A Control Method for Permanent Magnet Synchronous Motors Based on Third-Order Superhelical Sliding Mode

Abstract

This invention relates to the field of permanent magnet synchronous motor control technology, specifically to a control method for permanent magnet synchronous motors based on third-order superspiral sliding mode. By using third-order superspiral sliding mode control, the system robustness is effectively improved and chattering is reduced. Simultaneously, to address parameter uncertainties in the system, a fuzzy logic system is used to estimate and compensate for nonlinear terms containing parameter uncertainties. Furthermore, preset performance control is employed to constrain the tracking error, ensuring that the tracking error does not exceed the preset performance boundary during system operation. To prevent disturbances during initial system startup from causing the tracking error to exceed the preset performance boundary and thus rendering the system inoperable, preset time control is introduced within the preset performance framework. This allows the error to quickly converge to the preset performance boundary, improving the feasibility of preset performance control in practical scenarios and demonstrating application potential in high-precision industrial applications.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor control technology, specifically to a control method for a permanent magnet synchronous motor based on a third-order superhelical sliding mode. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in industrial drives, new energy vehicles, and aerospace systems due to their high efficiency, high power density, and fast dynamic effects. However, in actual operation, PMSMs are inevitably affected by uncertainties such as parameter changes, load torque disturbances, and unmodeled dynamic characteristics. Therefore, developing robust and high-performance PMSM control strategies is of great significance. Current PMSM control methods include proportional-integral-derivative control, backstepping control, and model predictive control. Among them, sliding mode control stands out due to its strong robustness. However, because its control law contains a sign function, its output will experience severe chattering near the zero point, which can cause serious damage to the controller and the controlled object.

[0003] To alleviate the chattering problem, a high-order superspiral sliding mode control was proposed. However, during PMSM operation, device aging, operating conditions, and parameter measurement errors can lead to parameter uncertainties, making the high-order superspiral sliding mode control ineffective. To address this, proposed methods include using an extended state observer to estimate and compensate for lumped disturbances containing parameter uncertainties, designing adaptive laws to estimate unknown parameters in the system, and using fuzzy logic systems to approximate nonlinear terms containing unknown parameters. However, due to the special structure of the high-order superspiral sliding mode control law, the above methods are difficult to combine with high-order superspiral sliding mode control.

[0004] To avoid various constraints imposed by physical limitations, safety requirements, and performance specifications, algorithms based on barrier Lyapunov functions, prescribed performance control (PPC), and methods based on nonlinear mapping transformations have been proposed. Among these, prescribed performance control significantly improves transient and steady-state performance by designing an explicit prescribed performance boundary. Although it guarantees the preset tracking accuracy over an infinite time range, its applicability is limited. To address this issue, a continuous piecewise function is introduced, enabling the prescribed performance boundary to converge to the preset performance level within a finite time. During convergence, the PMSM needs to maintain good tracking performance while achieving rapid convergence within a finite time. However, the upper bound of the convergence time depends on the initial conditions and system parameters, which are difficult to obtain in practical applications. Therefore, fractional-order and odd-order feedback are introduced to determine the upper bound of the convergence time, resulting in fixed-time control, which greatly increases the complexity of controller design. To address this, a control method for permanent magnet synchronous motors based on third-order super-helical sliding mode is proposed. Summary of the Invention

[0005] To address the technical problems existing in the prior art, the present invention provides a control method for a permanent magnet synchronous motor based on a third-order super-helical sliding mode.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a control method for a permanent magnet synchronous motor based on a third-order superhelical sliding mode, the control method comprising the following steps:

[0007] S1, construct the physical model of the permanent magnet synchronous motor, read the motor position information through the motor encoder, and read the three-phase current information through the current sensor;

[0008] S2, analyze the physical model of the permanent magnet synchronous motor, construct the relationship between the physical quantities of the motor, convert each physical quantity into a state-space expression, and use the difference between the actual rotor position and the target rotor position as the tracking error;

[0009] S3. Construct a preset performance boundary function for the tracking error and perform a nonlinear mapping transformation on the tracking error to make the tracking error before the transformation closer to the boundary and the tracking error after the transformation approach infinity, ensuring that the tracking error converges along the desired trajectory and achieving effective constraint on the tracking error.

