A fixed-time adaptive sliding mode control method and system for improving the anti-disturbance performance of a downhole permanent magnet synchronous motor

Abstract

This invention discloses a fixed-time adaptive sliding mode control method and system for improving the disturbance rejection performance of downhole permanent magnet synchronous motors (PMSMs). The method includes: establishing a mathematical model of the PMSM considering parameter uncertainties and external load disturbances, defining parameter uncertainties and external load disturbances as lumped disturbances; constructing a fixed-time extended state observer to observe the lumped disturbances in real time based on fixed-time stability theory and obtain an estimate of the lumped disturbances; designing a fixed-time adaptive sliding mode control law based on the lumped disturbance estimate, generating a q-axis reference current, and realizing speed control of the PMSM; wherein, the adaptive sliding mode control law is derived by combining a non-singular fast terminal sliding surface, a fixed-time reaching law, an adaptive gain based on a variable gain rate smoothing factor, and the lumped disturbance estimate. This invention achieves fast and accurate convergence of disturbance errors within a fixed time.

Description

Technical Field

[0001] This invention relates to the field of motor drive control technology, and in particular to a fixed-time adaptive sliding mode control method and system for improving the anti-disturbance performance of downhole permanent magnet synchronous motors. Background Technology

[0002] With the continued growth of global energy demand, oil and gas exploration and development are gradually expanding into deeper formations, the deep sea, and complex geological environments. Improving drilling technology and equipment has become a key approach to achieving efficient and economical exploration and development of various oil and gas resources. Downhole electric drilling tools, with their advantages of high drilling efficiency, fast dynamic response, excellent control precision, and large information transmission capacity, have broad engineering application prospects. Permanent magnet synchronous motors, with their significant advantages of high power density, high efficiency, and wide speed range, have become the preferred choice for downhole electric drilling tools.

[0003] However, oil drilling conditions are highly complex and uncertain. During rock breaking, the drill bit is affected by abrupt changes in rock lithology, fluctuations in drilling pressure, and stick-slip vibrations. This causes the motor load torque to exhibit highly nonlinear, strongly coupled, and abruptly large changes, leading to drastic changes in motor speed and making it prone to stalling or overspeeding. This significantly increases the difficulty of maintaining stable speed control. Furthermore, the high-temperature, high-pressure environment downhole causes parameter perturbations in stator inductance, stator resistance, and permanent magnet flux linkage. The frictional torque of the slender shaft system is also difficult to model accurately, making it difficult for traditional control strategies based on precise models to maintain the expected control performance. The variability of geological conditions and operating conditions requires drilling control systems to have high adaptability and flexibility. To improve drilling efficiency and prevent drill string damage, the control system must have extremely fast dynamic response speed to quickly adjust the electromagnetic torque and maintain a constant speed during large disturbances.

[0004] To improve the system's disturbance rejection capability, observer-based control has become the mainstream trend. The extended state observer, as the core of active disturbance rejection control, can treat internal parameter perturbations and external loads as lumped disturbances for real-time estimation and compensation. However, traditional linear extended state observers suffer from limited convergence speed, and the convergence time is heavily dependent on the initial error. When facing large-amplitude sudden load changes in downhole conditions, the dynamic recovery time of linear methods is long, making it difficult to meet the requirements for rapid response.

[0005] To address robustness issues, sliding mode control is widely used due to its complete robustness to matched disturbances and parameter uncertainties. However, traditional linear sliding mode control has two main drawbacks: first, the system state can only converge asymptotically in infinite time, failing to guarantee finite-time convergence; second, the use of sign functions introduces high-frequency chattering in the control input, causing mechanical wear and heat loss, and even exciting unmodeled high-frequency dynamics in the system. To improve convergence speed, finite-time control theory has been introduced, such as terminal sliding mode control and fast terminal sliding mode control. These methods achieve finite-time convergence of the system state by introducing nonlinear fractional power terms into the sliding surface or reaching law. However, an inherent limitation of finite-time control is that its convergence time depends on the initial state of the system. When the initial error is large, such as during motor startup or encountering large sudden disturbances, the convergence time increases significantly. In contrast, the convergence time of a system under fixed-time control theory is independent of the initial state; the controller can ensure that the system state is adjusted to the equilibrium point within a preset time, demonstrating good application potential in the high dynamic response control of nonlinear systems. Furthermore, the switching gain of traditional sliding mode control is selected based on the upper bound of the disturbance. However, in the downhole environment, the upper bound of the disturbance is often unknown and time-varying. If the gain is too large, it will aggravate chattering; if it is too small, it will not effectively suppress the disturbance. Therefore, this invention proposes a fixed-time adaptive sliding mode control method and system for improving the disturbance rejection performance of downhole permanent magnet synchronous motors to solve the above problems. Summary of the Invention

[0006] To address the technical problems existing in the prior art, this invention proposes a fixed-time adaptive sliding mode control method and system for improving the anti-disturbance performance of downhole permanent magnet synchronous motors. It has the advantages of strong anti-disturbance capability and fast dynamic response speed, and solves the problem that the system's long recovery time under severe load disturbances leads to unstable speed control.

