A permanent magnet motor sliding mode speed control method and system for underground coal mine transportation equipment

Abstract

The application discloses a kind of permanent magnet motor sliding mode speed control methods for coal mine underground transport equipment, comprising the following steps: combining motor electromagnetic torque equation, write motor mechanical motion equation into the form of first-order linear differential equation set, obtain mechanical motion equation set;According to mechanical motion equation set, construct model compensation cascade extended state observer, estimate out lumped disturbance;Lumped disturbance is multiplied by the negative reciprocal of controller gain to obtain disturbance feedforward compensation control law, and the disturbance feedforward compensation control law is applied to the control system, to obtain the nominal system of control system without considering disturbance;Combined with nominal system, select sliding mode variable and sliding surface function, construct adaptive coefficient with sliding surface function as variable F ( S );The adaptive nonsingular fast terminal sliding mode controller output speed tracking control law is constructed, which is used for feedback adjustment based on tracking error.The application can improve the dynamic performance and robustness of the system under the conditions of load mutation, parameter perturbation, etc.

Description

Technical Field

[0001] This invention relates to the control of permanent magnet synchronous motors, and more particularly to a method and system for controlling the sliding speed of a permanent magnet motor in underground coal mine transportation equipment. Background Technology

[0002] In underground coal mine transportation systems, permanent magnet synchronous motors (PMSMs), with their high power density, high efficiency, and excellent reliability, have become the core drive source for high-power continuous transportation equipment, widely used in key equipment such as mine belt conveyors, scraper conveyors, endless rope continuous traction vehicles, and underground drainage pumping stations. However, the underground coal mine environment is extremely unique, and transportation equipment often faces frequent heavy-load starts and stops, drastic load changes, and complex nonlinear frictional disturbances (such as conveyor belt deviation resistance, scraper chain jamming, and vibrations caused by track irregularities). These operating conditions place extremely high demands on the dynamic response speed, disturbance rejection capability, and steady-state accuracy of the drive system.

[0003] PMSM is inherently a multivariable, strongly coupled, and nonlinear system, and its mathematical model is highly dependent on motor parameters (such as stator resistance, inductance, and flux linkage). In actual operation, due to large variations in downhole ambient temperature, long-term heavy-load operation of equipment leading to parameter drift, and the randomness and unpredictability of load disturbances, traditional linear control strategies based on precise mathematical models (such as PI control) struggle to achieve fast and accurate speed tracking while ensuring system stability. Especially during sudden load changes, traditional control often exhibits significant overshoot or excessively long recovery times, affecting transportation efficiency and even causing mechanical failures.

[0004] To improve system robustness, sliding mode control (SMC) has attracted much attention due to its inherent invariance to parameter perturbations and external disturbances. However, traditional sliding mode control suffers from inherent chattering, which easily induces mechanical resonance and accelerates actuator wear. While terminal sliding mode control (TSMC) can achieve finite-time convergence and improve dynamic response, it may face singularity problems, leading to control divergence. Furthermore, existing state observation techniques (such as LESO) often rely on models, making it difficult to adapt to the strong model uncertainties under complex and variable underground operating conditions. This results in large disturbance observation errors and phase lag, weakening the feedforward compensation effect and limiting the improvement of overall control performance. While some existing technologies have attempted to address this through high-order observers or complex compensation algorithms, such solutions typically involve high computational costs, difficult parameter tuning, and high processor resource requirements, making it difficult to meet the stringent engineering requirements of high reliability, real-time performance, and ease of maintenance for underground coal mine equipment.

[0005] Therefore, for permanent magnet motor drive applications in underground coal mine transportation equipment, how to design a speed control method that combines fast convergence, no singularity, strong disturbance rejection capability, and easy engineering implementation under conditions of strong nonlinear friction, drastic load changes, and uncertain model parameters, accurately identify the total disturbance of the system through an improved observer, and achieve high-performance control by combining advanced sliding mode strategies has become a key technical problem that urgently needs to be solved for this type of system. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a sliding mode speed control method and system for permanent magnet synchronous motors in underground coal mine transportation equipment, so as to achieve robust speed control of permanent magnet synchronous motors under disturbances such as sudden changes in load torque and perturbations of rotational inertia parameters.

