Adaptive integral sliding mode control method for permanent magnet synchronous motor based on command filter

Abstract

The application relates to the technical field of permanent magnet synchronous motor control, in particular to a permanent magnet synchronous motor adaptive integral sliding mode control method based on a command filter, a second-order derivative and a third-order derivative of a position tracking error and a first-order derivative and a second-order derivative of a d-axis current tracking error are used to construct a second-order and third-order integral sliding mode surface based on the command filter, the inhibition capability of lumped interference is effectively enhanced, and the robustness of the system is significantly improved; for state-related uncertainty and time-varying interference, a radial basis function neural network is introduced to realize online approximation, and an interference adaptive law is combined to realize real-time estimation of the interference, effective estimation and compensation control of the radial basis function neural network and the interference adaptive law based on a scaling factor on the model uncertainty and time-varying interference of the permanent magnet synchronous motor are realized, so that the reliability and anti-interference performance of the controller are greatly improved without an accurate system model, and the tracking error is effectively reduced.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor control technology, and specifically to an adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in elevators, electric vehicles, robot servos and other fields due to their high efficiency, high power / torque density and excellent dynamic performance. However, in actual operation, they are easily affected by external environmental disturbances and load changes, which can lead to a significant decrease in their speed or position tracking accuracy. Therefore, how to suppress load disturbances and improve the steady-state accuracy and dynamic response of the system has become a key technical problem.

[0003] Existing research often employs radial basis function neural networks, state observers, and sliding mode control to improve disturbance rejection performance and tracking accuracy. However, these control strategies still have shortcomings when dealing with strong disturbances, uncertainties, and real-time requirements under complex operating conditions, making it difficult to balance high accuracy, strong robustness, and engineering feasibility. Therefore, sliding mode control, due to its strong robustness and excellent disturbance rejection performance, is widely used in permanent magnet synchronous motor control. Related research combines integral sliding mode, model predictive control, improved reaching laws, and disturbance observers to improve current and speed tracking performance and suppress chattering.

[0004] However, in high-order performance optimization, the velocity loop is subject to complex disturbances such as uncertainty and time-varying load, which restricts the design and control performance improvement of high-order sliding surfaces. Although some studies have used third-order superspiral observers to estimate lumped disturbances, the following shortcomings still exist: the upper bound of the disturbance is difficult to obtain accurately in advance, which leads to difficulties in observer parameter tuning and a decrease in estimation accuracy; at the same time, the disturbance estimation error and the tracking error are coupled with each other, making stability analysis complex and parameter constraints strict, which is not conducive to engineering implementation.

[0005] Furthermore, since the dynamic model of the quadrature axis (q-axis) of the permanent magnet synchronous motor has third-order characteristics, existing control methods often use the backstepping method to design the voltage control law, but this introduces coupling terms caused by the virtual control law. If not handled properly, this will reduce the degree of freedom of parameter design and affect control performance. Existing stability analysis methods have strong limitations on disturbance compensation errors and are difficult to apply to complex nonlinear systems. Although coupling terms can be eliminated through the equivalent transformation of the double sliding surface, the small parameters such as the motor's moment of inertia and stator inductance will significantly amplify the coupling coefficient, affecting the numerical stability and engineering feasibility of the control law.

[0006] Furthermore, while methods such as adaptive sliding mode control based on radial basis function neural networks and disturbance observer compensation have certain effects, the system reliability still needs to be improved. When the extended state observer and neural network are used for joint estimation, the disturbance estimation error and the weight error are strongly coupled and difficult to decouple. This not only increases the difficulty of stability analysis but also narrows the adjustable range of parameters, resulting in limited robustness and adaptability of the system under varying operating conditions and strong disturbances. Therefore, an adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters is proposed. Summary of the Invention

[0007] To address the technical problems existing in the prior art, the present invention provides an adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters.

[0008] To solve the above technical problems, the present invention provides the following technical solution: an adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters, wherein the integral sliding mode control method includes the following steps:

[0009] S1. Construct a mathematical model of the position, speed and current system of a permanent magnet synchronous motor with uncertainties and time-varying disturbances. The uncertainties are mainly caused by the mechanical structure and load, and the current system includes q-axis current and d-axis current.

