving the performance of model-free control.

[0100] S4. Introduce a compensation function to construct an improved extended state observer, correct the estimation error, and thus design a model-free controller.

[0101] Specifically, to enhance the perturbation estimation capability, a compensation function is introduced. The expression used to correct the estimation error of F(t) is as follows:

[0102]

[0103] in, It is a compensation function that can adaptively adjust to improve the estimation accuracy of F(t), and a first-order low-pass filter is used: λ is the filter factor, which controls... The adjustment rate, s is the symbol for the frequency domain, which is used in control and is divided into the frequency domain and the time domain.

[0104] Thus, the improved extended state observer is obtained as follows:

[0105]

[0106] in, The first derivative of the compensation function, It is a compensation function. Gradually approximate F(t) to improve the accuracy of disturbance estimation, where λ is the filtering factor.

[0107] Furthermore, the model-free controller is based on the estimated F(t), and a feedback linearization control is designed with the following control law:

[0108]

[0109] in, It is the v-th derivative of the expected output; e(t) is the tracking error, e(t) = y r (t)-y(t), g c (e(t)) is the error feedback term, and its common form is: Among them, K p K is the proportionality coefficient. I K is the integral coefficient. d The differential coefficients are... It is the first derivative of the error.

[0110] In summary, this invention addresses the problem of significant performance degradation of traditional control strategies under conditions where modeling accuracy is difficult to guarantee or model parameters are unknown. This invention further investigates a model-free control method that does not require an accurate model. Within a hyperlocal model framework, the system dynamics are reconstructed as a combination of control gain and unknown disturbances. The system disturbances are estimated using the online response of the input and output signals, and a feedback linearized control law is designed to achieve precise tracking control of the output state. To improve the stability of the model-free control method under high-frequency disturbances and dynamic environments, this invention proposes an improved extended state observer structure. By introducing a filtering compensation mechanism, high-frequency noise interference in disturbance estimation is suppressed, improving the observer's frequency domain performance and the system's dynamic response speed.

[0111] Example 2, refer to Figures 2-10 Tables 1 and 2, which are the second embodiment of the present invention, provide experimental simulation data of the improved extended state observer model-free control method under random load disturbance conditions to further verify the technical solution of the present invention.

[0112] Reference Figure 2 During coal unloading at railway freight yards, the unloading crawler device faces complex unloading conditions. Uncertainties in coal pile morphology, compaction, and mass distribution cause dynamic load responses coupled from multiple sources. This dynamic load is a major factor limiting unloading efficiency and equipment stability. These factors not only determine the scraper cutting resistance and load fluctuation type but also directly affect the accuracy and robustness of the speed control system.

[0113] The natural accumulation of coal creates physical characteristics such as particle stratification, varying density distribution, and uneven inclination angles. This results in a dynamic change in the coal pile slope during unloading, initially steepening and then gradually decreasing. In the initial stage, the coal is relatively loose, and the load is low. Once the slope reaches a critical value, friction between coal particles increases, and the load rises rapidly. Near the bottom of the unloading process, the high-compactness coal seam further increases the load, leading to periodic load fluctuations. The angle of repose of the coal is a key parameter determining the cutting resistance of the scraper bucket. Different moisture contents, particle diameters, and coal types cause variations in the angle of repose, thus affecting load characteristics. When the coal pile slope is steep (approaching or exceeding the angle of repose), the scraper bucket cutting the coal seam is prone to causing local collapse, leading to a significant increase in instantaneous load and a surge in motor torque demand, potentially triggering overload protection and causing the equipment to lose power output. On the other hand, when the coal pile slope is gentle (much less than the angle of repose), the cohesion and adhesion of coal particles increase, resulting in a decrease in scraper bucket cutting resistance, a reduction in the amount of coal unloaded per unit time, and a longer operating cycle. A slope that is too gentle may form a high-pressure coal seam, which can actually increase the cutting resistance of the scraper bucket, leading to increased energy consumption. Therefore, if the speed control system cannot adapt to the nonlinear load changes caused by this dynamic inclination angle, the scraper bucket may get stuck in the high-load area, affecting the continuity of coal unloading operations.