[0010] S4, using the tracking error after nonlinear mapping transformation combined with a preset time adjustment function to design a preset time sliding surface and a reaching law;

[0011] S5. The uncertainty of parameters in the physical model of permanent magnet synchronous motor is approximated and compensated by fuzzy logic. Then, the controller is designed according to the fuzzy logic. The controller enables the system to converge to the vicinity of the zero domain within a preset time of the tracking error.

[0012] S6 inputs the electromagnetic torque output by the controller into the current loop regulator. The current loop regulator uses a PI controller, which outputs the d-axis voltage and q-axis voltage. The actual output voltage values ​​of the d-axis voltage and q-axis voltage are then obtained through Park transformation. The obtained voltage values ​​are output to the inverter to control the PMSM, so as to ensure that the motor rotor position moves according to the preset trajectory.

[0013] Preferably, in step S1, the rotor position data of the motor is read by the motor encoder. Calculate rotor position data per unit time Changes as rotor speed data The three-phase current data of the motor is obtained through a current sensor. , , The d-axis current is obtained through Clark transformation. and q-axis current .

[0014] Preferably, in step S2, a physical model of the permanent magnet synchronous motor is constructed based on known physical laws. The physical quantities include rotor position, rotor speed, q-axis current, d-axis current, damping coefficient, and load torque. The relationship between the constructed physical quantities is expressed as follows:

[0015] ;

[0016] In the formula, The derivative of the motor rotor position data. The derivative of the rotor speed data, For electromagnetic torque, For rotational inertia, For load torque, The damping coefficient is due to There is uncertainty, therefore ,in, This is the nominal value. It is uncertain;

[0017] Transform the above physical quantities into state-space expressions, and let the state... , , , Control input ,parameter ; ,definition ,in, , ; The system state-space expression is then:

[0018] ;

[0019] set up The trajectory for the target location. The tracking error is the derivative of the trajectory at the target position. The derivative of the tracking error .

[0020] Preferably, in step S3, the nonlinear mapping transformation that constrains the tracking error takes the following form:

[0021] ;

[0022] In the formula, The tracking error is the result of the nonlinear mapping transformation. The lower boundary of the preset performance boundary. The upper boundary of the preset performance boundary. first derivative for:

[0023] ;

[0024] In the formula, The derivative of the lower boundary of the preset performance boundary. Let the derivative be the upper boundary of the preset performance, then Second derivative for:

[0025] ;

[0026] In the formula, The second derivative of the lower boundary of the preset performance boundary. The second derivative of the upper boundary of the preset performance boundary. , The second derivative of the tracking error is given, where the preset performance boundary function is:

[0027] ;

[0028] ;

[0029] In the formula, For performance constraint functions, For design parameters, This is the initial value of the error. This is the decay function of the initial error;

[0030] Since the initial upper and lower boundaries in the preset performance boundary form of this preset performance control are on both sides of the initial tracking error, a decay function for the initial error is defined. The upper and lower boundaries are shifted to both sides of the initial tracking error. As the preset performance upper and lower boundaries converge to constant values ​​set according to the task requirements, the influence of the initial tracking error on the preset performance boundaries converges to 0.

[0031] Preferably, in step S3, a performance constraint function is set. and The expressions for its first and second derivatives are:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] In the formula, These are adjustable parameters. At that time, adjust the speed when the boundary converges. Time represents the final value to which the boundary finally converges. The time set for the boundary value to converge from the initial value to the final value. For system uptime, This represents the convergence rate of the effect of the initial error on the boundary translation.

[0039] Preferably, step S4 includes the following steps:

[0040] S41, using the method in step S3 Set a preset time sliding surface for:

[0041] ;

[0042] In the formula, Adjust the system convergence speed accordingly; This is a preset time adjustment function; The derivative of the preset time adjustment function;

[0043] Preset time adjustment function Defined as:

[0044] ;

[0045] In the formula, and These are the initial and final values ​​of the time-varying gain, respectively. The preset time is set. Define auxiliary variables for system runtime. , , The first derivative and the second derivative are respectively:

[0046] ;

[0047] ;

[0048] S42, to ensure that the system converges to the vicinity of the zero region according to the designed trajectory, let the convergence law be:

[0049] ;

[0050] In the formula, The first derivative of the perturbation The law of convergence, The second derivative of the perturbation The law of convergence, , , ,in, , , The gain adjusted to achieve the desired control effect. For a sign function, when hour, ;when hour, .