[0007] Technical solution: A method for sliding mode speed control of permanent magnet motors for underground coal mine transportation equipment, comprising the following steps:

[0008] Combining the electromagnetic torque equation of the motor, the mechanical motion equation of the motor is written in the form of a first-order linear differential equation system, thus obtaining the mechanical motion equation system.

[0009] Based on the aforementioned set of mechanical motion equations, a model compensation cascaded expansion state observer is constructed to estimate the lumped disturbance;

[0010] Multiplying the lumped disturbance by the negative reciprocal of the controller gain yields the disturbance feedforward compensation control law. Applying the disturbance feedforward compensation control law to the control system yields the nominal system of the control system without considering the disturbance.

[0011] By combining the nominal system to select sliding mode variables and sliding mode surface functions, an adaptive coefficient F(S) with the sliding mode surface function as the variable is constructed;

[0012] An adaptive non-singular fast terminal sliding mode controller is constructed by combining the adaptive coefficient F(S), the adaptive switching control law, and the adaptive equivalent control law. The speed tracking control law output by the adaptive non-singular fast terminal sliding mode controller is used for feedback regulation based on the tracking error.

[0013] By combining the disturbance feedforward compensation control law and the speed tracking control law into a composite control law, a dual-loop collaborative composite control structure is formed, achieving robust and disturbance-resistant speed control of the permanent magnet synchronous motor.

[0014] Furthermore, based on the aforementioned set of mechanical motion equations, the steps for constructing a model-compensated cascaded expansion state observer are as follows:

[0015] SC1, rewrite the mechanical equations of motion as a system of first-order linear differential equations:

[0016] ,

[0017] In the formula, x1= ω r u = i q * These are system output and control input, respectively; i q ω is the reference input for the q-axis current of the current loop, d1 is the lumped disturbance, and h1 is the derivative of d1; r For the mechanical rotational speed, b0 = 3P n ψ f / 2J is the controller gain. P represents the moment of inertia. n Let ψ be the extreme logarithm. f For permanent magnet flux linkage;

[0018] SC2, based on the mechanical motion equations, constructs the state equations of the first-stage linear extended state observer of the model-compensated cascaded extended state observer, which are expressed as follows:

[0019] ,

[0020] In the formula, z 11 Let z be an estimate of x1. 12 This is an estimate of d1. and For observer gain; This represents the error in the first rotational speed estimation.

[0021] SC3, design the state equation for the second-stage linear extended state observer, the expression of which is:

[0022] ,

[0023] In the formula, z 12 As the known input to the second-level linearly extended state observer, z 21 The estimated value of x1 is used as the control input, z 22 The remaining total disturbance is d2 = d1 - z 12 The estimated value; and For observer gain; This is the estimated difference for the second rotational speed.

[0024] Furthermore, the expression for the disturbance feedforward compensation control law is as follows:

[0025] ,

[0026] In the formula, u2 is the disturbance feedforward compensation control law of the control system.

[0027] Furthermore, the steps to obtain the speed tracking control law include:

[0028] SD1, constructing a nominal system that does not consider the effects of disturbances, is expressed as: ;

[0029] SD2, combined with the nominal system expression, the sliding mode variable is:

[0030] ;

[0031] Select the surface variable S of the sliding mode surface:

[0032] ,

[0033] In the formula, , , , These are the control gains, and p and q must both be odd numbers.

[0034] SD3, design the coefficient F(S) that adaptively adjusts with the sliding surface variable S, the expression is as follows:

[0035] ,

[0036] In the formula, a, b, c, d, e, and h are all positive real numbers, and satisfy the following condition: The upper and lower bounds of the coefficient F(S) are respectively and The inflection point is located in the interval Inside;

[0037] SD4, constructing an adaptive switching control law The expression is:

[0038] ,

[0039] In the formula, k is the positive real gain; sat(S) is the saturation function used to reduce high-frequency chattering, and its expression is:

[0040] ,

[0041] Where parameters It is the saturation boundary of its linear interval;

[0042] An adaptive mechanism and an integral element are introduced into the traditional equivalent control law to construct an adaptive equivalent control law, as shown in the following expression:

[0043] ,

[0044] ,

[0045] In the formula, F(2h - S) is a symmetric function of the adaptive coefficient F(S) with respect to S = h, and A b With A c It is a positive real gain;

[0046] An adaptive non-singular fast terminal sliding mode controller is constructed using an adaptive switching control law and an adaptive equivalent control law; the speed tracking control law is then output from the adaptive non-singular fast terminal sliding mode controller. The expression is:

[0047] .