[0007] On the one hand, to achieve the above objectives, the present invention provides a fixed-time adaptive sliding mode control method for improving the disturbance rejection performance of downhole permanent magnet synchronous motors, comprising: A mathematical model of a permanent magnet synchronous motor considering parameter uncertainties and external load disturbances is established, and the parameter uncertainties and external load disturbances are defined as lumped disturbances; A fixed-time extended state observer is constructed to observe the lumped disturbance in real time based on the fixed-time stability theory, and the estimated value of the lumped disturbance is obtained. Based on the lumped disturbance estimate, a fixed-time adaptive sliding mode control law is designed to generate the q-axis reference current and realize the speed control of the permanent magnet synchronous motor. The adaptive sliding mode control law is derived by combining a non-singular fast terminal sliding surface, a fixed-time approach law, an adaptive gain based on a variable gain rate smoothing factor, and a lumped disturbance estimate.

[0008] Preferably, constructing the fixed-time extended state observer includes: The lumped perturbation is expanded into a new state variable, and an observer equation containing a nonlinear correction function is constructed, specifically as follows: ; In the formula, This is the derivative of the estimated motor speed. The derivative of the lumped disturbance estimate; u This is the output control quantity of the controller; This represents the error between the estimated and actual motor speed. This is the estimated value of the lumped disturbance; All are nonlinear correction functions; This is the nominal value of the control gain; The nonlinear correction function employs a double power-law approach, specifically: ; In the formula, , , , All are power terms, and , , , ; All are observer gains. It is a nonlinear correction function; This is a nonlinear correction function.

[0009] Preferably, the non-singular fast terminal sliding surface is designed as follows: ; In the formula, It is a non-singular fast terminal sliding surface; , All are sliding surface gain coefficients; , All are sliding surface index design items. , ; This is for speed tracking error; This is the derivative of the speed tracking error.

[0010] Preferably, the fixed-time approach law is: ; In the formula, This is a fixed-time approach law; and All are reaching-law gain coefficients, and , ; and All are exponents of power terms, satisfying and .

[0011] Preferably, designing the adaptive gain based on the variable gain rate smoothing factor includes: Calculate the target gain based on the non-singular fast terminal sliding surface variables; A variable gain rate smoothing factor is introduced to dynamically adjust the update rate of the adaptive gain, wherein the variable gain rate smoothing factor is adaptively adjusted based on the sliding surface variable. The actual output gain is dynamically updated using the variable gain rate smoothing factor to obtain the adaptive gain at the current moment.

[0012] Preferably, the target gain is calculated as follows: ; ; In the formula, For target gain; The preset minimum gain value; This is the gain adjustment coefficient; It is a nonlinear saturated smoothing function. For linear interval thresholds; The parameter is a power-law parameter.

[0013] Preferably, dynamically updating the actual output gain using the variable gain rate smoothing factor includes: ; ; In the formula, It is a variable gain rate smoothing factor; Based on the update rate; Gain is adjusted for rate. is the base of the natural logarithm; This is the derivative of the actual output gain; For target gain; This represents the actual output gain.

[0014] Preferably, the fixed-time adaptive sliding mode control law is: ; In the formula, It is a fixed-time adaptive sliding mode control law; This is the nominal control gain; The second derivative of the speed command value; This is the derivative of the total disturbance term; All are sliding surface gain coefficients. ; , All are sliding surface index design items. , ; This is the second derivative of the motor speed error; This is the term of the approach law function.

