Model-free control method of improved extended state observer under random load disturbance working condition

Abstract

The invention discloses a model-free control method for an improved extended state observer under a random load disturbance working condition, and relates to the technical field of speed control under nonlinear load and disturbance working conditions, and the method comprises the steps: building a mechanical motion equation of a coal unloading crawler device; the coal unloading crawler device is composed of a chain system, a scraper bucket, a tensioning mechanism, a driving motor and a main body frame. According to a model-free control theory, establishing a super-local model of the coal unloading crawler device, and rewriting an expansion state equation; aiming at the limitation of a finite difference method, introducing an extended state observer to estimate all unknown dynamic states in real time; and introducing a compensation function to construct an improved extended state observer, and correcting an estimation error so as to design a model-free controller. The improved extended state observer structure is provided, high-frequency noise interference in disturbance estimation is suppressed by introducing a filtering compensation mechanism, and the frequency domain performance of the observer and the dynamic response speed of the system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of speed regulation control under nonlinear loads and disturbance conditions, and particularly to a model-free control method for improving an extended state observer under random load disturbance conditions. Background Art

[0002] Bulk cargo (such as coal, ore, grain, etc.) occupies an important position in the fields of national energy supply, industrial production, and transportation, and is an indispensable raw material support for basic industries such as electric power, steel, metallurgy, and grain processing. With the rapid development of the global economy and the continuous optimization of the industrial structure, the transportation demand for bulk cargo continues to grow, and the stability and transportation efficiency of its supply chain are directly related to the stable operation of the national economy. As the core mode of bulk cargo transportation, railway transportation has become a key link in national energy transportation and industrial logistics due to its advantages of large transportation volume, low cost, small impact of weather, and high transportation stability, and undertakes the long-distance and high-efficiency transportation tasks of bulk materials. In railway transportation, the unloading operation efficiency directly determines the operation efficiency of the entire logistics chain. The unloading process of bulk cargo usually 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 operation rhythm of its industrial chain. For example, in high-demand industries such as coal and ore, if the unloading operation efficiency is insufficient, it may lead to obstacles in the turnover of railway freight yards, increased transportation costs, and a decline in the overall supply chain efficiency, thus 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] Facing complex coal pile shapes, high compaction degrees, frozen coal, and special track conditions, existing coal unloading equipment is difficult to meet the unloading requirements of high efficiency, intelligence, and environmental protection. As a new type of intelligent coal unloading equipment, the crawler-type coal unloading device can crawl independently, adjust speed precisely, and adapt to different coal pile shapes, overcoming the problems of large operation limitations, much manual intervention, and incomplete unloading of traditional equipment, and providing a more flexible, efficient, and environmental protection solution for the unloading of railway bulk cargo. In practical engineering applications, the coal unloading crawler device is a direct-drive motor system, and the operating environment of the motor is usually full of high uncertainty. Especially under strong disturbance and non-stationary conditions such as coal unloading crawler devices, system parameters change dynamically with factors such as load, temperature, and wear, making it difficult for the controller based on an accurate model to maintain stable performance for a long time. Typically, the stator resistance of the motor changes with temperature rise, the d / q-axis inductance shifts due to magnetic saturation, and the rotor magnetic flux drifts due to the working state, etc. These parameter changes not only change the transient response characteristics of the system but may also cause significant errors in control links such as decoupling, observation, or feedforward compensation, thus affecting the stability and energy efficiency performance of the entire speed regulation system. Summary of the Invention

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

[0005] Therefore, the present invention provides an improved extended state observer model-free control method under random load disturbance conditions to solve the problem of studying a control mechanism that does not rely on high-precision modeling and has an adaptive ability in the context of motor parameter drift or difficulty in accurately obtaining the model.

[0006] To solve the above technical problems, the present invention provides the following technical solutions:

[0007] The present invention provides an improved extended state observer model-free control method under random load disturbance conditions, which includes establishing the mechanical motion equation of the coal unloading crawler device; the coal unloading crawler device is composed of a chain system, a scraper bucket, a tensioning mechanism, a driving motor, and a main frame; according to the model-free control theory, establishing a hyperlocal model of the coal unloading crawler device and rewriting the extended state equation; aiming at the limitations of the finite difference method, introducing an extended state observer to estimate all unknown dynamics in real time; introducing a compensation function to construct an improved extended state observer to correct the estimation error, thereby designing a model-free controller.