[0010] S2, calculate the position and velocity tracking error based on the mathematical model of position and velocity and the desired position reference signal, and construct a command filter based on the measurement output of the velocity and q-axis current sensors, and obtain an approximate value of the second derivative of the position tracking error through the command filter;

[0011] Then, based on the single integral of the position tracking error, the position tracking error, the first derivative of the position tracking error, and the second derivative of the position tracking error, a third-order sliding surface based on the position tracking error of the permanent magnet synchronous motor is designed.

[0012] S3 uses a radial basis function neural network based on the length contraction factor to approximate the uncertainty in the velocity loop, and estimates the time-varying disturbance based on the disturbance adaptive law of the length contraction factor.

[0013] A virtual control law is constructed based on the mathematical model of position and velocity, command filter, scale reduction coefficient, scale reduction factor, radial basis function neural network, q-axis current tracking error, disturbance adaptive law, measurement output of velocity and q-axis current sensors, and the first integral of q-axis current tracking error.

[0014] S4. Based on the mathematical model of the q-axis current, the virtual control law, and the measurement output of the q-axis current sensor, design the first-order sliding surface of the q-axis current tracking error, and obtain the approximate value of the first-order derivative of the virtual control law based on the virtual control law and the command filter.

[0015] S5 uses a radial basis function neural network based on the length contraction factor to approximate the uncertainty in the q-axis of the current loop, and estimates the time-varying disturbance based on the disturbance adaptive law of the length contraction factor.

[0016] Then, based on the mathematical model of the q-axis current, the length contraction factor, the radial basis function neural network, and the q-axis current tracking error, the control input voltage for the q-axis is designed. ;

[0017] S6. Based on the mathematical model of the d-axis current and the desired current reference signal, construct the d-axis current tracking error. Design a command filter based on the measurement output of the d-axis current sensor. Then, based on the first integral of the d-axis current tracking error, the d-axis current tracking error, and the approximate value of the first derivative of the d-axis current tracking error obtained by the command filter, design the second-order sliding surface of the d-axis current tracking error.

[0018] S7 uses a radial basis function neural network based on the length contraction factor to approximate the uncertainty in the d-axis of the current loop, and estimates the time-varying disturbance based on the disturbance adaptive law of the length contraction factor.

[0019] Based on the mathematical model of d-axis current, command filter, scaling factor, radial basis function neural network, d-axis current tracking error, interference adaptive law, and the measurement output of d-axis current sensor, the control input voltage U of d-axis is designed. d ;

[0020] S8 combines the third-order sliding surface of position tracking error, the weight estimation error of the radial basis function neural network of velocity loop, the adaptive estimation error of velocity loop disturbance, the first-order sliding surface of current loop q-axis current tracking error, the weight estimation error of current loop q-axis radial basis function neural network, the adaptive estimation error of current loop q-axis disturbance, the second-order sliding surface of current loop d-axis current tracking error, the weight estimation error of current loop d-axis radial basis function neural network, and the adaptive estimation error of current loop d-axis disturbance. A Lyapunov function is constructed, and the disturbance adaptive law and the radial basis function neural network weight adaptive law in each link are analyzed. Based on the disturbance and weight adaptive laws, a controller is designed, and the controller is used to control the permanent magnet synchronous motor.

[0021] Preferably, in step S1, a mathematical model of the position, velocity, and current system is established based on the fundamental laws of electromagnetics of motors, Clarke or Park coordinate transformation, and the rotor field-oriented control principle. This model is a nonlinear model of the permanent magnet synchronous motor, specifically:

[0022] (1)

[0023] in, For mechanical angles; The derivative of the mechanical angle; It is the mechanical angular velocity; The derivative of the mechanical angular velocity; This is the q-axis current; The derivative of the q-axis current; This refers to the d-axis current. The derivative of the d-axis current; Lumped disturbance for the velocity loop; The lumped interference along the q-axis; The lumped interference along the d-axis; It is a time variable; For containing variables , , as well as augmented variables (e.g.) or , (represents the transpose of a vector). This is the control input voltage for the q-axis; This is the control input voltage for the d-axis; This represents the load torque; the remaining parameters and variables are defined as follows:

[0024] ; ; ;

[0025] ; ; ;

[0026] ; ; ; ;

[0027] In the formula, It is the extreme logarithm; For permanent magnet flux linkage; It is the moment of inertia; It is the coefficient of viscous friction; It is the q-axis inductance; It is the d-axis inductance; Stator resistance; This represents the load torque.