[0015] On the other hand, to achieve the above objectives, the present invention also provides a fixed-time adaptive sliding mode control system for improving the disturbance rejection performance of downhole permanent magnet synchronous motors, comprising: The signal acquisition module is used to acquire the speed and three-phase current signals of the permanent magnet synchronous motor. The coordinate transformation module, connected to the signal acquisition module, is used to convert the acquired three-phase current signal into current components in the synchronous rotating dq coordinate system. A fixed-time extended state observer, connected to the signal acquisition module, is used to receive rotational speed signals and perform real-time observation of lumped disturbances based on fixed-time stability theory, and output lumped disturbance estimates. A fixed-time adaptive sliding mode controller is connected to the coordinate transformation module and the fixed-time extended state observer, respectively. It is used to receive the rotation speed command, the current component after coordinate transformation, and the lumped disturbance estimate, and execute the control method to output the q-axis reference voltage. The modulation module, connected to the fixed-time adaptive sliding mode controller, is used to generate a drive signal based on the q-axis reference voltage and the preset d-axis reference voltage, control the inverter, and drive the permanent magnet synchronous motor.

[0016] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the fixed-time adaptive sliding mode control method for improving the anti-disturbance performance of downhole permanent magnet synchronous motors.

[0017] Compared with the prior art, the present invention has the following advantages and technical effects: 1. This invention enhances the online estimation capability of large-amplitude time-varying lumped disturbances in motor systems caused by load abrupt changes and parameter perturbations through the designed fixed-time extended state observer, realizing rapid and accurate convergence of disturbance errors within a fixed time, and significantly improving the real-time performance and accuracy of disturbance estimation compared with traditional observers. 2. This invention utilizes fixed-time control theory to design a controller, ensuring that the time it takes for the motor speed to recover to a stable state after being subjected to external shocks has a clear theoretical upper limit. This guarantees that the system's convergence speed does not lag significantly with the increase of initial error, resulting in a faster dynamic response speed. In extreme working conditions such as sudden stuck drill bit or encountering uneven hard rock formations, it effectively suppresses drastic fluctuations in rotational speed, preventing fatigue breakage of the drill string caused by stick-slip vibration. 3. The sliding mode approach law in this invention adopts an adaptive gain adjustment mechanism, which can dynamically adjust the switching gain according to the real-time state of the system sliding surface variables. While ensuring the strong robustness of the system, it effectively balances the smoothness of the control process. By optimizing the switching term amplitude online, the inherent chattering phenomenon of sliding mode control is weakened, thereby reducing the switching stress of inverter power devices and the heat loss of motor windings. Attached Figure Description

[0018] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a fixed-time adaptive sliding mode control method for improving the anti-disturbance performance of downhole permanent magnet synchronous motors according to an embodiment of the present invention; Figure 2 This is a schematic diagram comparing the estimation performance of the fixed-time extended state observer and the traditional linear extended state observer for lumped disturbance (load torque) in an embodiment of the present invention. Figure 3 The following is a comparison of the speed response of different control strategies under the step load disturbance condition in the embodiments of the present invention. Among them, (a) is the speed response curve under traditional PI control, (b) is the speed response curve under linear sliding mode control, and (c) is the speed response curve under fixed-time adaptive sliding mode control. Figure 4 This is a dynamic curve of the adaptive gain changing over time according to an embodiment of the present invention. Detailed Implementation

[0019] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0020] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0021] This embodiment proposes a fixed-time adaptive sliding mode control method for improving the disturbance rejection performance of downhole permanent magnet synchronous motors, including: A mathematical model of a permanent magnet synchronous motor considering parameter uncertainties and external load disturbances is established, and the parameter uncertainties and external load disturbances are defined as lumped disturbances; A fixed-time extended state observer is constructed to observe the lumped disturbance in real time based on the fixed-time stability theory, and the estimated value of the lumped disturbance is obtained. Based on the lumped disturbance estimate, a fixed-time adaptive sliding mode control law is designed to generate the q-axis reference current and realize the speed control of the permanent magnet synchronous motor. The adaptive sliding mode control law is derived by combining a non-singular fast terminal sliding surface, a fixed-time approach law, an adaptive gain based on a variable gain rate smoothing factor, and a lumped disturbance estimate.

[0022] Furthermore, a mathematical model for a permanent magnet synchronous motor considering parameter uncertainties and external load disturbances is established, including: The speed and three-phase stator current signals of the permanent magnet synchronous motor drive system are collected, and the stator current in the abc stationary coordinate system is converted to the synchronous rotating dq coordinate system by Park transformation.

[0023] Based on the vector control strategy, the mechanical motion equations and torque equations of the permanent magnet synchronous motor are obtained as follows: ; in, This represents the angular velocity of the motor. This is the moment of inertia of the motor. It is the coefficient of viscous friction; It is the extreme logarithm; For permanent magnet flux linkage; Electromagnetic torque; This represents the externally applied load torque; t For time; This represents the q-axis current of the motor.