[0114] The degree of coal compaction in the stockpile determines the instantaneous load and system energy consumption during bucket cutting. Coal piled up for extended periods, under the influence of gravity from the overlying coal layer, experiences reduced interparticle spacing, forming a high-compaction coal seam. This significantly increases shear strength and penetration resistance. Studies show that in high-compaction coal seams, the bucket cutting resistance is 30%–50% higher than in loose coal seams, leading to a sudden spike in motor current and severe fluctuations in chain tension. If the control system response is delayed, it may cause motor stalling or chain skipping, even resulting in equipment damage. Furthermore, coal particles in high-compaction coal seams may detach as lumps during bucket cutting, impacting the conveyor trough walls and creating impact vibrations. This causes severe fluctuations in motor output torque, exacerbating system instability. The variation pattern of coal compaction exhibits spatial unevenness and dynamic temporal changes during the unloading process. In the coal pile, the bottom layer of coal, due to long-term compression, has the highest compaction degree and bears the greatest load during bucket cutting; while the upper layer of coal is relatively loose, with lower compaction and a smaller load. Therefore, the load on the scraper varies significantly when operating at different depths, requiring the speed control system to monitor load changes in real time and perform dynamic compensation.

[0115] The mass distribution within a coal pile is typically uneven, with significant variations in density, particle size, and moisture content across different regions. This causes the load characteristics of the scraper bucket to exhibit random and abrupt changes. The stratification effect of coal particles leads to large coal lumps accumulating on the top layer, while fine coal powder fills the bottom. This stratification phenomenon causes drastic fluctuations in the load on the scraper bucket during coal unloading. When the scraper bucket enters the fine coal powder area, the increased adhesion between particles raises cutting resistance and motor torque, potentially causing problems such as unstable chain tension and increased energy consumption. Conversely, when the scraper bucket enters the large coal particle area, the coal pile is relatively loose with lower friction, resulting in decreased cutting resistance and a momentary reduction in load. However, the sudden entry of large coal lumps can cause short-term blockages or impact vibrations, affecting equipment stability. Furthermore, uneven mass distribution can lead to localized instability in the coal pile; coal slippage or collapse can trigger sudden load changes, increasing the uncertainty of equipment operation.

[0116] To verify the control performance of the proposed model-free controller based on the improved extended state observer (ESO) under complex nonlinear conditions, this paper compares and analyzes the response effects of three control methods in a typical application scenario of a coal unloading crawler: ① a traditional proportional-integral-derivative (PID) controller, ② a model-free controller based on traditional ESO (Traditional MFC), and ③ the proposed model-free controller based on improved ESO (Improved MFC).

[0117] Controller ①i q =g c (e(t)), where e is the error in rotational speed;

[0118] Controller ② Combined Mode Japanese style

[0119] Controller ③ Combined Mode Japanese style

[0120] Comparative simulations were conducted under typical complex conditions, including nonlinear disturbances, periodic loads, and high-frequency noise, to evaluate the performance differences of different control strategies in terms of system stability, disturbance suppression capability, tracking accuracy, and response speed. Complex load disturbance conditions involve load characteristics that exhibit strong nonlinearity, randomness, and periodicity over time and space. The specific complex load disturbance condition model is as follows:

[0121]

[0122] Among them, T0 is the basic load term, representing the basic torque requirement of the unit when there is no external coal resistance. It mainly includes system static friction and the basic torque during no-load operation, and is usually a constant, reflecting the light load characteristics at the initial stage of coal unloading. γ(vt) n This is a nonlinear load growth term that simulates the increased resistance of the compacted coal seam encountered as the scraper gradually penetrates deeper into the coal pile during coal unloading. Here, v is the propulsion speed, t is time, n is the nonlinear order (usually 2 or 3), and γ is the resistance growth coefficient. This term increases exponentially with time, reflecting the significant nonlinear influence of coal seam compaction on the cutting load. A p sin(2πf d t) represents the periodic disturbance term, simulating the regular changes caused by the slope structure of the coal pile, such as the scraper passing through the high and low fluctuation zones of the coal pile, or the density fluctuations between coal seam layers. This term is a sine function, A p f is the amplitude of the periodic disturbance. d The disturbance frequency represents the periodic load fluctuations during coal unloading. ση(t) is the random disturbance term, simulating random disturbances caused by factors such as uneven coal density, particle size variation, and moisture content fluctuations. This term is a zero-mean Gaussian white noise model, where σ is the disturbance intensity and η(t) is a standard Gaussian noise sequence, representing the random influence of local coal pile characteristics on the load. ∑A k δ(tt k This is used to simulate instantaneous impact loads caused by events such as large coal chunks collapsing, the scraper encountering hard blocks, or localized slippage. k Let δ(tt) be the amplitude of the kth impact. k Let be the unit impact function, simulating the sudden event occurring at time t. kTiming. This reflects the uncertainties and discontinuous disturbances present during the coal unloading process. Specific parameters are shown in Table 1.