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

[0009]

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

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

[0012]

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

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

[0015]

[0016] As a preferred embodiment of the model-free control method with an improved extended state observer under random load disturbance according to the present 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 equation:

[0018]

[0019] where y(t) is the system output, u(t) is the system input, y (v) (t) and u (y) (t) represent the higher-order derivatives of the output and input respectively, and 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] where represents the inherent dynamic characteristics of the system, represents the input gain, and d(t) represents the external disturbance;

[0023] Further considering the uncertainty of the system, the system model is modified to:

[0024]

[0025] where represents the unmodeled dynamics and parameter uncertainties of the system;

[0026] If the input gain of the system is set to a constant α, it is simplified to:

[0027] y (v) (t) = F(t) + ξu(t);

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

[0029] As a preferred embodiment of the model-free control method with an improved extended state observer under random load disturbance according to the present invention, the establishment of the ultra-local model of the coal unloading crawler device refers to rewriting the mechanical motion equation of the coal unloading crawler device into the ultra-local model of the coal unloading crawler device according to the model-free control theory, and the expression is

[0030]

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

[0032] The extended state equation is,

[0033]

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

[0035] As a preferred scheme of the model-free control method with an improved extended state observer under the random load disturbance condition described in the present invention, wherein: the extended state observer is:

[0036]

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

[0038] As a preferred scheme of the model-free control method with an improved extended state observer under the random load disturbance condition described in the present invention, wherein: the improved extended state observer refers to introducing a compensation function to correct the estimation error of F(t), and thus the improved extended state observer is,

[0039]

[0040] wherein, is the first-order differential of the compensation function, is the compensation function, and λ is the filtering factor.

[0041] As a preferred scheme of the model-free control method with an improved extended state observer under the random load disturbance condition described in the present invention, wherein: the model-free controller refers to designing a feedback linearization control based on the estimated F(t), and the control law is as follows,

[0042]

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

[0044] The beneficial effects of the present invention are as follows: Under the framework of the super-local model, the system dynamics are reconstructed into a combined form of control gain and unknown disturbance. The system disturbance is estimated by using the online response of the input and output signals, and a feedback linearization 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, an improved extended state observer structure is proposed. By introducing a filtering compensation mechanism, the high-frequency noise interference in the disturbance estimation is suppressed, and the frequency-domain performance of the observer and the dynamic response speed of the system are improved. Description of the Drawings

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. 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.

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

[0047] Figure 2 It is the load characteristic of the coal unloading crawler device under the coal unloading condition of the model-free control method with an improved extended state observer under random load disturbance conditions in an embodiment of the present invention.

[0048] Figure 3 It is the simulation curve of the load condition of the model-free control method with an improved extended state observer under random load disturbance conditions in an embodiment of the present invention.

[0049] Figure 4 It is the dynamic response simulation curve of different control strategies under complex load disturbance conditions of the model-free control method with an improved extended state observer under random load disturbance conditions in an embodiment of the present invention.

[0050] Figure 5 It is the partial enlarged view of the initial state of the dynamic response simulation curve of different control strategies under complex load disturbance conditions of the model-free control method with an improved extended state observer under random load disturbance conditions in an embodiment of the present invention.

[0051] Figure 6 It is the partial enlarged view of the first impact moment of the dynamic response simulation curve of different control strategies under complex load disturbance conditions of the model-free control method with an improved extended state observer under random load disturbance conditions in an embodiment of the present invention.

[0052] Figure 7 It is the partial enlarged view of the second impact moment of the dynamic response simulation curve of different control strategies under complex load disturbance conditions of the model-free control method with an improved extended state observer under random load disturbance conditions in an embodiment of the present invention.

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

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

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

[0056] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following detailed description of the specific implementation manners of the present invention will be given in conjunction with the accompanying drawings of the specification.

[0057] In the following description, many specific details are set forth to facilitate a thorough understanding of the present invention. However, the present invention can also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0058] Secondly, the so-called "one embodiment" or "embodiment" herein refers to specific features, structures, or characteristics that can be included in at least one implementation manner of the present invention. The "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment that excludes other embodiments.