[0024] In actual downhole operations, the high temperature and high pressure environment causes magnetic flux to... Moment of inertia and viscous friction coefficient Parameter perturbations occur, and the actual load on the motor is affected by frictional torque and the heterogeneity of the rock, exhibiting severe fluctuations, nonlinearity, and randomness. All uncertainties in the motor's dynamic equations and external disturbances are defined as lumped disturbances. The rotational speed equation is rewritten in the following second-order form: ; In the formula, This is the derivative of the motor speed with respect to time; The nominal value of the control gain is specifically expressed as: ,in These are the nominal values ​​of the permanent magnet flux linkage and moment of inertia, respectively. This is the reference value for the q-axis current. The lumped disturbance is specifically represented as a set containing parameter perturbation terms and external load perturbation terms. .

[0025] Furthermore, the fixed-time extended state observer is constructed by including: Based on the fixed-time stability theory and the double power-law approach, an observer is designed to estimate unknown lumped disturbances.

[0026] According to Lemma 1: Suppose there exists a Lyapunov function. satisfy: ; In the formula, This is the time derivative of the Lyapunov function; For the p-th power term of the Lyapunov function; This represents the state vector of the system as it evolves over time. For the q-th power term of the Lyapunov function; All are scalars and satisfy the conditions , , , If the system is stable at a fixed time, its upper bound on convergence time is independent of the initial state, and can be expressed as: This lemma forms the theoretical basis for the design of the observer and subsequent control law in this invention.

[0027] The lumped perturbation is extended into a new state variable, and an observer equation containing a nonlinear correction function is constructed, specifically as follows: ; In the formula, This is the derivative of the estimated motor speed. The derivative of the lumped disturbance estimate; u This is the output control quantity of the controller; This represents the error between the estimated and actual motor speed. This is the estimated value of the lumped disturbance; All are nonlinear correction functions; This is the nominal value of the control gain; The nonlinear correction function employs a double power-law approach, specifically: ; In the formula, , , , All are power terms, and , , , ; All are observer gains. , These are all nonlinear correction functions. Parameters need to be selected to ensure that the corresponding error matrix... For the Hurwitz matrix: , ; The low-power term ensures fast convergence when the error is small, while the high-power term dominates the convergence process when the state is far from the equilibrium point. This enables the system to quickly estimate the total disturbance of the system within a fixed time, without being affected by the magnitude of the initial error.

[0028] Furthermore, the speed tracking error is defined. ,in, This is the speed command value. These are observed values. The non-singular fast terminal sliding surface is designed as follows: ; In the formula, It is a non-singular fast terminal sliding surface; All are sliding surface gain coefficients; exponential terms , ; This is for speed tracking error; This is the derivative of the speed tracking error.

[0029] Specifically, targeting but For special operating conditions, this sliding surface mathematically avoids the occurrence of negative exponents when inverting the control law, thus solving the singularity problem. The upper bound of the system's convergence time along this sliding surface... It is a constant value, that is It can be determined through parameter tuning.

[0030] Furthermore, to ensure To converge to 0 within a fixed time, the following fixed-time convergence law is used: ; In the formula, This is a fixed-time approach law; and All are reaching-law gain coefficients, and , ; and All are exponents of power terms, satisfying and .

[0031] use The exponential term dominates the dynamic characteristics of the stage far from the sliding surface to achieve rapid convergence, utilizing... The exponential term dominates the dynamic characteristics of the approaching sliding surface stage to achieve rapid convergence, ensuring that the system state converges to zero within a preset fixed time.

[0032] Furthermore, the adaptive gain based on the variable gain rate smoothing factor is designed, including: Calculate the target gain based on the non-singular fast terminal sliding surface variables; A variable gain rate smoothing factor is introduced to dynamically adjust the update rate of the adaptive gain, wherein the variable gain rate smoothing factor is adaptively adjusted based on the sliding surface variable. The actual output gain is dynamically updated using the variable gain rate smoothing factor to obtain the adaptive gain at the current moment.

[0033] Specifically, for the reaching law gain coefficients (collectively referred to as adaptive gain) ), and design an adaptive adjustment mechanism.

[0034] Target gain The design principle is to provide a larger gain when the system state is far from the sliding surface to accelerate the approach speed, and to maintain a smaller gain when the system state is near the sliding surface to suppress chattering.

[0035] The formula for calculating the target gain is as follows: ; ; In the formula, For target gain; The preset minimum gain value; This is the gain adjustment coefficient; It is a nonlinear saturated smoothing function. For linear interval thresholds; The parameter is a power parameter, and its value is... This function has a large error. The system utilizes nonlinear characteristics for rapid response within a small error range. The linearity characteristic is used to avoid abrupt changes in gain near the origin.