[0048] Furthermore, the composite control law is used as the reference input for the q-axis current of the current loop, and its expression is:

[0049] ,

[0050] In the formula, u1 is the speed tracking control law, and u2 is the disturbance feedforward compensation control law of the control system. It is a composite control law.

[0051] A sliding mode speed control system for permanent magnet motors in underground coal mine transportation equipment, used to execute any of the above-mentioned permanent magnet motor sliding mode speed control methods, comprising:

[0052] The model conversion module is used to obtain the mechanical motion equations in the form of a set of first-order linear differential equations combining the motor and electromagnetic torque equations.

[0053] The lumped disturbance observation module is used to estimate the lumped disturbance of the system by constructing a model-compensated cascaded extended state observer;

[0054] A robust speed tracking module is used to achieve robust speed tracking of the nominal system by constructing an adaptive non-singular fast terminal sliding mode controller;

[0055] The composite control law dual-loop coordinated control module estimates the lumped disturbance and multiplies it by the negative reciprocal of the controller gain to obtain the disturbance feedforward compensation control law, which constitutes the inner loop control structure of the control system and is used to observe and compensate for the lumped disturbance of the system in real time. The speed tracking control law output by the adaptive non-singular fast terminal sliding mode controller constitutes the outer loop control structure of the control system and is used for feedback adjustment based on the tracking error.

[0056] Compared with the prior art, the significant advantages of this invention are as follows:

[0057] 1. The MC-CESO of this invention, combined with the electromagnetic torque equation, expresses the motion equations of the permanent magnet synchronous motor and the mechanical system as a set of first-order linear differential equations. MC-CESO features tight coupling and rapid compensation. Its first-stage LESO uses system model information to pre-estimate some lumped disturbances, and the second-stage LESO introduces this estimation result as a dynamic compensation term into the observer equation to correct the system model. Compared with traditional LESO, MC-CESO improves disturbance estimation accuracy without increasing the bandwidth frequency, and can better balance the system's disturbance rejection performance and noise suppression capability.

[0058] 2. The A-NFTSMC of the present invention, by designing an adaptive equivalent control law and an adaptive switching control law, and introducing an integral term in the equivalent control law, enhances the convergence capability in the dynamic process and reduces chattering in the steady state stage, thereby better coordinating the contradiction between fast convergence and chattering suppression in the traditional NFTSMC.

[0059] 3. This invention designs a dual-loop collaborative composite control structure for the speed loop. The lumped disturbance estimated by MC-CESO is multiplied by the reciprocal of the control gain to obtain the disturbance feedforward compensation control law, which serves as the inner loop control structure to counteract the impact of the lumped disturbance on the control system. The speed tracking control law output by A-NFTSMC is used as the outer loop control structure to achieve robust speed tracking of the control system. Both mechanisms together improve the dynamic performance and robustness of the system under complex conditions such as sudden load changes and parameter perturbations. Attached Figure Description

[0060] Figure 1 This is a structural block diagram of MC-CESO provided in one embodiment of the present invention;

[0061] Figure 2 Bode plot of the MC-CESO transfer function provided in one embodiment of the present invention;

[0062] Figure 3 This is a schematic diagram of the A-NFTSMC system structure based on MC-CESO provided in one embodiment of the present invention;

[0063] Figure 4 This is a flowchart of the permanent magnet motor speed control method of the present invention;

[0064] Figure 5 The figure shows the comparison test results of the load torque step change when the motor is running at 300 rpm in one embodiment of the present invention, where (a) is the A-NFTSMC based on the traditional LESO, (b) is the traditional NFTSMC based on MC-CESO, and (c) is the A-NFTSMC based on MC-CESO.