[0051] Preferably, step S5 includes the following steps:

[0052] S51, to address the uncertainty in the damping coefficient beyond its nominal value caused by environmental factors or component aging, fuzzy logic is used to approximate and compensate for this uncertainty. The uncertain term is... The basis function for fuzzy logic is a Gaussian function.

[0053] According to the characteristics of fuzzy logic:

[0054] ;

[0055] In the formula, The weights of each basis function in the fuzzy logic are... ; , which are the basis functions of fuzzy logic; The approximation error is: ;

[0056] S52, the control input designed in combination with steps S3 and S4 The expression is:

[0057] ;

[0058] In the formula, , These are the parameters for the permanent magnet synchronous motor system; This refers to the motor speed. The second derivative of the reference signal; For the tracking error of the rotor position, The tracking error of the rotor speed, and satisfying Relationship; This is a preset time adjustment function. The first derivative of the preset time adjustment function. The second derivative of the preset time adjustment function; Parameter uncertainty in systems approximated by fuzzy logic; The sliding surface designed for the system; , , The gain is adjusted according to the desired control effect;

[0059] S53, Update Law of Fuzzy Logic Parameters for:

[0060] ;

[0061] In the formula, hour, As a parameter to be adjusted based on the actual control effect, For projection operators, for ;

[0062] definition ,ensure If the system is bounded and therefore will not become infinitely large, thus preventing the system from becoming unusable, then the projection operator takes the form:

[0063] ;

[0064] In the formula, for The maximum value;

[0065] Electromagnetic torque output by the controller Ensure that the tracking error of the motor rotor position can converge to near the zero domain.

[0066] Preferably, in step S6, the electromagnetic torque output in step S5 is... Through formula ,Will Converted to q-axis current ,in, This represents the number of pole pairs in a permanent magnet synchronous motor. The permanent magnet flux linkage of the permanent magnet synchronous motor is then output as the q-axis voltage through a current loop regulator. and d-axis voltage ;

[0067] q-axis voltage and d-axis voltage Three-phase voltages are obtained through the Park transform. , , The signal is modulated by space vector pulse width and output to the motor driver for position control of the PMSM.

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0069] 1. This invention effectively improves the robustness of the system and reduces chattering by using third-order super-helical sliding mode control. At the same time, in order to cope with the parameter uncertainty in the position control system of permanent magnet synchronous motor, a fuzzy logic system is used to estimate and compensate the nonlinear terms containing parameter uncertainty, and a preset performance control is used to constrain the tracking error, which can ensure that the tracking error does not exceed the preset performance boundary during system operation.

[0070] 2. In order to prevent the tracking error from exceeding the preset performance boundary due to disturbances in the early stage of system startup, thus causing the system to fail to operate, the present invention introduces preset time control under the preset performance framework, so that the error can quickly converge to the preset performance boundary, improve the feasibility of preset performance control in actual scenarios, thereby reducing the risk that the system will fail to operate due to exceeding the boundary during the boundary convergence process, and showing application potential in high-precision industrial scenarios. Attached Figure Description

[0071] Figure 1 This is a control architecture diagram of the present invention;

[0072] Figure 2 This is a rotor position curve of the motor used in the pre-set performance comparison experiment of the present invention;

[0073] Figure 3 This is a preset performance comparison experiment tracking error curve diagram for the present invention;

[0074] Figure 4This is the input curve graph for the controller in the pre-set performance comparison experiment of the present invention;

[0075] Figure 5 This is a curve diagram of the sliding surface of the pre-set experimental comparison experiment of the present invention;

[0076] Figure 6 This is a rotor position curve of the motor used in the comparative experiment of the third-order super-helical sliding mode of this invention;

[0077] Figure 7 This is a comparison experiment tracking error curve of the third-order superspiral sliding mode of this invention;

[0078] Figure 8 This is a graph showing the rotor position of the motor in a comparative experiment of the system of the present invention;

[0079] Figure 9 This is a comparative experiment tracking error curve of the system of the present invention;

[0080] Figure 10 This is a graph showing the rotor position of the motor in the pre-set performance-time comparison experiment of this invention.