[0059] Embodiment 1, referring to Figure 1 , this embodiment provides a model-free control method with an improved extended state observer under random load disturbance conditions, including the following steps:

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

[0061] Specifically, the coal unloading crawler device is composed of a chain system, a scraper bucket, a tensioning mechanism, a driving motor, and a main frame. It relies on the driving motor as the 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 circular motion along the set trajectory, thereby driving the scraper bucket to complete the processes of coal grabbing, conveying, and unloading.

[0062] The mechanical motion equation of the coal unloading crawler device is:

[0063]

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

[0065] This equation shows that the angular acceleration of the coal unloading crawler device depends on three factors: the electromagnetic torque As the main driving force, the electromagnetic force generated by the internal winding of the motor acts on the rotor to form a driving torque; the load torque T1 represents the external resistance when the motor drives the load, and increasing the load will reduce the speed of the motor; the frictional torque fω m As the speed increases, the frictional resistance gradually increases, which has an inhibitory effect on the motor speed.

[0066] Usually, the d-axis current i d = 0 is set to reduce the reactive power loss and optimize the efficiency. At this time, the electromagnetic torque is simplified as:

[0067]

[0068] where P is the number of pole pairs of the motor, φ f is the electromotive force constant, i d is the stator current component in the d-axis direction, and i q is 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] where this formula is the mechanical motion equation of the coal unloading crawler device, and the controller is designed based on this formula.

[0072] S2. According to the model-free control theory, establish the ultra-local model of the coal unloading crawler device and rewrite the extended state equation;

[0073] Specifically, the 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 equation:

[0075]

[0076] where y(t) is the system output, u(t) is the system input, and y (v) (t) and u (y) (t) represent the higher-order derivatives of the output and input respectively, represent the first-order differentials of the system output and input respectively, and M p() represents the unknown dynamic model of the system, which may be linear or non-linear; the external disturbance terms not shown 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] where, represents the inherent dynamic characteristics of the system, represents the input gain, which may be a non-linear function, and d(t) represents external disturbances such as environmental noise and load disturbances.

[0080] Further considering the uncertainty of the system, the system model is modified as:

[0081]

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

[0083] If the control gain of the system is approximated as a constant α, it is simplified to:

[0084] y (v) (t) = F(t) + ξu(t);

[0085] where, At this time, all unknown dynamic characteristics, unmodeled dynamics and disturbances are summarized as F(t), which is the standard form of the super-local model. v depends on the controlled object, usually taking v = 1 or v = 2, and ξ is the control gain of the experiment, so that ξu(t) and y (v) (t) have the same order of magnitude.

[0086] According to the model-free control theory, the mechanical motion equation of the coal unloading crawler device is rewritten as the super-local model of the coal unloading crawler device, and the expression is

[0087]

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

[0089] Furthermore, the extended state equation is

[0090]

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

[0092] S3. In view of 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 as follows:

[0094] Since F(t) directly affects the 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 through input-output data. Assuming that u(t) has time continuity, F(t) can be approximately estimated by the finite difference method:

[0095]

[0096] Among them, is the estimated value of the disturbance; T s is the sampling period; i q (t - T s ) represents the input at the previous moment to avoid algebraic loops. In the ideal case, when T s →0, there is: Even if the system model is unknown, F(t) can still be estimated online through input-output data, and then a controller can be designed to compensate for its influence. However, in practical applications, the selection of T s is restricted by the hardware sampling rate, computing power, noise influence, and stability problems, resulting in defects in controller design: in digital implementation, T s >>0 is inevitable, making it difficult for the finite difference method to accurately estimate F(t) in the case of high-frequency dynamic changes.

[0097] Furthermore, the extended state observer is:

[0098]

[0099] Among them, is the estimate of x1 = y, is the estimate of x2 = F(t), that is, the unmodeled dynamics of the system, is the first-order differential of the estimated value of x1, is the first-order differential of the estimated value of x2. β1 and β2 are the observation gains of the extended state observer, and appropriate values are usually selected to ensure good convergence. When the observation gains β1 and β2 are selected 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 disturbance estimation ability, a compensation function is introduced to correct the estimation error of F(t), and the expression is

[0102]

[0103] where is the compensation function, which can be adaptively adjusted to improve the estimation accuracy of F(t), and a first-order low-pass filter is adopted: λ is the filtering factor, controlling the adjustment rate of, s is the symbol in the frequency domain, used to control the frequency domain and time domain in.