[0036] To optimize the dynamic performance of the gain, a variable gain rate smoothing factor is introduced. : ; In the formula, Based on the update rate; This is for rate-adjustable gain.

[0037] The variable gain rate smoothing factor utilizes the modified characteristics of the Sigmoid function: when the system is subjected to a large disturbance leading to error... When it increases, As the system error increases, it quickly updates the gain; when the system error increases... When the decrease approaches a steady state, Falling back to the base value The system updates the gain at a slower rate, thus avoiding a rapid drop in gain after the system stabilizes, which would lead to insufficient anti-disturbance capability and smooth the control signal.

[0038] use For actual output gain Dynamic updates are performed, with the following update law: ; In the formula, This is the derivative of the actual output gain; For target gain; This represents the actual output gain.

[0039] The current adaptive gain is obtained by integrating the above differential equation.

[0040] Furthermore, based on the aforementioned non-singular fast terminal sliding surface and fixed-time approach law, the final control law expression is derived.

[0041] For sliding surfaces Regarding time Taking the first derivative, we get as follows: ; In the formula, This is the derivative of the motor speed error; This is the second derivative of the motor speed error.

[0042] According to the motor speed equation considering disturbances, the second derivative of the speed... It can be represented as: ; In the formula, This is the nominal control gain; The derivative of the q-axis current reference value; This is the derivative of the total disturbance term.

[0043] According to the definition of speed tracking error, the second derivative of the error is: ; In the formula, It is the second derivative of the motor speed command value.

[0044] To ensure the system state moves along the sliding surface and converges rapidly, let the derivative of the sliding surface... This equals the designed reaching law, and the unknown terms are replaced with the perturbation observations obtained from the observer. To simplify the final expression, the reaching law function term is defined as follows: After simplification, the control law expression is obtained: ; In the formula, It is a fixed-time adaptive sliding mode control law; This is the nominal control gain; The second derivative of the speed command value; This is the derivative of the total disturbance term; All are sliding surface gain coefficients; , All are sliding surface index design items; This is the second derivative of the motor speed error; This is the term of the approach law function.

[0045] Ultimately through the Integrating the components yields the q-axis reference current. : .

[0046] This embodiment also provides a fixed-time adaptive sliding mode control system for improving the disturbance rejection performance of downhole permanent magnet synchronous motors, including: The signal acquisition module is used to acquire the speed and three-phase current signals of the permanent magnet synchronous motor. The coordinate transformation module, connected to the signal acquisition module, is used to convert the acquired three-phase current signal into current components in the synchronous rotating dq coordinate system. A fixed-time extended state observer, connected to the signal acquisition module, is used to receive rotational speed signals and perform real-time observation of lumped disturbances based on fixed-time stability theory, and output lumped disturbance estimates. A fixed-time adaptive sliding mode controller is connected to the coordinate transformation module and the fixed-time extended state observer, respectively. It is used to receive the rotation speed command, the current component after coordinate transformation and the lumped disturbance estimate, and execute the fixed-time adaptive sliding mode control method to improve the disturbance rejection performance of the downhole permanent magnet synchronous motor, and output the q-axis reference voltage. The modulation module, connected to the fixed-time adaptive sliding mode controller, is used to generate a drive signal based on the q-axis reference voltage and the preset d-axis reference voltage, control the inverter, and drive the permanent magnet synchronous motor.

[0047] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a fixed-time adaptive sliding mode control method for improving the disturbance rejection performance of a downhole permanent magnet synchronous motor.

[0048] To more clearly illustrate the technical solution of the present invention, specific embodiments are provided below for description: This embodiment uses a permanent magnet synchronous motor with parameters as shown in Table 1 below as an example to illustrate the technical solution of the present invention.

[0049] Table 1 like Figure 1 As shown, a fixed-time adaptive sliding mode control method for improving the disturbance rejection performance of downhole permanent magnet synchronous motors includes the following specific steps: S1: Establish a mathematical model of the permanent magnet synchronous motor that takes into account parameter uncertainties and external load disturbances.

[0050] The speed and three-phase stator current signals of the permanent magnet synchronous motor drive system are acquired, and the stator current in the abc stationary coordinate system is transformed to the synchronous rotating dq coordinate system using Park transformation. Based on the vector control strategy, the mechanical motion equations and torque equations of the permanent magnet synchronous motor are obtained as follows: ; In the formula, This represents the angular velocity of the motor. This is the moment of inertia of the motor. It is the coefficient of viscous friction; It is the extreme logarithm; For permanent magnet flux linkage; Electromagnetic torque; This represents the externally applied load torque; t For time; For motor q Axis current.