[0081] Figure 11 This is a curve showing the tracking error in the performance-time comparison experiment of the present invention.

[0082] Figure 12 This is the input curve of the controller for the preset performance-time comparison experiment of the present invention;

[0083] Figure 13 The sliding surface curve is a pre-set performance time comparison experiment curve of the present invention. Detailed Implementation

[0084] The present invention will be further described below with reference to the accompanying drawings and embodiments, which illustrate the above and other technical features and advantages of the present invention. However, the following embodiments are merely preferred embodiments of the present invention and are not exhaustive.

[0085] Example 1:

[0086] like Figure 1 As shown, this invention provides a control method for a permanent magnet synchronous motor based on a third-order superspiral sliding mode. The control method includes the following steps:

[0087] S1, construct the physical model of the permanent magnet synchronous motor, read the motor position information through the motor encoder, and read the three-phase current information through the current sensor;

[0088] S2, analyze the physical model of the permanent magnet synchronous motor, construct the relationship between the physical quantities of the motor, convert each physical quantity into a state-space expression, and use the difference between the actual rotor position and the target rotor position as the tracking error;

[0089] S3. Construct a preset performance boundary function for the tracking error and perform a nonlinear mapping transformation on the tracking error to make the tracking error before the transformation closer to the boundary and the tracking error after the transformation approach infinity, ensuring that the tracking error converges along the desired trajectory and achieving effective constraint on the tracking error.

[0090] S4, using the tracking error after nonlinear mapping transformation combined with a preset time adjustment function to design a preset time sliding surface and a reaching law;

[0091] S5 uses fuzzy logic to approximate and compensate for the parameter uncertainties in the physical model of the permanent magnet synchronous motor, and designs a controller based on fuzzy logic. The controller enables the system to converge to the vicinity of the zero domain within a preset time of the tracking error (due to the uncertainty of the parameters and the existence of disturbances, it cannot completely converge to zero, so it will converge to the vicinity of the zero domain).

[0092] S6 inputs the electromagnetic torque output by the controller into the current loop regulator. The current loop regulator uses a PI controller, which outputs the d-axis voltage and q-axis voltage. The actual output voltage values ​​of the d-axis voltage and q-axis voltage are then obtained through Park transformation. The obtained voltage values ​​are output to the inverter to control the PMSM, so as to ensure that the motor rotor position moves according to the preset trajectory.

[0093] In this embodiment, a permanent magnet synchronous motor is used to support the platform, and the tracking signal is... t deg, load torque is The Nm value is sufficient for most demanding industrial environments. The parameters of the permanent magnet synchronous motor are shown in Table 1.

[0094] Table 1. Parameters of Permanent Magnet Synchronous Motor

[0095]

[0096] In this embodiment, in step S1, the rotor position data of the motor is read through the motor encoder. Calculate rotor position data per unit time Changes as rotor speed data The three-phase current data of the motor is obtained through a current sensor. , , The d-axis current is obtained through Clark transformation. and q-axis current .

[0097] In this embodiment, in step S2, a physical model of the permanent magnet synchronous motor is constructed based on known physical laws. The physical quantities include rotor position, rotor speed, q-axis current, d-axis current, damping coefficient, and load torque. The relationship between the constructed physical quantities is expressed as follows:

[0098] ;

[0099] in, The derivative of the motor rotor position data. The derivative of the rotor speed data, For electromagnetic torque, For rotational inertia, The damping coefficient is... This is the load torque;

[0100] It should be noted that, In this system, it serves as the controller input. There may be some uncertainty due to environmental changes or device aging, therefore, the definition , For parameter nominal values, Due to the uncertainty of the parameters, It changes differently depending on the task being performed, so it is treated as an unknown time-varying function here;

[0101] Transform the above physical quantities into state-space expressions, and let the state... , , , Control input ,parameter ; ,definition ,in, , ; The system state-space expression is then:

[0102] ;

[0103] set up The trajectory for the target location. The tracking error is the derivative of the trajectory at the target position. The derivative of the tracking error .