[0104] Thus, the improved extended state observer is

[0105]

[0106] where is the first derivative of the compensation function, is the compensation function, gradually approaches F(t), improving the disturbance estimation accuracy, and λ is the filtering factor.

[0107] Furthermore, the model-free controller designs a feedback linearization control based on the estimated F(t), and the control law is as follows

[0108]

[0109] where is the v-th derivative of the desired output; e(t) is the tracking error, e(t) = y r (t) - y(t), g c (e(t)) is the error feedback term, and the common form is where K p is the proportional coefficient, K I is the integral coefficient, K d is the differential coefficient, is the first derivative of the error.

[0110] In summary, in view of the problem that the performance of traditional control strategies significantly degrades when it is difficult to ensure the modeling accuracy of the system or the model parameters are unknown, the present invention further studies a model-free control method that does not require an accurate model. Under the framework of the hyper-local model, the system dynamics are reconstructed into a combined form of control gain and unknown disturbance. The system disturbance is estimated by using the online response of the input and output signals, and a feedback linearization control law is designed to achieve precise tracking control of the output state. To improve the stability of the model-free control method in high-frequency disturbance and dynamic environments, the present 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 frequency-domain performance of the observer and the dynamic response speed of the system.

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

[0112] Referring to Figure 2 , during the coal unloading process in a railway freight yard, the coal unloading crawler device faces complex coal unloading conditions. Among them, uncertainties such as the shape, compactness, and mass distribution of the coal pile will cause a dynamic load response with multi-source coupling. This dynamic load is the main factor restricting the coal unloading efficiency and equipment stability. These factors not only determine the cutting resistance of the scraper bucket and the type of load fluctuation, but also directly affect the accuracy and robustness of the speed control system.

[0113] The natural accumulation of coal forms physical characteristics such as particle stratification, density distribution changes, and uneven inclination angles, resulting in a dynamic change in the coal pile slope during the coal unloading process, showing a trend of being steep first and then gentle. In the initial stage, the coal is relatively loose and the load is low; when the coal pile slope reaches the critical value, the friction between coal particles increases and the load rises rapidly; when the coal unloading approaches the bottom, the high-compactness coal seam causes the load to further increase, forming a periodic load fluctuation. Among them, the natural angle of repose of coal is the key parameter determining the cutting resistance of the scraper bucket. Different moisture contents, particle diameters, and coal types will cause changes in the natural angle of repose, thereby affecting the load characteristics. When the coal pile slope is steep (close to or exceeding the natural angle of repose), the scraper bucket cutting the coal seam is likely to cause local collapse, resulting in a sharp increase in the instantaneous load and a surge in the motor torque demand, and even triggering overload protection, causing the equipment to lose power output. On the other hand, when the coal pile slope is gentle (much smaller than the natural angle of repose), the cohesion and adhesion of coal particles increase, resulting in a decrease in the cutting resistance of the scraper bucket, a reduction in the coal unloading volume per unit time, and an extension of the operation cycle. Too gentle a slope may form a high-compactness coal seam, increasing the cutting resistance of the scraper bucket instead, resulting in an increase in equipment energy consumption. Therefore, if the speed control system cannot adapt to this non-linear load change caused by the dynamic inclination angle, it may cause the scraper bucket to get stuck in the high-load area, affecting the continuity of the coal unloading operation.