[0065] Figure 6 The figure shows the parameter perturbation comparison test results of the motor running at 300 rpm in one embodiment of the present invention, where (a) is the A-NFTSMC based on the traditional LESO, (b) is the traditional NFTSMC based on MC-CESO, and (c) is the A-NFTSMC based on MC-CESO. Detailed Implementation

[0066] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0067] like Figure 1 The diagram shown is a structural block diagram of the MC-CESO of this invention. The lumped disturbance observation module constructs the MC-CESO (Model-Compensated Cascaded ESO) based on the motor's mechanical motion equations. It is used to observe the lumped disturbances experienced by the system, including load torque, reluctance torque, friction torque, parameter perturbations, and external disturbances. The estimated lumped disturbance is multiplied by the reciprocal of the control gain to obtain the disturbance feedforward compensation control law. This law is used as part of the speed loop control output, forming the inner loop control structure of the control system. The construction steps of the MC-CESO and the disturbance feedforward compensation control law are as follows:

[0068] Step A1: Substitute the electromagnetic torque equation of the IPMSM (Inner-mounted Permanent Magnet Synchronous Motor) into the mechanical motion equation, where the IPMSM electromagnetic torque equation is:

[0069] ,

[0070] In the formula, P n Let ψ be the extreme logarithm. f For permanent magnet flux linkage, L d L q These are the inductances of the IPMSM along the d-axis and q-axis, respectively. d i q These are the currents of the IPMSM on the d-axis and q-axis, respectively. This indicates the output torque of the permanent magnet motor.

[0071] Combining the electromagnetic torque equations above, the mechanical motion equations of the IPMSM can be written in the following form:

[0072] ,

[0073] In the formula, ω r For the mechanical rotational speed, b0 = 3P n ψf / 2J is the controller gain, B is the friction coefficient, and T is the controller gain. L For load torque, It represents the moment of inertia.

[0074] Step A2: Rewrite the mechanical motion equations as a system of first-order linear differential equations:

[0075] ,

[0076] In the formula, x1= ω r u = i q * These are the system output and control input, respectively. q * d1 is the reference input for the q-axis current; d1 includes the lumped disturbances, including load torque, reluctance torque, friction torque, parameter perturbations, and external disturbances; h1 is the derivative of d1.

[0077] Step A3: Construct the first-level linear extended state observer (LESO1) of MC-CESO based on the mechanical motion equations. The expression of the state equations is as follows:

[0078] ,

[0079] In the formula, z 11 Let x1 be the estimated value (i.e., the LESO1 rotational speed estimate), and z be the estimated value. 12 This is an estimate of d1. and For observer gain, This represents the estimation error for the first rotational speed.

[0080] Step A4, design the second-stage linear extended state observer (LESO2), the expression of the state equation is:

[0081] ,

[0082] In the formula, z 12 As the known input for the second-level LESO, z 21 The estimated value of x1 (i.e., the LESO2 speed estimate) is used as the control input, z 22 The remaining total disturbance is d2 = d1 - z 12 The estimated value, and For observer gain; This represents the second rotational speed estimation error.

[0083] Step A5: Multiply the lumped disturbance estimated by MC-CESO by the negative reciprocal of the control gain and use it as the disturbance feedforward compensation control law input to the speed loop; the expression of the disturbance feedforward compensation control law is:

[0084] ,

[0085] In the formula, u2 is the disturbance feedforward compensation control law of the control system.

[0086] from Figure 2 It can be seen that MC-CESO has significantly smaller estimation errors for lumped disturbances in the mid-to-low frequency band, and its estimation accuracy is better than LESO. Furthermore, the disturbance estimation performance of MC-CESO improves even more significantly with increasing bandwidth. Even though the bandwidth frequencies of the two cascaded LESOs in MC-CESO are lower than those of traditional ESO, the disturbance estimation accuracy of MC-CESO is still higher than that of traditional LESO in the mid-to-low frequency band. In addition, the bandwidth of the second-stage LESO in MC-CESO can be smaller than that of the first-stage LESO. This indicates that MC-CESO can overcome bandwidth limitations while balancing system noise immunity and noise reduction performance, thus improving noise reduction effectiveness.

[0087] like Figure 3 As shown, this invention presents a dual-loop coordinated composite control structure (A-NFTSMC system structure). The lumped disturbance estimated by the dual-loop coordinated control module is multiplied by the reciprocal of the controller's negative gain to obtain the disturbance feedforward compensation control law, forming the inner-loop control structure of the control system. This structure is used to observe and compensate for the system's lumped disturbance in real time. The speed tracking control law output by the A-NFTSMC (Adaptive Non-Singular Fast Terminal Sliding Mode Control) forms the outer-loop control structure of the control system, used for feedback adjustment based on the tracking error. The steps for obtaining the composite control law from the dual-loop coordinated composite control structure are as follows:

[0088] Step B1: Construct a nominal system representation that does not consider the effects of disturbances;

[0089] The output of the system control speed loop can be expressed as:

[0090] ,

[0091] In the formula, u1 is the speed tracking control law output by A-NFTSMC, and u2 is the disturbance feedforward compensation control law of the control system. It is a composite control law.