[0104] In this embodiment, the form of the nonlinear mapping transformation that constrains the tracking error in step S3 is as follows:

[0105] ;

[0106] In the formula, The tracking error is the result of the nonlinear mapping transformation. The lower boundary of the preset performance boundary. The upper boundary of the preset performance boundary. first derivative for:

[0107] ;

[0108] In the formula, The derivative of the lower boundary of the preset performance boundary. Let the derivative be the upper boundary of the preset performance, then Second derivative for:

[0109] ;

[0110] In the formula, The second derivative of the lower boundary of the preset performance boundary. The second derivative of the upper boundary of the preset performance boundary. , The second derivative of the tracking error is given, where the preset performance boundary function is:

[0111] ;

[0112] ;

[0113] In the formula, For performance constraint functions, For design parameters, This is the initial value of the error. This is the decay function of the initial error;

[0114] Since the initial upper and lower boundaries in the preset performance boundary form of this preset performance control are on both sides of the initial tracking error, a decay function for the initial error is defined. The upper and lower boundaries are shifted to both sides of the initial tracking error. As the preset performance upper and lower boundaries converge to constant values ​​set according to the task requirements, the influence of the initial tracking error on the preset performance boundaries converges to 0.

[0115] In this embodiment, in step S3, the performance constraint function is set. and The expressions for its first and second derivatives are:

[0116] ;

[0117] ;

[0118] ;

[0119] ;

[0120] ;

[0121] ;

[0122] In the formula, These are adjustable parameters. At that time, adjust the speed when the boundary converges. Time represents the final value to which the boundary finally converges. The time set for the boundary value to converge from the initial value to the final value. For system uptime, This represents the convergence rate of the effect of the initial error on the boundary translation.

[0123] In this embodiment, step S4 includes the following steps:

[0124] S41, using the method in step S3 Set a preset time sliding surface for:

[0125] ;

[0126] In the formula, Adjust the system convergence speed accordingly; This is a preset time adjustment function; The derivative of the preset time adjustment function;

[0127] Preset time adjustment function Defined as:

[0128] ;

[0129] In the formula, and These are the initial and final values ​​of the time-varying gain, respectively. The preset time is set. Define auxiliary variables for system runtime. , , The first derivative and the second derivative are respectively:

[0130] ;

[0131] ;

[0132] S42, to ensure that the system converges to the vicinity of the zero region according to the designed trajectory, let the convergence law be:

[0133] ;

[0134] In the formula, The first derivative of the perturbation The law of convergence, The second derivative of the perturbation The law of convergence, , , ,in, , , The gain adjusted to achieve the desired control effect. For a sign function, when hour, ;when hour, .

[0135] In this embodiment, step S5 includes the following steps:

[0136] S51, to address the uncertainty in the damping coefficient beyond its nominal value caused by environmental factors or component aging, fuzzy logic is used to approximate and compensate for this uncertainty. The uncertain term is... The basis function for fuzzy logic is a Gaussian function.

[0137] According to the characteristics of fuzzy logic:

[0138] ;

[0139] In the formula, The weights of each basis function in the fuzzy logic are... ; , which are the basis functions of fuzzy logic; The approximation error is: ;

[0140] S52, the control input designed in combination with steps S3 and S4 The expression is:

[0141] ;

[0142] In the formula, , These are the parameters for the permanent magnet synchronous motor system; This refers to the motor speed. The second derivative of the reference signal; For the tracking error of the rotor position, The tracking error of the rotor speed, and satisfying Relationship; This is a preset time adjustment function. The first derivative of the preset time adjustment function. The second derivative of the preset time adjustment function; Parameter uncertainty in systems approximated by fuzzy logic; The sliding surface designed for the system; , , The gain is adjusted according to the desired control effect;

[0143] S53, Update Law of Fuzzy Logic Parameters for:

[0144] ;

[0145] In the formula, hour, As a parameter to be adjusted based on the actual control effect, For projection operators, for ;

[0146] definition ,ensure If the system is bounded and therefore will not become infinitely large, thus preventing the system from becoming unusable, then the projection operator takes the form:

[0147] ;

[0148] In the formula, for The maximum value;

[0149] Electromagnetic torque output by the controller Ensure that the tracking error of the motor rotor position can converge to near the zero domain.