[0114] The compaction degree of coal in the storage yard determines the instantaneous load during the cutting of the scraper bucket and the energy consumption of the system. Due to the gravitational force of the upper-layer coal, the internal particle gaps of the coal stacked for a long time are reduced, forming a high-compaction coal seam, which significantly increases the shear strength and penetration resistance. Research shows that in a high-compaction coal seam, the cutting resistance of the scraper bucket is 30% - 50% higher than that in a loose coal seam, resulting in an instantaneous surge in the motor current and severe fluctuations in the chain tension. If the control system responds laggishly, it may cause the motor to stall or the chain to skip, and even lead to equipment damage. In addition, the coal particles in the high-compaction coal seam may fall off as a whole block during the cutting of the scraper bucket, hitting the wall of the conveying trough, forming impact vibration, and causing severe fluctuations in the motor output torque, exacerbating the instability of the system. The change pattern of coal compaction shows the characteristics of uneven spatial distribution and dynamic temporal variation with the coal unloading process. In the coal pile, the bottom-layer coal has the highest compaction degree due to long-term pressure and bears the largest load during the cutting of the scraper bucket; while the upper-layer coal is relatively loose with a lower compaction degree and a smaller load. Therefore, there are significant differences in the load when the scraper bucket operates at different depths, requiring the speed control system to be able to monitor the load changes in real time and perform dynamic compensation.

[0115] The mass distribution inside the coal pile is usually uneven, and there are significant variations in the density, particle size, and moisture content of the coal in different regions, making the load characteristics of the scraper bucket show random mutation characteristics. The particle stratification effect of coal causes large coal lumps to be easily stacked on the upper layer, while fine coal powder fills the bottom layer. This stratification phenomenon leads to severe fluctuations in the load during the coal unloading process. When the scraper bucket enters the fine coal powder area, due to the increased adhesion force between particles, the cutting resistance rises, the motor torque increases, which may cause problems such as unstable chain tension and increased energy consumption. On the contrary, when the scraper bucket enters the large-particle coal area, the coal pile is relatively loose, the friction force is small, the cutting resistance decreases, resulting in an instantaneous reduction in the load, but when suddenly encountering large coal lumps, it may cause short-term blockage or impact vibration, affecting the equipment stability. In addition, the uneven mass distribution may lead to local instability of the coal pile, and the sudden change in load may be caused by the sliding or collapse of the coal, 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 non-linear working conditions, this paper comparatively analyzes the response effects of three control methods in the typical application scenarios of the coal unloading crawler, namely: ① the traditional proportional-integral-differential (PID) controller, ② the model-free controller based on the traditional ESO (Traditional MFC), and ③ the proposed model-free controller based on the improved ESO (Improved MFC), specifically:

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

[0118] Combined type of controller ② Type And type

[0119] Combined type of controller ③ Type And type

[0120] The comparative simulation is carried out considering typical complex factors such as non - linear disturbances, periodic loads, and high - frequency noises, aiming to evaluate the performance differences of different control strategies in terms of system stability, disturbance rejection ability, tracking accuracy, and response speed. The complex load and disturbance conditions include that the load characteristics show strong non - linearity, randomness, and periodicity with time and space variations. The specific complex load and disturbance condition model is as follows:

[0121]

[0122] Among them, T0 is the basic load term, representing the basic torque demand of the device when there is no external coal resistance, mainly including system static friction, basic torque during no - load operation, etc., usually being a constant, reflecting the light - load characteristics in the initial stage of coal unloading. γ(vt) n is the non - linear load growth term, which simulates the phenomenon that the resistance of the compaction coal seam increases as the scraper bucket gradually penetrates into the coal pile during the coal unloading process. Among them, v is the propulsion speed, t is the time, n is the non - linear order (usually taken as 2 or 3), and γ is the resistance growth coefficient. This term increases exponentially with time, reflecting the significant non - linear influence of coal seam compaction on the cutting load. A p sin(2πf d t) is the periodic disturbance term, simulating the regular changes brought about by the slope structure of the coal pile, such as the high - low fluctuation area of the scraper bucket passing through the coal pile, or the density fluctuation between the stacked coal layers. This term is a sine function, A p is the amplitude of the periodic disturbance, f d is the disturbance frequency. It reflects the periodic load fluctuation characteristics during the coal unloading process. ση(t) is the random disturbance term, simulating the random disturbances caused by factors such as uneven coal density, particle size variation, and moisture content fluctuation. This term is a zero - mean Gaussian white - noise model, σ is the disturbance intensity, and η(t) is the standard Gaussian noise sequence, representing the random influence of local coal pile characteristics on the load. ∑A k δ(t - t k ) is used to simulate the instantaneous impact loads caused by events such as the collapse of large - sized coal, the scraper bucket encountering hard lumps, and local sliding. A k is the amplitude of the k - th impact, δ(t - t k ) is the unit impulse function, simulating that this sudden event occurs at t kMoment. This item reflects the uncertainties and discontinuous disturbances existing in the coal unloading process. The specific parameters are referred to Table 1.