[0092] The disturbance feedforward compensation control law of the control system is expressed as:

[0093] ,

[0094] In the formula, we assume that the estimated value of the lumped disturbance is equal to the actual lumped disturbance z. 21 + z 22 = d1.

[0095] Substituting the above u2 expression into the proposed IPMSM mechanical motion equation, we obtain the nominal system expression considered by A-NFTSMC as follows:

[0096] .

[0097] Step B2: Select the sliding mode variables and sliding surface functions;

[0098] The sliding mode variable is selected as:

[0099] ,

[0100] In the formula, s1 is the speed tracking error, s2 is the integral of the speed tracking error, and ω r * This is the reference speed.

[0101] Combining the nominal system expression, the sliding mode variable can be rewritten as:

[0102] .

[0103] Selecting sliding surface variables :

[0104] ;

[0105] In the formula, , , , Let p and q be the control gains, respectively, and both p and q must be odd numbers.

[0106] Step B3: Design a coefficient F(S) that adaptively adjusts with the sliding surface variable S, as shown in the following expression:

[0107] ,

[0108] In the formula, a, b, c, d, e, and h are all positive real numbers, and satisfy the following condition: This function is continuously differentiable over the entire real number field. The function value varies with... Monotonically increasing, with upper and lower bounds respectively. and The inflection point is located in the interval Inside.

[0109] Step B4: Construct the adaptive switching control law and the adaptive equivalent control law to obtain the speed tracking control law output by A-NFTSMC;

[0110] Constructing an adaptive switching control law for:

[0111] ,

[0112] In the formula, k is the positive real gain, and sat(S) is the saturation function used to reduce high-frequency chattering, which has the following specific form:

[0113] ,

[0114] Where parameters It is the saturation boundary of its linear interval.

[0115] Differentiating with respect to the sliding surface, we obtain the equivalent control law for traditional non-singular terminal sliding modes:

[0116] .

[0117] By introducing an adaptive mechanism and an integral element into the traditional equivalent control law, the following adaptive equivalent control law is constructed:

[0118] ,

[0119] In the formula, F(2h - S) is a symmetric function of the adaptive coefficient F(S) with respect to S = h, and A b With A c It is a positive real gain.

[0120] Combining the adaptive switching control law and the adaptive equivalent control law described above, the speed tracking control law for the A-NFTSMC output can be obtained. The expression is:

[0121] ,

[0122] In the formula, the control performance is optimized through the dynamic adjustment of the adaptive coefficients F(S) and F(2h-S). When the system state is far from the sliding surface ( When it is relatively large, there is and At this point, the switching control gain increases and the equivalent control gain decreases. The system uses a strong switching control action to quickly drive the state towards the sliding surface, thereby significantly improving the dynamic convergence speed. When the system enters steady state ( When it is smaller, then it satisfies and At this point, the switching control gain automatically decreases, and the equivalent control effect is correspondingly enhanced, effectively suppressing high-frequency chattering caused by high-frequency switching while maintaining tracking accuracy. Through the above adaptive mechanism, the adaptive non-singular fast terminal sliding mode control enhances convergence capability during dynamic processes and reduces chattering in the steady-state phase, thus better coordinating the contradiction between fast convergence and chattering suppression in traditional adaptive non-singular fast terminal sliding mode control.

[0123] Step B5: Construct a composite control law dual-loop coordinated control structure to obtain the composite control law;

[0124] Composite control law As a reference input for the q-axis current of the current loop, it can be expressed as:

[0125] ,

[0126] In the formula, the estimated lumped disturbance multiplied by the reciprocal of the controller gain yields the disturbance feedforward compensation control law, which constitutes the inner-loop control structure of the control system and is used to observe and compensate for the lumped disturbance in real time. The speed tracking control law output by A-NFTSMC constitutes the outer-loop control structure of the control system and is used for feedback adjustment based on the tracking error. The resulting dual-loop collaborative composite control structure jointly improves the dynamic performance and robustness of the system under complex operating conditions such as sudden load changes and parameter perturbations.