[0150] In this embodiment, in step S6, the electromagnetic torque output in step S5 is... Through formula ,Will Converted to q-axis current ,in, This represents the number of pole pairs in a permanent magnet synchronous motor. The permanent magnet flux linkage of the permanent magnet synchronous motor is then output as the q-axis voltage through a current loop regulator. and d-axis voltage ;

[0151] q-axis voltage and d-axis voltage Three-phase voltages are obtained through the Park transform. , , The signal is modulated by space vector pulse width and output to the motor driver for position control of the PMSM.

[0152] Example 2:

[0153] To verify the effectiveness of the proposed time-integral sliding mode control method for permanent magnet synchronous motors based on an extended state observer, the following comparative experiments were conducted on a permanent magnet synchronous motor support platform.

[0154] Experiment 1: Comparative analysis of two control schemes. Scheme 1 uses a combination of Three-Order Super-Twisting Sliding Mode Control (TSTSMC) and Prescribed Performance Control (PPC), while Scheme 2 uses TSTSMC alone. Unknown parameters in both experiments are approximated using a fuzzy logic system. Under the condition that other parameters are consistent, the rotor position of the motor is as follows: Figure 2 As shown, the tracking error of the target rotor position trajectory is as follows: Figure 3 As shown, the electromagnetic torque of the system control input is as follows: Figure 4 As shown, the sliding surface controlled by sliding mode is as follows: Figure 5 As shown.

[0155] Depend on Figure 2 and Figure 3 It can be seen that the second group using a single TSTSMC approaches stability in about 0.7 seconds, but the tracking error reaches a maximum of 30° in steady state; while the first group using a combination of TSTSMC and PPC control approaches stability in about 0.7 seconds, and the steady-state error remains within 4°. This shows that the preset performance control effectively constrains the error to not exceed the preset performance boundary, and significantly improves the robustness to unknown load torque.

[0156] Depend on Figure 4 It can be seen that the controller input for group 1 is between ±0.5, while the controller input for group 2 is between ±2.5. Therefore, it can be concluded that by adding preset performance control, the system can achieve better control results with lower control costs. Figure 5 It can be seen that after the system enters steady state, the sliding surface of the first group is within ±50, while the sliding surface of the second group is within ±1500. This shows that the addition of preset performance can greatly reduce the chattering problem caused by sliding mode control.

[0157] Example 3:

[0158] Experiment 2: Comparative Analysis of Two Control Schemes. Group 1 uses TSTSMC, and Group 2 uses Super-Twisting Sliding Mode Control (STSMC). The unknown parameters in both experiments are approximated using a fuzzy logic system. Under the condition that other parameters are consistent, the motor rotor position is as follows: Figure 6 As shown, the tracking error for the target rotor position is as follows: Figure 7 As shown.

[0159] Depend on Figure 6 and Figure 7 As shown, under the action of unknown load torque, the first group using TSTSMC can track the target rotor position with a tracking error within 20°, while the first group using STSMC can hardly track the target rotor position. Therefore, it can be concluded that TSTSMC is much more robust than STSMC when facing unknown load torque.

[0160] Example 4:

[0161] Experiment 3: Comparative Analysis of Two Control Schemes. Group 1 uses a combination of TS-TSMC and PPC control, while Group 2 uses a combination of STSMC and PPC control. The unknown parameters in both experiments are approximated using a fuzzy logic system. Under the condition that all other parameters are the same, the motor rotor position is as follows: Figure 8 As shown, the tracking error of the target rotor position and the electromagnetic torque input to the controller are as follows: Figure 9 As shown.

[0162] Depend on Figure 8 and Figure 9 As shown, under the preset performance framework, the tracking error of the first group using the combination of STSMC and PPC control can remain within the boundary as the preset performance boundary converges, and the system can operate stably. However, the tracking error of the second group using the combination of STSMC and PPC control exceeds the preset performance boundary in the early stage of system operation, causing the system to fail to operate.

[0163] Therefore, under the preset performance framework, TSTSMC is more robust than STSMC and is more likely to be used in some scenarios with high accuracy requirements.

[0164] Example 5:

[0165] Experiment 4: Comparative Analysis of Three Control Schemes. All three schemes use a combination of TSTSMC and PPC control. Unknown parameters are approximated using fuzzy logic. The convergence time of the preset performance boundary is set to 1 second for scheme 1, 3 seconds for scheme 2, and 5 seconds for scheme 3. With other parameters remaining the same, the rotor position of the motor is as follows: Figure 10 As shown, the tracking error of the target rotor position trajectory is as follows: Figure 11 As shown, the electromagnetic torque of the system control input is as follows: Figure 12 As shown, the sliding surface controlled by sliding mode is as follows: Figure 13 As shown.