[0051] In actual downhole operations, the high temperature and high pressure environment causes the permanent magnet magnetic flux to... Moment of inertia of the motor and viscous friction coefficient Parameter perturbations occur, and the actual load on the motor is affected by frictional torque and the heterogeneity of the rock, exhibiting severe fluctuations, nonlinearity, and randomness. All uncertainties in the motor's dynamic equations and external disturbances are defined as lumped disturbances. The rotational speed equation is rewritten in the following second-order form: ; In the formula, This is the derivative of the motor speed with respect to time; The nominal value of the control gain is specifically expressed as: ,in These are the nominal values ​​of the permanent magnet flux linkage and moment of inertia, respectively. This is the reference value for the q-axis current. The lumped disturbance is specifically represented as a set containing parameter perturbation terms and external load perturbation terms. .

[0052] S2: Construct a fixed-time extended state observer to observe and compensate for system lumped disturbances in real time.

[0053] Based on the fixed-time stability theory and the double power-law approach, an observer is designed to estimate unknown lumped disturbances.

[0054] According to Lemma 1: Suppose there exists a Lyapunov function. satisfy: ; In the formula, This is the time derivative of the Lyapunov function; For the p-th power term of the Lyapunov function; This represents the state vector of the system as it evolves over time. For the q-th power term of the Lyapunov function; All are scalars and satisfy the conditions , , , If the system is stable at a fixed time, its upper bound on convergence time is independent of the initial state, and can be expressed as: This lemma forms the theoretical basis for the design of the observer and subsequent control law in this invention.

[0055] aggregated disturbance Expand into new state variables Let the original rotational speed be The equations for the fixed-time extended state observer are constructed as follows: ; In the formula, This is the derivative of the estimated motor speed. The derivative of the lumped disturbance estimate; u This is the output control quantity of the controller; This represents the error between the estimated and actual motor speed. This is the estimated value of the lumped disturbance; All are nonlinear correction functions. To achieve fixed-time convergence, a double power-law approach is used: ; The power term in the formula must satisfy the following conditions: , , , (Satisfies the homogeneity condition); All are observer gains, all greater than 0. Parameters need to be selected to ensure that the corresponding error matrix... For the Hurwitz matrix: , .

[0056] The low-power term ensures fast convergence when the error is small, while the high-power term dominates the convergence process when the state is far from the equilibrium point. This enables the system to quickly estimate the total disturbance of the system within a fixed time, without being affected by the magnitude of the initial error.

[0057] S3: Design a control law based on adaptive fixed-time nonsingular fast terminal sliding mode.

[0058] Step S3 specifically includes the following sub-steps: S3.1 Constructing a non-singular fast terminal sliding surface: Define speed tracking error ,in This is the speed command value. These are the observed values.

[0059] The non-singular fast terminal sliding surface is designed as follows: ; In the formula, It is a non-singular fast terminal sliding surface; All are sliding surface gain coefficients; exponential terms , ; This is for speed tracking error; This is the derivative of the speed tracking error.

[0060] against but For special operating conditions, this sliding surface mathematically avoids the occurrence of negative exponents when inverting the control law, thus solving the singularity problem. The upper bound of the system's convergence time along this sliding surface... It is a constant value, that is It can be determined through parameter tuning.

[0061] S3.2 Design a fixed-time approach law: To ensure To converge to 0 within a fixed time, the following fixed-time convergence law is used: ; In the formula, This is a fixed-time approach law; and All are reaching-law gain coefficients, and , ; and The exponent of the power term satisfies and .

[0062] use The exponential term dominates the dynamic characteristics of the stage far from the sliding surface to achieve rapid convergence, utilizing... The exponential term dominates the dynamic characteristics of the approaching sliding surface stage to achieve rapid convergence, ensuring that the system state converges to zero within a preset fixed time.

[0063] S3.3 Design an adaptive gain based on a variable gain rate smoothing factor: For the reaching law gain coefficients in S3.2 (collectively referred to as adaptive gain) Design an adaptive adjustment mechanism. Target gain The design principle is to provide a larger gain when the system state is far from the sliding surface to accelerate the approach speed, and to maintain a smaller gain when the system state is near the sliding surface to suppress chattering. The formula for calculating the target gain is as follows: ; ; In the formula, The preset minimum gain value is used to ensure the basic robustness of the system in steady state. This is the gain adjustment coefficient, used to adjust the sensitivity of the gain to changes in error; It is a nonlinear saturated smoothing function. For linear interval thresholds; The parameter is a power parameter, and its value is... This function has a large error. The system utilizes nonlinear characteristics for rapid response within a small error range. The linearity characteristic is used to avoid abrupt changes in gain near the origin.