[0127] Reference Figure 4 This invention discloses a non-singular fast terminal sliding mode speed control method for permanent magnet motors in underground coal mine transportation equipment. The method specifically includes the following steps:

[0128] Step S100: Combining the electromagnetic torque equation, the mechanical motion equation is transformed into a set of first-order linear differential equations, thus obtaining the mechanical motion equation set.

[0129] In step S200, by combining the mechanical motion equations, a model compensation cascaded expansion state observer is constructed to estimate the lumped disturbance of the system.

[0130] In step S300, the estimated lumped disturbance is multiplied by the reciprocal of the control gain to obtain the disturbance feedforward compensation control law, which is then substituted into the differential equation system in S100 to obtain the nominal system corresponding to the system without considering the disturbance.

[0131] In step S400, considering the obtained nominal system, construct an adaptive non-singular fast terminal sliding mode controller with a corresponding output speed tracking control law.

[0132] In step S500, the disturbance feedforward compensation control law is used as the inner loop control structure, and the speed tracking control law is used as the outer loop control structure to realize a composite control structure with dual-loop coordination.

[0133] An exemplary embodiment of the present invention provides an adaptive non-singular fast terminal sliding mode speed control system for permanent magnet motors in underground coal mine transportation equipment, with reference to... Figure 3 The permanent magnet synchronous motor control system can be implemented as all or part of the terminal through software, hardware, or a combination of both. This adaptive non-singular fast terminal sliding mode speed control system for permanent magnet motors in underground coal mine transportation equipment includes:

[0134] The model conversion module is used to obtain the mechanical motion equations in the form of a set of first-order linear differential equations combining the motor and electromagnetic torque equations.

[0135] The lumped disturbance observation module is used to estimate the lumped disturbance of the system by constructing MC-CESO;

[0136] A robust speed tracking module is used to achieve robust speed tracking of the nominal system by constructing an A-NFTSMC;

[0137] The dual-loop coordinated control module employs a composite control law. The estimated lumped disturbance is multiplied by the negative reciprocal of the controller gain to obtain the disturbance feedforward compensation control law, forming the inner-loop control structure of the control system. This law is used to observe and compensate for the system's lumped disturbance in real time. The speed tracking control law output by the A-NFTSMC forms the outer-loop control structure, used for feedback adjustment based on the tracking error. This combined dual-loop coordinated composite control structure enhances the system's dynamic performance and robustness under complex conditions such as sudden load changes and parameter perturbations.

[0138] Continue to refer to Figure 3 As shown, in one embodiment, a non-singular fast terminal sliding mode speed control method for permanent magnet motors in underground coal mine transportation equipment is proposed. The specific working process of this method is as follows:

[0139] The mechanical speed equation of the motor is combined with the electromagnetic torque equation and written in the form of a first-order linear differential equation system. Based on the electromagnetic torque equation, an MC-CESO is designed. First, a LESO is constructed as the first-stage observer of the MC-CESO. The lumped disturbance estimated by the first-stage LESO is taken as a known quantity and used as the control input of the second-stage LESO constructed based on the electromagnetic torque equation. The second-stage LESO performs residual re-estimation based on the lumped disturbance estimated by the first-stage LESO, outputting a more accurate lumped disturbance. The estimated lumped disturbance is multiplied by the negative reciprocal of the system's control gain to obtain the disturbance feedforward compensation control law, which is input to the speed loop. The control system eliminates the influence of the lumped disturbance on the control system, resulting in a nominal system that does not consider the disturbance's influence. Based on the nominal system, sliding mode variables and sliding mode functions are selected, and adaptive coefficients are designed to construct an adaptive switching control law and an adaptive equivalent control law. The combination of these two is used as the speed tracking control law to achieve robust tracking of the motor speed. The disturbance feedforward compensation control law is used as the inner-loop control structure of the speed control system, and the speed tracking control law is used as the outer-loop control structure of the speed control system, constructing a dual-loop coordinated composite control structure.

[0140] The beneficial effects of this invention were verified through experiments with a 750W permanent magnet synchronous motor.