[0123] Table 1 Parameter Setting of Complex Load Disturbance Conditions

[0124] parameter description numerical value <![CDATA[T0]]> base load 500 N·m γ nonlinear coefficient 0.05 v propulsion speed 0.5 m / s n nonlinear power 2 <![CDATA[A p > amplitude of periodic perturbation 100 N·m <![CDATA[f d > frequency of periodic perturbation 0.3 Hz σ intensity of random perturbation 25 N·m <![CDATA[A k > impact amplitude 200 N·m <![CDATA[t k > impact time 2.1 s, 4.6 s

[0125] As Figure 3 shown, this figure is the dynamic change curve of the system load over time under complex load disturbance conditions, reflecting the actual load characteristics under the superposition of various factors during the coal unloading process. It can be seen from Figure 3 that the system load mainly fluctuates around 500 N·m, presenting three types of composite characteristics of periodic oscillation, random disturbance and instantaneous impact as a whole, and its composition is consistent with the complex load disturbance condition model. Specifically: the load curve changes in a quasi-sine form at a frequency of about 0.3 Hz, which is the periodic disturbance caused by the coal pile slope structure, reflecting the actual characteristics of the periodic cutting load fluctuation during the scraper bucket propulsion process. There are small-amplitude jitters with high frequency on the curve surface, which are caused by the Gaussian white noise term σ = 25 N·m, simulating the instantaneous disturbances brought 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 shows a short-term sharp rise, up to about 800 N·m at most, which is caused by the superposition of the instantaneous impact term A k = 200 N·m, simulating the strong disturbances to the system caused by discontinuous events such as coal block sliding and scraper bucket impact during the coal unloading process.

[0126] To verify the speed regulation control performance of the model-free control method based on the improved extended state observer (Improved ESO) proposed in this paper under complex load disturbance conditions, this paper carried out simulation analysis based on a typical coal unloading load model, and compared it with the traditional model-free control (MFC + linear ESO) and the conventional PID control strategy. By quantitatively comparing the response speed, steady-state error and jitter degree of the control system under disturbance conditions, the control accuracy, dynamic adaptability and robustness advantages of the proposed improved MFC method under non-ideal conditions are systematically verified. The specific parameters are referred to Table 2.

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

[0128] parameter description numerical value <![CDATA[K p > proportionality coefficient 4000 <![CDATA[K I > integral coefficient 100 <![CDATA[K d > differential coefficient 10 <![CDATA[β1]]> observer first state gain 100 <![CDATA[β2]]> observer second state gain 2500 α model-free control input gain 1000 λ weight parameter of compensation filter 50

[0129] As Figures 4 to 7 shown, this figure is the dynamic response simulation curve of different control strategies under complex load disturbance conditions. Among them, with the target speed of 100 rad / s as the set value, under the condition of introducing multi-source disturbances (periodic disturbance, random noise, non-linear load growth and instantaneous impact), specifically refer to Figure 3 . It can be seen from Figure 4It can be seen that all three controllers can maintain a certain speed tracking ability during the entire 5s operation cycle, but there are significant differences in their performance. The improved MFC always maintains a small error amplitude in each stage, with the smallest overall fluctuation, showing good stability and robustness. The traditional MFC performs better than the PID control in most time periods, but there are certain low-frequency deviations and disturbance coupling fluctuations; while under the influence of complex disturbances, the error fluctuations of the PID controller are severe, especially in the high-frequency disturbance region, where significant oscillation phenomena occur and the control effect is not ideal. Figure 5 It is a partial enlarged view of the error response in the initial startup stage (0 - 0.4s). It can be seen that the PID control shows obvious overshoot and large-amplitude oscillation at the moment of startup (0 - 0.05s), and its error peak is close to ±4rad / s. Subsequently, the oscillation lasts for a long time, the adjustment process is slow, and the stability is poor. The traditional MFC suppresses part of the initial fluctuation compared with the PID, but there is still a certain tracking delay during the acceleration process. In contrast, the improved MFC can quickly stabilize the error within 0.1s, with a faster initial response and almost no obvious overshoot, having a better dynamic response speed. Figure 6 What is shown is the local response when the first sudden disturbance (around 2.1s) occurs. From Figure 6 it can be clearly observed that the errors of all three controllers mutate instantaneously at the moment of disturbance, but the disturbance response amplitude of the improved MFC is the smallest and the recovery time is the shortest; although the traditional MFC has a certain suppression ability, transient fluctuations still occur under the influence of the disturbance; while the PID control is severely affected by the impact, the error spikes are obvious, and it is difficult to quickly return to the set speed, reflecting its limited ability to suppress uncertain disturbances. Figure 7 It is the local response when the second impact disturbance occurs (4.6s). From Figure 7 it can be seen that the improved MFC once again demonstrates a strong disturbance suppression ability, and the error can return to near the steady-state value within a short time; there is a certain disturbance amplification effect under the traditional MFC control, and the fluctuation duration is slightly longer; while the PID controller shows a relatively serious speed deviation in this stage, and the system stability and tracking consistency are significantly inferior to the former two. Therefore, through the simulation comparison in the complex load disturbance environment, it can be obtained that the improved MFC proposed in this paper still has higher steady-state accuracy, faster response speed and stronger anti-disturbance robustness under the combined action of nonlinear disturbances, sudden loads and high-frequency noises, which is significantly better than the traditional MFC and PID controllers.