[0064] To optimize the dynamic performance of the gain, a variable gain rate smoothing factor is introduced. : ; In the formula, Based on the update rate; This is for rate-adjustable gain.

[0065] The variable gain rate smoothing factor utilizes the modified characteristics of the Sigmoid function: when the system is subjected to a large disturbance leading to error... When it increases, As the system error increases, it quickly updates the gain; when the system error increases... When the decrease approaches a steady state, Falling back to the base value The system updates the gain at a slower rate, thus avoiding a rapid drop in gain after the system stabilizes, which would lead to insufficient anti-disturbance capability and smooth the control signal.

[0066] Using variable gain rate smoothing factor For actual output gain Dynamic updates are performed, with the following update law: ; In the formula, This is the derivative of the actual output gain.

[0067] The current adaptive gain is obtained by integrating the differential equation.

[0068] S3.4. Derive and design the final control law: Based on the above non-singular fast terminal sliding surface (S3.1) and fixed-time approach law (S3.2), the final control law expression is derived.

[0069] For sliding surfaces Regarding time Taking the first derivative, we get as follows: ; In the formula, This is the derivative of the motor speed error; This is the second derivative of the motor speed error.

[0070] According to the motor speed equation considering disturbances, the second derivative of the speed... It can be represented as: ; In the formula, This is the nominal control gain; The derivative of the q-axis current reference value; This is the derivative of the total disturbance term.

[0071] According to the definition of speed tracking error, the second derivative of the error is: ; In the formula, It is the second derivative of the motor speed command value.

[0072] To ensure the system state moves along the sliding surface and converges rapidly, let the derivative of the sliding surface... This is equal to the reaching law designed in S3.2, and the unknown terms are replaced with the perturbation observations obtained from the observer. To simplify the final expression, the reaching law function term is defined as... After simplification, the control law expression is obtained: ; Ultimately through the Integrating the components yields the q-axis reference current. : .

[0073] like Figure 2 As shown, at t=0.1s, the system suddenly applied 90% of the motor's rated load torque. The estimation effects of the linear extended state observer and the fixed-time extended state observer of this invention on the load torque were compared. The dashed line represents the actual step load command. The thin solid line represents the estimation curve of the linear observer, and the thick solid line represents the estimation curve of the fixed-time observer of this invention. The fixed-time observer can track the step change of the load more quickly in a shorter time than the linear extended state observer, exhibiting faster convergence speed and higher observation accuracy. Figure 3 The comparison of speed response curves for three different control strategies is shown under the same step load disturbance condition. Figure 3 (a) uses PI control, which results in the largest drop in motor speed, with the maximum speed dropping to 206 r / min, and the recovery time is relatively long, with obvious oscillations in the adjustment process. Figure 3 (b) uses linear sliding mode control, which improves the speed drop to about 105 r / min, but the recovery speed is still limited by the characteristics of the linear sliding surface. Figure 3 (c) is the fixed-time adaptive sliding mode control of the present invention, with a speed drop of 77 r / min, the drop amplitude is reduced by 63% compared with the conventional PI control method, and the time for the speed to recover to the given speed is shortened by more than 60%. Figure 4 This is the dynamic curve of the adaptive gain of the sliding mode control reaching law in this invention as a function of time. For example... Figure 4 As shown, when the motor starts and the system is subjected to external disturbances, the adaptive gain increases rapidly to generate a sufficiently large control torque to suppress the disturbances and cause the system state to quickly return to the sliding surface; when the system enters the steady state or sliding motion stage, the gain will automatically decrease and remain at a low level.

[0074] As can be seen from the above comparison, the fixed-time adaptive sliding mode control method for improving the anti-disturbance performance of downhole permanent magnet synchronous motors provided by the present invention can enhance the online estimation capability of lumped disturbances in the motor control system, improve the dynamic response speed of the system, significantly reduce speed fluctuations caused by load disturbances, and has superior anti-disturbance capability.