[0123] Table 1 Parameter settings for complex load conditions

[0124] parameter describe numerical values <![CDATA[T0]]> Basic load 500 N·m γ Nonlinear coefficients 0.05 v propulsion speed 0.5m / s n Nonlinear power 2 <![CDATA[A p ]]> Periodic disturbance amplitude 100 N·m <![CDATA[f d ]]> Periodic perturbation frequency 0.3Hz σ random disturbance strength 25 N·m <![CDATA[A k ]]> Impact amplitude 200 N·m <![CDATA[t k ]]> Impact moment 2.1s, 4.6s

[0125] like Figure 3 As shown in the figure, this is the dynamic change curve of the system load over time under complex load conditions, reflecting the actual load characteristics under the superposition of multiple factors during coal unloading. From Figure 3 As can be seen, the system load mainly fluctuates around 500 N·m, exhibiting a composite characteristic of three types: periodic oscillation, random disturbance, and instantaneous impact. This composition is consistent with the complex load disturbance model. Specifically, the load curve exhibits a sinusoidal change at a frequency of approximately 0.3 Hz, which is due to periodic disturbances caused by the coal pile slope structure, reflecting the actual characteristics of periodic cutting load fluctuations during the scraper advance. High-frequency, small-amplitude jitter exists on the curve surface, caused by the Gaussian white noise term σ = 25 N·m, simulating instantaneous disturbances caused by microscopic non-uniform factors such as coal seam particle size, humidity, and density. At t = 2.1 s and t = 4.6 s, the load experiences a short-term, sharp increase, reaching a maximum of approximately 800 N·m, which is due to the instantaneous impact term A. k =200 N·m superposition caused, simulating the strong disturbance to the system caused by discontinuous events such as coal block slippage and scraper impact during coal unloading.

[0126] To verify the speed control performance of the proposed model-free control method based on the Improved Extended State Observer (ISO) under complex load disturbance conditions, this paper conducts simulation analysis based on a typical coal unloading load model and compares it with traditional model-free control (MFC + linear ESO) and conventional PID control strategies. By quantitatively comparing the response speed, steady-state error, and jitter of the control system under disturbance conditions, the paper systematically verifies the control accuracy, dynamic adaptability, and robustness advantages of the proposed improved MFC method under non-ideal conditions. Specific parameters are shown in Table 2.

[0127] Table 2 Parameters of the Improved ESO Model-Free Controller

[0128] parameter describe numerical values <![CDATA[K p ]]> proportionality coefficient 4000 <![CDATA[K I ]]> Integral coefficient 100 <![CDATA[K d ]]> Differential coefficients 10 <![CDATA[β1]]> Observer first-state gain 100 <![CDATA[β2]]> Observer second-state gain 2500 α Model-free control input gain 1000 λ Compensation filter weight parameters 50