[0130] Under complex load disturbance conditions, the current response characteristics are an important index for evaluating the stability and robustness of control strategies. Figure 8 And Figure 9 respectively show the dynamic response of the q-axis current under the improved MFC controller and the traditional PID controller, and there are obvious differences in their control stability, disturbance suppression ability and execution efficiency. From Figure 8It can be seen that under the action of the improved MFC controller, i q the overall fluctuation range of the current is small, always maintained between 7A and 15A, and shows a stable dynamic adjustment process with the disturbance of the load cycle. At 2.1s and 4.6s, due to the sudden impact load disturbance, i q the current rises instantaneously but can still quickly fall back to the normal level without overshoot or continuous oscillation, indicating that the proposed disturbance compensation mechanism can effectively sense and quickly suppress strong interference to ensure the stable operation of the system.

[0131] In contrast, the PID controller in Figure 9 shows extremely poor current response performance under the same disturbance conditions. i q The current has severe high-frequency fluctuations, with the maximum amplitude exceeding 6000A and the minimum dropping to -4000A, far beyond the safe operating range of the motor. This abnormal high-amplitude current oscillation may not only trigger the overload protection of the driver but also pose a risk of damaging the power device, seriously threatening the stability and safety of the system. The main reason for this phenomenon is that the traditional PID controller cannot sense the source of complex disturbances, and its feedback regulation lags behind the dynamic changes of the system, resulting in i q the current frequently overshoots and is continuously corrected, thus triggering the high-frequency resonance problem.

[0132] As Figure 10 shown, this figure is the comparison simulation curve of the observation and tracking performance of the improved MFC and the traditional MFC for the simulated load. From the overall trend, both observers can effectively track the main change trend of the load disturbance, indicating that the constructed super-local model and ESO structure have a certain disturbance sensing ability. However, there are obvious differences in the estimation accuracy and response sensitivity between the two: the improved ESO has a higher fitting degree to the real load curve, especially during the load cycle fluctuation process, it can better capture the detailed changes of the load rising and falling, showing a smoother and more accurate estimation trajectory; while the estimated values of the traditional ESO deviate in multiple sections, especially in the intervals where the load rises or falls rapidly, there are obvious lags or under-fitting phenomena in its estimation. At the two typical impact disturbances of 2.1s and 4.6s, the estimation results of the improved ESO show a faster response speed and higher disturbance reconstruction ability, and can quickly reflect the sharp rising trend of the load and recover quickly; in contrast, the response of the traditional ESO is relatively slow, there is an estimation lag at the mutation moment, and the peak height is significantly lower than the real disturbance, with a large error.