[0166] Depend on Figure 10-13 It can be seen that the first group of control methods converges the tracking error of the rotor position faster than the second group, while the third group is the slowest. However, the electromagnetic torque and sliding surface of the control input are the same, which meets the design expectations. Therefore, it can be seen that the preset performance boundary time can be adjusted according to the actual application scenario, and the system can operate stably. The system design is more flexible.

[0167] In summary, the method of the present invention is superior to the existing solutions in both suppressing chattering and improving convergence speed and system robustness.

[0168] The above description is merely a preferred embodiment of the present invention and is illustrative rather than restrictive. Those skilled in the art will understand that many changes, modifications, and even equivalents can be made within the spirit and scope defined by the claims of the present invention, all of which will fall within the protection scope of the present invention.

Claims

1. A control method for a permanent magnet synchronous motor based on a third-order superspiral sliding mode, characterized in that, The control method includes the following steps: S1, construct the physical model of the permanent magnet synchronous motor, read the motor position information through the motor encoder, and read the three-phase current information through the current sensor; S2, analyze the physical model of the permanent magnet synchronous motor, construct the relationship between the physical quantities of the motor, convert each physical quantity into a state-space expression, and use the difference between the actual rotor position and the target rotor position as the tracking error; S3. Construct a preset performance boundary function for the tracking error and perform a nonlinear mapping transformation on the tracking error so that the tracking error before the transformation is closer to the boundary and the tracking error after the transformation approaches infinity, ensuring that the tracking error converges along the desired trajectory and achieving effective constraint on the tracking error. S4, using the tracking error after nonlinear mapping transformation combined with a preset time adjustment function to design a preset time sliding surface and a reaching law; S5. The uncertainty of parameters in the physical model of permanent magnet synchronous motor is approximated and compensated by fuzzy logic. Then, the controller is designed according to the fuzzy logic. The controller enables the system to converge to the vicinity of the zero domain within a preset time of the tracking error. S6 inputs the electromagnetic torque output by the controller into the current loop regulator. The current loop regulator uses a PI controller, which outputs the d-axis voltage and q-axis voltage. The actual output voltage values ​​of the d-axis voltage and q-axis voltage are then obtained through Park transformation. The obtained voltage values ​​are output to the inverter to control the PMSM, so as to ensure that the motor rotor position moves according to the preset trajectory.

2. The control method for a permanent magnet synchronous motor based on a third-order superspiral sliding mode as described in claim 1, characterized in that, In step S1, the rotor position data of the motor is read through the motor encoder. Calculate rotor position data per unit time Changes as rotor speed data The three-phase current data of the motor is obtained through a current sensor. , , The d-axis current is obtained through Clark transformation. and q-axis current .

3. The permanent magnet synchronous motor control method based on third-order superspiral sliding mode as described in claim 1, characterized in that, In step S2, a physical model of the permanent magnet synchronous motor is constructed based on known physical laws. The physical quantities include rotor position, rotor speed, q-axis current, d-axis current, damping coefficient, and load torque. The relationship between these physical quantities is expressed as follows: ； In the formula, The derivative of the motor rotor position data. The derivative of the rotor speed data, For electromagnetic torque, For rotational inertia, For load torque, The damping coefficient is due to There is uncertainty, therefore ,in, This is the nominal value. It is uncertain; Transform the above physical quantities into state-space expressions, and let the state... , , , Control input ,parameter ; ,definition ,in, , ; The system state-space expression is then: ； set up The trajectory for the target location. The tracking error is the derivative of the trajectory at the target position. The derivative of the tracking error .