[0028] Preferably, in step S2, the position tracking error Speed ​​tracking error ,in, For position reference signal, Let be the derivative of the position reference signal, and ;

[0029] Position tracking error is obtained based on the following command filter. The approximate values ​​of the second and third derivatives are as follows:

[0030] (2)

[0031] In the formula, , as well as Parameters that are greater than 0; For position tracking error An approximate value of the first derivative; For position tracking error Approximate value of the second derivative; For position tracking error Approximate value of the third derivative;

[0032] Design position tracking error of permanent magnet synchronous motor Third-order sliding surface :

[0033] (3)

[0034] In the formula, For position tracking error A first integral; For position tracking error The first derivative; , , as well as It is a constant greater than 0.

[0035] Preferably, in step S3, the lumped interference of the velocity loop is... Decompose into uncertainty and time-varying interference ,definition: q-axis current tracking error ,in, , where is the length contraction coefficient;

[0036] For position tracking error Third-order sliding surface Differentiation yields:

[0037] (4)

[0038] In the formula, Third-order sliding surface The first derivative; , , For the aggregate bounded time-varying disturbance, For interference The estimated quantity, This is to account for the estimation error due to interference.

[0039] in:

[0040] ;

[0041] In the formula, These are the basis functions of a radial basis function neural network. For the ideal weight vector, , For weight estimation error, Let be the approximation error of the radial basis function neural network, and satisfy . , It is a constant greater than 0; and Let be the length contraction factor, and be a constant greater than 0; the virtual control law obtained from the analysis. for:

[0042] (5)

[0043] In the formula, , A constant greater than 0; q-axis current tracking error A first integral; It is a constant greater than 0.

[0044] Preferably, in step S4, the q-axis current tracking error is analyzed based on the mathematical model of the q-axis current, the virtual control law, and the measurement output of the q-axis current sensor. First-order sliding surface for:

[0045] (6)

[0046] The virtual control law is obtained based on the following command filter. Approximate values ​​of the first and second derivatives:

[0047] (7)

[0048] In the formula, , as well as Parameters that are greater than 0; For virtual control laws Approximate value; For virtual control laws An approximate value of the first derivative; For virtual control laws Approximate value of the second derivative.

[0049] Preferably, in step S5, the lumped interference of the q-axis is... Decompose into uncertainty and time-varying interference Then, based on the q-axis current tracking error... First-order sliding surface Differentiation yields:

[0050] (8)

[0051] In the formula, First-order sliding surface The derivative of , For interference The estimated quantity, , This is to account for the estimation error due to interference.

[0052] in:

[0053] ;

[0054] In the formula, These are the basis functions of a radial basis function neural network; For the ideal weight vector, , This represents the weight estimation error. Let be the approximation error of the radial basis function neural network, and satisfy . , It is a constant greater than 0; and is the length contraction factor, and is a constant greater than 0;

[0055] Analysis yields the control input voltage of the q-axis. for:

[0056] (9)

[0057] In the formula, , It is a constant greater than 0.

[0058] Preferably, in step S6, the d-axis current tracking error is constructed. The d-axis current reference signal is 0, and then the d-axis current tracking error is obtained based on the following command filter. Approximate values ​​of the first and second derivatives:

[0059] (10)

[0060] In the formula, , as well as Parameters that are greater than 0; For d-axis current tracking error Approximate value; For d-axis current tracking error An approximate value of the first derivative; For d-axis current tracking error Approximate value of the second derivative;

[0061] Design based on d-axis current tracking error of permanent magnet synchronous motor The second-order sliding surface is:

[0062] ; (11)

[0063] in, For d-axis current tracking error A first integral; For d-axis current tracking error The first derivative; , as well as It is a constant greater than 0.