[0075] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A fixed-time adaptive sliding mode control method for improving the disturbance rejection performance of downhole permanent magnet synchronous motors, characterized in that, include: A mathematical model of a permanent magnet synchronous motor considering parameter uncertainties and external load disturbances is established, and the parameter uncertainties and external load disturbances are defined as lumped disturbances; A fixed-time extended state observer is constructed to observe the lumped disturbance in real time based on the fixed-time stability theory, and the estimated value of the lumped disturbance is obtained. Based on the lumped disturbance estimate, a fixed-time adaptive sliding mode control law is designed to generate the q-axis reference current and realize the speed control of the permanent magnet synchronous motor. The adaptive sliding mode control law is derived by combining a non-singular fast terminal sliding surface, a fixed-time approach law, an adaptive gain based on a variable gain rate smoothing factor, and a lumped disturbance estimate.

2. The method according to claim 1, characterized in that, Constructing the fixed-time extended state observer includes: The lumped perturbation is expanded into a new state variable, and an observer equation containing a nonlinear correction function is constructed, specifically as follows: ； In the formula, This is the derivative of the estimated motor speed. The derivative of the lumped disturbance estimate; u The output control quantity of the controller; This represents the error between the estimated and actual motor speed. This is the estimated value of the lumped disturbance; All are nonlinear correction functions; This is the nominal value of the control gain; The nonlinear correction function employs a double power-law approach, specifically: ； In the formula, , , , All are power terms, and , , , ; All are observer gains. , All of them are nonlinear correction functions.

3. The method according to claim 1, characterized in that, The non-singular fast terminal sliding surface is designed as follows: ； In the formula, It is a non-singular fast terminal sliding surface; , All are sliding surface gain coefficients; , All are sliding surface index design items. , ; This is for speed tracking error; This is the derivative of the speed tracking error.

4. The method according to claim 3, characterized in that, The fixed-time approach law is as follows: ； In the formula, This is a fixed-time approach law; and All are reaching-law gain coefficients, and , ; and All are exponents of power terms, satisfying and .

5. The method according to claim 4, characterized in that, The design of the adaptive gain based on the variable gain rate smoothing factor includes: Calculate the target gain based on the non-singular fast terminal sliding surface variables; A variable gain rate smoothing factor is introduced to dynamically adjust the update rate of the adaptive gain, wherein the variable gain rate smoothing factor is adaptively adjusted based on the sliding surface variable. The actual output gain is dynamically updated using the variable gain rate smoothing factor to obtain the adaptive gain at the current moment.

6. The method according to claim 5, characterized in that, The target gain is calculated as follows: ； ； In the formula, For target gain; The preset minimum gain value; This is the gain adjustment coefficient; It is a nonlinear saturated smoothing function. For linear interval thresholds; The parameter is a power-law parameter.

7. The method according to claim 5, characterized in that, The actual output gain is dynamically updated using the variable gain rate smoothing factor, including: ； ； In the formula, It is a variable gain rate smoothing factor; Based on the update rate; Gain is adjusted for rate. is the base of the natural logarithm; This is the derivative of the actual output gain; For target gain; This represents the actual output gain.

8. The method according to claim 1, characterized in that, The fixed-time adaptive sliding mode control law is as follows: ； In the formula, It is a fixed-time adaptive sliding mode control law; This is the nominal control gain; The second derivative of the speed command value; This is the derivative of the total disturbance term; All are sliding surface gain coefficients. ; , All are sliding surface index design items. , ; This is the second derivative of the motor speed error; This is the term of the approach law function.

9. A fixed-time adaptive sliding mode control system for improving the anti-disturbance performance of downhole permanent magnet synchronous motors, characterized in that, include: The signal acquisition module is used to acquire the speed and three-phase current signals of the permanent magnet synchronous motor. The coordinate transformation module, connected to the signal acquisition module, is used to convert the acquired three-phase current signal into current components in the synchronous rotating dq coordinate system. A fixed-time extended state observer, connected to the signal acquisition module, is used to receive rotational speed signals and perform real-time observation of lumped disturbances based on fixed-time stability theory, and output lumped disturbance estimates. A fixed-time adaptive sliding mode controller is connected to the coordinate transformation module and the fixed-time extended state observer, respectively, for receiving rotational speed commands, current components after coordinate transformation, and the lumped disturbance estimate, and executing the control method according to any one of claims 1-8, and outputting the q-axis reference voltage; The modulation module, connected to the fixed-time adaptive sliding mode controller, is used to generate a drive signal based on the q-axis reference voltage and the preset d-axis reference voltage, control the inverter, and drive the permanent magnet synchronous motor.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the fixed-time adaptive sliding mode control method for improving the anti-disturbance performance of downhole permanent magnet synchronous motors as described in any one of claims 1-8.

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