4. The control method for a permanent magnet synchronous motor based on a third-order superspiral sliding mode as described in claim 1, characterized in that, In step S3, the nonlinear mapping transformation that constrains the tracking error takes the following form: ； In the formula, The tracking error is the result of the nonlinear mapping transformation. The lower boundary of the preset performance boundary. The upper boundary of the preset performance boundary. first derivative for: ； In the formula, The derivative of the lower boundary of the preset performance boundary. Let the derivative be the upper boundary of the preset performance, then Second derivative for: ； In the formula, The second derivative of the lower boundary of the preset performance boundary. The second derivative of the upper boundary of the preset performance boundary. , The second derivative of the tracking error is given, where the preset performance boundary function is: ； ； In the formula, For performance constraint functions, For design parameters, This is the initial value of the error. This is the decay function of the initial error; Since the initial upper and lower boundaries in the preset performance boundary form of this preset performance control are on both sides of the initial tracking error, a decay function for the initial error is defined. The upper and lower boundaries are shifted to both sides of the initial tracking error. As the preset performance upper and lower boundaries converge to constant values ​​set according to the task requirements, the influence of the initial tracking error on the preset performance boundaries converges to 0.

5. The permanent magnet synchronous motor control method based on a third-order superspiral sliding mode as described in claim 4, characterized in that, In step S3, the performance constraint function is set. and The expressions for its first and second derivatives are: ； ； ； ； ； ； In the formula, These are adjustable parameters. At that time, adjust the speed when the boundary converges. Time represents the final value to which the boundary finally converges. The time set for the boundary value to converge from the initial value to the final value. For system uptime, This represents the convergence rate of the effect of the initial error on the boundary translation.

6. The control method for a permanent magnet synchronous motor based on a third-order superspiral sliding mode as described in claim 1, characterized in that, Step S4 includes the following steps: S41, using the method in step S3 Set a preset time sliding surface for: ； In the formula, Adjust the system convergence speed accordingly; This is a preset time adjustment function; The derivative of the preset time adjustment function; Preset time adjustment function Defined as: ； In the formula, and These are the initial and final values ​​of the time-varying gain, respectively. The preset time is set. Define auxiliary variables for system runtime. , , The first derivative and the second derivative are respectively: ； ； S42, to ensure that the system converges to the vicinity of the zero region according to the designed trajectory, let the convergence law be: ； In the formula, The first derivative of the perturbation The law of convergence, The second derivative of the perturbation The law of convergence, , , ,in, , , The gain adjusted to achieve the desired control effect. For a sign function, when hour, ;when hour, .

7. The control method for a permanent magnet synchronous motor based on a third-order superspiral sliding mode as described in claim 1, characterized in that, Step S5 includes the following steps: S51, to address the uncertainty in the damping coefficient beyond its nominal value caused by environmental factors or component aging, fuzzy logic is used to approximate and compensate for this uncertainty. The uncertain term is... The basis function for fuzzy logic is a Gaussian function. According to the characteristics of fuzzy logic: ； In the formula, The weights of each basis function in the fuzzy logic are... ; , which are the basis functions of fuzzy logic; The approximation error is: ; S52, the control input designed in combination with steps S3 and S4 The expression is: ； In the formula, , These are the parameters for the permanent magnet synchronous motor system; This refers to the motor speed. The second derivative of the reference signal; For the tracking error of the rotor position, The tracking error of the rotor speed, and satisfying Relationship; This is a preset time adjustment function. The first derivative of the preset time adjustment function. The second derivative of the preset time adjustment function; Parameter uncertainty in systems approximated by fuzzy logic; The sliding surface designed for the system; , , The gain is adjusted according to the desired control effect; S53, Update Law of Fuzzy Logic Parameters for: ； In the formula, hour, As a parameter to be adjusted based on the actual control effect, For projection operators, for ; definition ,ensure If the system is bounded and therefore will not become infinitely large, thus preventing the system from becoming unusable, then the projection operator takes the form: ； In the formula, for The maximum value; Electromagnetic torque output by the controller Ensure that the tracking error of the motor rotor position can converge to near the zero domain.

8. The control method for a permanent magnet synchronous motor based on a third-order superspiral sliding mode as described in claim 1, characterized in that, In step S6, the electromagnetic torque output in step S5 is... ,pass ,Will Converted to q-axis current ,in, This refers to the number of pole pairs in a permanent magnet synchronous motor. The permanent magnet flux linkage of the permanent magnet synchronous motor is then output as the q-axis voltage through a current loop regulator. and d-axis voltage ; q-axis voltage and d-axis voltage Three-phase voltage is obtained through Park transformation. , , The signal is modulated by space vector pulse width and output to the motor driver for position control of the PMSM.

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