[0129] like Figures 4-7 As shown in the figure, the dynamic response simulation curves of different control strategies under complex load disturbance conditions are presented. The target velocity is 100 rad / s as the setpoint, and the simulation is performed under conditions of multi-source disturbances (periodic disturbance, random noise, nonlinear load growth, and instantaneous impact). Specific details are referenced below. Figure 3 .from Figure 4It can be seen that all three controllers can maintain a certain speed tracking capability throughout the entire 5-second operating cycle, but their performance differs significantly. The improved MFC maintains a small error amplitude throughout each stage, exhibiting minimal overall fluctuation and demonstrating good stability and robustness. The traditional MFC outperforms PID control for most of the time, but suffers from some low-frequency deviations and disturbance coupling fluctuations; while the PID controller exhibits severe error fluctuations under complex disturbances, especially in the high-frequency disturbance region, where significant oscillations occur, resulting in unsatisfactory control performance. Figure 5 This is a magnified view of the error response during the initial startup phase (0–0.4 s). It can be seen that the PID control exhibits significant overshoot and large oscillations during the initial startup phase (0–0.05 s), with a peak error approaching ±4 rad / s. Subsequently, the oscillations are prolonged, the adjustment process is slow, and stability is poor. Traditional MFC suppresses some initial fluctuations compared to PID, but still exhibits a certain tracking delay during acceleration. In contrast, the improved MFC can quickly stabilize the error within 0.1 s, has a faster initial response, and almost no significant overshoot, demonstrating superior dynamic response speed. Figure 6 This demonstrates the local response at the occurrence of the first sudden disturbance (approximately 2.1 seconds). From Figure 6 It can be clearly observed that all three controllers exhibit sudden error changes at the moment of disturbance, but the improved MFC has the smallest disturbance response amplitude and the shortest recovery time; although the traditional MFC has a certain suppression capability, it still produces transient fluctuations under the influence of disturbance; while the PID control is severely affected by shocks, with obvious error spikes, and it is difficult to recover to the set speed quickly, reflecting its limited ability to suppress uncertain disturbances. Figure 7 This represents the local response at the time of the second impact disturbance (4.6 s). From... Figure 7 As can be seen, the improved MFC once again demonstrates a strong disturbance suppression capability, with the error quickly returning to near the steady-state value. Traditional MFC control exhibits a certain disturbance amplification effect, with fluctuations lasting slightly longer. The PID controller, on the other hand, shows significant speed deviation during this phase, with system stability and tracking consistency significantly inferior to the former two. Therefore, simulation comparisons under complex load conditions show that the proposed improved MFC, even under the combined effects of nonlinear disturbances, sudden load changes, and high-frequency noise, still possesses higher steady-state accuracy, faster response speed, and stronger disturbance rejection robustness, significantly outperforming both the traditional MFC and PID controllers.

[0130] Under complex load conditions, current response characteristics are an important indicator for evaluating the stability and robustness of control strategies. Figure 8 and Figure 9 The dynamic response of the q-axis current under the improved MFC controller and the traditional PID controller are shown respectively, and the two controllers exhibit significant differences in control stability, disturbance suppression capability, and execution efficiency. Figure 8It is evident that, under the improved MFC controller, i q The overall current fluctuation range is small, consistently remaining between 7A and 15A, and exhibits a stable dynamic adjustment process with load cycle disturbances. At 2.1s and 4.6s, due to sudden impact load disturbances, i q The current rises instantaneously but quickly returns to normal levels without overshoot or continuous oscillation, indicating that the proposed disturbance compensation mechanism can effectively sense and quickly suppress strong interference, ensuring stable system operation.

[0131] In contrast, Figure 9 The PID controller in the example exhibits extremely poor current response performance under the same disturbance conditions. q The current exhibits severe high-frequency fluctuations, with amplitudes exceeding 6000A at their maximum and dropping to as low as -4000A, far exceeding the motor's safe operating range. This abnormally high-amplitude current oscillation may not only trigger the driver's overload protection but also pose a risk of damaging power devices, seriously threatening the system's stability and safety. The main reason for this phenomenon is that traditional PID controllers cannot detect complex disturbance sources, and their feedback regulation lags behind the system's dynamic changes, leading to... q Frequent overshooting and constant correction of the current can lead to high-frequency resonance problems.

[0132] like Figure 10 As shown in the figure, this is a simulation curve comparing the observation and tracking performance of the improved MFC and the traditional MFC for simulated loads. From the overall trend, both observers can effectively track the main changing trends of load disturbances, indicating that the constructed hyperlocal model and ESO structure have a certain disturbance sensing capability. However, there are significant differences between the two in terms of estimation accuracy and response sensitivity: the improved ESO has a higher fit to the real load curve, especially during load cycle fluctuations, it can better capture the detailed changes in load fluctuations, presenting a smoother and more accurate estimation trajectory; while the traditional ESO estimation shows deviations in multiple segments, especially in the range where the load rises or falls rapidly, its estimation exhibits significant lag or underfitting. During two typical impact disturbances at 2.1s and 4.6s, the improved ESO estimation results show a faster response speed and higher disturbance reconstruction capability, quickly reflecting the sharp rise in load and recovering rapidly; in contrast, the traditional ESO response is relatively slow, with estimation lag at abrupt changes, and the peak height is significantly lower than the real disturbance, exhibiting a large error.