[0141] The parameters of the motor used are as follows:

[0142] Table 1 Motor Parameters

[0143]

[0144] Figure 5 The diagram shows the experimental results of the step change in load torque for M1, M2, and the method described in this paper. Sudden increases and decreases in load torque were applied at times t1 and t2, respectively, with the load torque set as follows:

[0145] ,

[0146] In order to highlight the superiority of MC-CESO and A-NFTSMC designs, a comparative design experiment was conducted. Figure 5 (a) in the text refers to A-NFTSMC (abbreviated as M1) based on traditional LESO. Figure 5 (b) in the text refers to the traditional NFTSMC (abbreviated as M2) based on MC-CESO. Figure 5 In the diagram, (c) refers to A-NFTSMC based on MC-CESO (hereinafter referred to as "this method"). To ensure fairness in the above comparative experiments, the traditional LESO bandwidth was set to... The traditional NFTSMC switching control law is ,in For a fixed switching gain, the equivalent control law is: .

[0147] like Figure 5 As shown, after a sudden increase in load torque at time t1, the overshoot of this method is 7.73%, which is reduced by 3.74% and 1.07% compared to M1 and M2, respectively; the time required for this method to recover to steady state is 1.1s, which is shortened by 0.3s and 0.2s compared to M1 and M2, respectively. During this phase, the motor enters the stable load phase, and the steady-state peak-to-peak speed of this method is 20.4 rpm.

[0148] Figure 6 The experimental diagrams show the parameter perturbations of M1, M2, and the method described in this paper. The following parameter perturbations are introduced into the moment of inertia J at times t3 and t4:

[0149] ,

[0150] In order to highlight the superiority of MC-CESO and A-NFTSMC designs, a comparative design experiment was conducted. Figure 5 (a) in the text refers to A-NFTSMC (abbreviated as M1) based on traditional LESO. Figure 5 (b) in the text refers to the traditional NFTSMC (abbreviated as M2) based on MC-CESO. Figure 5 (c) is A-NFTSMC based on MC-CESO (hereinafter referred to as: this method).

[0151] like Figure 6 As shown, after the sudden increase in rotational inertia at t3, the peak-to-peak transient rotational speed of this method is 116.6 rpm, which is 12.0 rpm less than that of M2; the recovery steady-state time of this method is 0.3 s, which is 1.1 s and 0.1 s shorter than that of M1 and M2, respectively. After the motor recovers to steady state, and the moment of inertia decreases abruptly at time t4, the overshoot of this method is 12.47%, which is 1.40% less than that of M2. The steady-state recovery time of this method is 0.5s, which is 0.1s shorter than that of M2. In contrast, M1, limited by the computational power of LESO, causes the motor speed to drop by 70.4 rpm, stabilizing at 76.53% of the reference speed, i.e., 229.6 rpm. Therefore, the proposed method has satisfactory disturbance suppression and robust tracking performance.

[0152] The experimental results above show that the non-singular fast terminal sliding mode speed control method for permanent magnet motors in underground coal mine transportation equipment of the present invention can significantly improve dynamic process indicators such as overshoot and settling time under conditions such as load mutation and parameter perturbation, and significantly improve steady-state control accuracy, demonstrating better disturbance suppression capability, tracking performance and robustness.

[0153] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0154] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A sliding mode speed control method for permanent magnet motors in underground coal mine transportation equipment, characterized in that, The steps include the following: Combining the electromagnetic torque equation of the motor, the mechanical motion equation of the motor is written in the form of a first-order linear differential equation system, thus obtaining the mechanical motion equation system. Based on the aforementioned set of mechanical motion equations, a model compensation cascaded expansion state observer is constructed to estimate the lumped disturbance; Multiplying the lumped disturbance by the negative reciprocal of the controller gain yields the disturbance feedforward compensation control law. Applying the disturbance feedforward compensation control law to the control system yields the nominal system of the control system without considering the disturbance. By combining the nominal system to select sliding mode variables and sliding mode surface functions, an adaptive coefficient F(S) with the sliding mode surface function as the variable is constructed; An adaptive non-singular fast terminal sliding mode controller is constructed by combining the adaptive coefficient F(S), the adaptive switching control law, and the adaptive equivalent control law. The speed tracking control law output by the adaptive non-singular fast terminal sliding mode controller is used for feedback adjustment based on the tracking error; By combining the disturbance feedforward compensation control law and the speed tracking control law into a composite control law, a dual-loop collaborative composite control structure is formed, achieving robust and disturbance-resistant speed control of the permanent magnet synchronous motor.