[0133] In summary, aiming at the problems faced by the motor speed control system of the coal unloading crawler device under random load disturbance conditions, such as model uncertainty, high-frequency noise interference, and difficulty in modeling dynamic disturbances, a model-free control strategy based on the super-local model is constructed, and an improved ESO is introduced to enhance the disturbance estimation ability and control response performance of the system. By simplifying the modeling of the PMSM speed loop and constructing a super-local model to equivalently converge complex disturbances into observable variables, the dependence of the control system on the system structure is eliminated. On the basis of the traditional ESO structure, a disturbance compensation term and a low-pass filtering mechanism are introduced in this paper, effectively suppressing the jitter amplification problem of finite difference estimation under high-frequency disturbances and enhancing the robustness of the system to time-varying disturbances and measurement noise. Furthermore, an MFC controller based on disturbance feedback linearization is constructed to achieve high-precision speed control in a strong uncertain environment. The simulation analysis fully demonstrates the superiority of the proposed control strategy from three dimensions: tracking accuracy, current stability, and disturbance rejection ability.

[0134] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.

Claims

1. An improved model-free control method with an extended state observer under random load disturbance conditions, characterized in that: including, establish the mechanical motion equation of the coal unloading crawler device, which is composed of a chain system, scraper buckets, a tensioning mechanism, a driving motor and a main frame; establish the super-local model of the coal unloading crawler device according to the model-free control theory and rewrite the extended state equation; in view of the limitations of the finite difference method, introduce an extended state observer to estimate all unknown dynamics in real time; introduce a compensation function to construct an improved extended state observer to correct the estimation error, thereby designing a model-free controller.

2. The improved model-free control method of the extended state observer under the random carrier interference condition according to claim 1, wherein: The mechanical motion equation of the coal unloading crawler device is: where J is the moment of inertia, ω m is the mechanical angular velocity of the rotor, T e is the electromagnetic torque, T1 is the load torque, and f is the friction coefficient, represents the angular acceleration of the coal unloading crawler device; Set the d-axis current i d = 0, and at this time the electromagnetic torque is simplified to: where P is the number of pole pairs of the motor, φ f is the electromotive force constant, i d is the stator current component in the d-axis direction, i q is the stator current component in the q-axis direction; Substitute the electromagnetic torque equation into the mechanical motion equation of the coal unloading crawler device to obtain:

3. The model-free control method with an improved extended state observer under random carrier interference conditions according to 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 equation: where \(y(t)\) is the system output, \(u(t)\) is the system input, \(y\) (v) (t) and \(u\) (y) (t) represent the high-order derivatives of the output and input respectively, and \(M\) p ( ) represents the unknown dynamic model of the system; Set the input-output relationship of the system, expressed as: Among them, represents the inherent dynamic characteristics of the system, represents the input gain, and d(t) represents the external disturbance; Based on the uncertainty of the system, modify the system model to: Among them, represents the unmodeled dynamics and parametric uncertainties of the system; If the input gain of the system is set to a constant α, it simplifies to: y (v) (t) = F(t) + ξu(t); where F(t) is all unknown dynamics and ξ is the control gain of the experiment.

4. The model-free control method of an improved extended state observer under a random carrier interference condition according to claim 3, characterized in that: The establishment of the super-local model of the coal unloading crawler device means that according to the model-free control theory, the mechanical motion equation of the coal unloading crawler device is rewritten into the super-local model of the coal unloading crawler device, and the expression is Among them, As the control output, u = i q As the control input, is the control gain coefficient; The extended state equation is where x1 = y is the output of the system, and x2 = F(t) is the unmodeled dynamics, which is the rate of change of the disturbance F(t).

5. The model-free control method with an improved extended state observer under random carrier interference conditions according to claim 4, characterized in that: The extended state observer is: Among them, is the estimation of x1 = y, is the estimation of x2 = F(t), and β1 and β2 are the observation gains of the extended state observer.

6. The improved model-free control method of the extended state observer under the random carrier interference condition according to claim 5, characterized in that: The improved extended state observer refers to introducing a compensation function to correct the estimation error of F(t), so that the improved extended state observer is 7. The model-free control method of an improved extended state observer under a random carrier interference condition according to claim 6, characterized in that: The model-free controller refers to designing feedback linearization control based on the estimated F(t), and the control law is as follows Among them, is the v-th derivative to be expected; e(t) is the tracking error, and g c (e(t)) is the error feedback term.

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