[0133] In summary, addressing the challenges of model uncertainty, high-frequency noise interference, and difficulty in modeling dynamic disturbances in the motor speed control system of a coal unloading crawler under stochastic load conditions, a model-free control strategy based on a hyperlocal model is constructed. An improved ESO (Electronic Stability Evaluation) is introduced to enhance the system's disturbance estimation capability and control response performance. By simplifying the modeling of the PMSM (Polarization Motor Speed ​​Loop), a hyperlocal model is constructed to equivalently converge complex disturbances into observable variables, achieving independence of the control system from the system structure. Based on the traditional ESO structure, a disturbance compensation term and a low-pass filtering mechanism are introduced to effectively suppress the jitter amplification problem of finite difference estimation under high-frequency disturbances, enhancing the system's robustness to time-varying disturbances and measurement noise. Furthermore, an MFC (Mechanical Control Controller) based on disturbance feedback linearization is constructed, achieving high-precision speed control under highly uncertain environments. Simulation analysis, focusing on tracking accuracy, current stability, and disturbance suppression capability, fully demonstrates the superiority of the proposed control strategy.

[0134] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A model-free control method for an improved extended state observer under stochastic load disturbance conditions, characterized in that: include, The mechanical motion equations of the coal unloading crawler device are established. The coal unloading crawler device consists of a chain system, a scraper bucket, a tensioning mechanism, a drive motor, and a main frame. Based on model-free control theory, a hyperlocal model of the coal unloading crawler device is established, and the extended state equation is rewritten. To address the limitations of the finite difference method, an extended state observer is introduced to estimate all unknown dynamics in real time. An improved extended state observer is constructed by introducing a compensation function to correct the estimation error, thereby designing a model-free controller; The establishment of the hyperlocal model of the coal unloading crawler device refers to rewriting the mechanical motion equations of the coal unloading crawler device into the hyperlocal model of the coal unloading crawler device based on model-free control theory. The expression is as follows: ； ； in, As a control output As a control input It is the control gain coefficient; The extended state equation is: in, For the system output, For unmodeled dynamics, For disturbance The rate of change; The extended state observer is: in, Yes The estimate, Yes The estimate, and It is the observation gain of the extended state observer. for The first derivative of the estimated value, for The first derivative of the estimated value; The improved extended state observer refers to the introduction of a compensation function. , correct The estimation error is thus reduced, resulting in the improved extended state observer. in, The first derivative of the compensation function, It is a compensation function. This is the filter factor.

2. The improved extended state observer model-free control method for random load disturbance conditions as described in claim 1, characterized in that: The mechanical motion equation of the coal unloading crawler device is: ； in, For rotational inertia, The mechanical angular velocity of the rotor, For electromagnetic torque, For load torque, The coefficient of friction, This indicates the angular acceleration of the coal unloading crawler device; set up shaft current At this point, the electromagnetic torque simplifies to: ； in, This represents the number of pole pairs of the motor. Let be the electromotive force constant. for Stator current component in the axial direction, for Stator current component in the axial direction; Substituting the electromagnetic torque equation into the mechanical motion equation of the coal unloading crawler device, we get: 。 3. The improved extended state observer model-free control method for random load disturbance conditions as described in claim 1, characterized in that: The model-free control theory includes, Consider a class of single-input, single-output systems whose dynamic characteristics are described by the following ordinary differential equations: ； in, For system output, For system input, and These represent the higher-order derivatives of the output and input, respectively. , Let these represent the first derivatives of the system output and input, respectively. The unknown dynamic model of the system; The input-output relationship of the system is defined as follows: ； in, Represents the inherent dynamic characteristics of the system. Represents input gain. Represents external disturbances; Based on the uncertainty of the system, the system model is revised as follows: ； in, This represents the unmodeled dynamics and parameter uncertainties of the system. If the system's input gain Set as a constant Then it simplifies to: ； in, For all unknown dynamics, It is the control gain of the experiment.

4. The improved extended state observer model-free control method for random disturbance conditions as described in claim 3, characterized in that: The model-free controller refers to one based on estimation. Design a feedback linearization control with the following control law. ； in, This is the expected output. First derivative; It is tracking error. It is an error feedback term.

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