2. The method for sliding mode speed control of permanent magnet motors for underground coal mine transportation equipment according to claim 1, characterized in that, Based on the aforementioned set of mechanical motion equations, the steps for constructing a model-compensated cascaded expansion state observer are as follows: SC1, rewrite the mechanical equations of motion as a system of first-order linear differential equations: ， In the formula, x1=ω r u=i q * These are system output and control input, respectively; i q ω is the reference input for the q-axis current of the current loop, d1 is the lumped disturbance, and h1 is the derivative of d1; r For the mechanical rotational speed, b0 = 3P n ψ f / 2J is the controller gain. P represents the moment of inertia. n Let ψ be the extreme logarithm. f For permanent magnet flux linkage; SC2, based on the mechanical motion equations, constructs the state equations of the first-stage linear extended state observer of the model-compensated cascaded extended state observer, which are expressed as follows: ， In the formula, z 11 Let z be an estimate of x1. 12 This is an estimate of d1. and For observer gain; This represents the error in the first rotational speed estimation. SC3, design the state equation for the second-stage linear extended state observer, the expression of which is: ， In the formula, z 12 As the known input to the second-level linearly extended state observer, z 21 The estimated value of x1 is used as the control input, z 22 The remaining total disturbance is d2 = d1 - z 12 The estimated value; and For observer gain; This is the estimated difference for the second rotational speed.

3. The method for controlling the sliding mode speed of a permanent magnet motor for underground coal mine transportation equipment according to claim 2, characterized in that, The expression for the disturbance feedforward compensation control law is: ， In the formula, u2 is the disturbance feedforward compensation control law of the control system.

4. The method for sliding mode speed control of permanent magnet motors for underground coal mine transportation equipment according to claim 1, characterized in that, The steps to obtain the speed tracking control law include: SD1, constructing a nominal system that does not consider the effects of disturbances, is expressed as: ; SD2, combined with the nominal system expression, the sliding mode variable is: ； Select the surface variable S of the sliding mode surface: ， In the formula, , , , These are the control gains, and p and q must both be odd numbers. SD3, design the coefficient F(S) that adaptively adjusts with the sliding surface variable S, the expression is as follows: ， In the formula, a, b, c, d, e, and h are all positive real numbers, and satisfy the following condition: The upper and lower bounds of the coefficient F(S) are respectively and The inflection point is located in the interval Inside; SD4, constructing an adaptive switching control law The expression is: ， In the formula, k is the positive real gain; sat(S) is the saturation function used to reduce high-frequency chattering, and its expression is: ， Where parameters It is the saturation boundary of its linear interval; An adaptive mechanism and an integral element are introduced into the traditional equivalent control law to construct an adaptive equivalent control law, as shown in the following expression: ， ， where F(2h - S) is a symmetric function of the adaptive coefficient F(S) with respect to S = h, A b is a positive real gain; and c is a positive real gain; and An adaptive non-singular fast terminal sliding mode controller is constructed using an adaptive switching control law and an adaptive equivalent control law; the speed tracking control law is then output from the adaptive non-singular fast terminal sliding mode controller. The expression is: 。 5. The method for controlling the sliding mode speed of a permanent magnet motor for underground coal mine transportation equipment according to claim 1, characterized in that, Using the composite control law as the reference input for the q-axis current of the current loop, the expression is: ， In the formula, u1 is the speed tracking control law, and u2 is the disturbance feedforward compensation control law of the control system. It is a composite control law.

6. A sliding mode speed control system for a permanent magnet motor in underground coal mine transportation equipment, used to execute the sliding mode speed control method for a permanent magnet motor as described in any one of claims 1-5, characterized in that, include: The model conversion module is used to obtain the mechanical motion equations in the form of a set of first-order linear differential equations combining the motor and electromagnetic torque equations. The lumped disturbance observation module is used to estimate the lumped disturbance of the system by constructing a model-compensated cascaded extended state observer; A robust speed tracking module is used to achieve robust speed tracking of the nominal system by constructing an adaptive non-singular fast terminal sliding mode controller; The composite control law dual-loop coordinated control module estimates the lumped disturbance and multiplies it by the negative reciprocal of the controller gain to obtain the disturbance feedforward compensation control law, which constitutes the inner loop control structure of the control system and is used to observe and compensate for the lumped disturbance of the system in real time. The speed tracking control law output by the adaptive non-singular fast terminal sliding mode controller constitutes the outer loop control structure of the control system and is used for feedback adjustment based on the tracking error.

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