[0064] Preferably, in step S7, the lumped interference of the d-axis is... Decompose into uncertainty and time-varying interference And based on the d-axis current tracking error Second-order sliding surface Differentiation yields:

[0065] (12)

[0066] In the formula, Second-order sliding surface The first derivative; , For interference The estimated quantity, , This is to account for the estimation error due to interference.

[0067] in:

[0068] ;

[0069] In the formula, and is the length contraction factor, and is a constant greater than 0; These are the basis functions of a radial basis function neural network. For the ideal weight vector, , For weight estimation error, The approximation error of the radial basis function neural network is and satisfies , It is a constant greater than 0; the control input voltage of the d-axis is obtained through analysis. for:

[0070] (13)

[0071] In the formula, , It is a constant greater than 0.

[0072] Preferably, in step S8, the interference adaptive law and the radial basis function neural network weight adaptive law are analyzed using the Lyapunov function, specifically as follows:

[0073] (14)

[0074] In the formula, , and A constant greater than 0 , and They are positive definite symmetric matrices. , and The inverse matrix;

[0075] Analysis yields the interference adaptive law for different stages and the weight adaptive law for the radial basis function neural network:

[0076] (15)

[0077] (16)

[0078] (17)

[0079] (18)

[0080] (19)

[0081] (20)

[0082] In the formula, , , , , , Estimators , , , , , The first derivative.

[0083] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0084] 1. This invention constructs second- and third-order integral sliding surfaces based on the command filter by using the command filter, the second and third derivatives of the position tracking error, and the first and second derivatives of the d-axis current tracking error. This effectively enhances the ability to suppress lumped interference, which includes uncertainty and external interference, and significantly improves the robustness of the system.

[0085] 2. This invention addresses state-related uncertainties and time-varying disturbances by introducing a radial basis function neural network for online approximation and combining it with an adaptive disturbance law to estimate disturbances in real time. This achieves effective estimation and compensation control of model uncertainties and time-varying disturbances of permanent magnet synchronous motors based on the radial basis function neural network with the scaling factor and the adaptive disturbance law. Thus, without the need for an accurate system model, the reliability and anti-interference performance of the controller are greatly improved, and the tracking error is effectively reduced.

[0086] 3. This invention introduces scale-down transformation coefficients and scale-down factors through a control strategy to scale down the current signal. At the same time, it scales down the basis functions of the radial basis function neural network and the known information of the disturbance, thereby further optimizing the dynamic and steady-state control performance.

[0087] 4. This invention eliminates the coupling between control parameters by adding a coupling term based on the length contraction transformation coefficient to the controller, resulting in low coupling between various design parameters. Under limited control input, control performance can be improved by adjusting each parameter, thus balancing high reliability, strong robustness, and ease of parameter adjustment. This reduces the conservatism of the control method and expands its applicability. Attached Figure Description

[0088] Figure 1 This is a schematic diagram of the control architecture of the present invention;

[0089] Figure 2 This is a position response curve based on a third-order sliding surface, as shown in the present invention.

[0090] Figure 3 This is a position response curve based on a second-order sliding surface, as shown in the present invention.

[0091] Figure 4 This is a graph showing the position tracking error response under different scaling factors according to the present invention.

[0092] Figure 5 The graph shows the position tracking error response curves of the neural network with and without radial basis functions according to the present invention.

[0093] Figure 6 The bar chart shows various performance indicators of the neural network with or without radial basis functions according to the present invention. Detailed Implementation

[0094] 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.

[0095] Example 1:

[0096] The Easy-To-Lab benchtop motor loading experimental platform from [Company Name] was used. The main parameters of the motor were: rated output power of 200W, rated voltage of 36V, rated current of 7.5A, and rated torque of [Specific parameters missing]. The number of pole pairs is 5, and the rotor resistance is... Line inductance is The rotor permanent magnet flux linkage is 0.0086 Wb, and the moment of inertia is... The coefficient of viscous friction is 1.3. 10 N m.

[0097] The parameters in the controller are: , , , , , , , , ;

[0098] , , , , , , , , ;

[0099] , , , , , , , , ;

[0100] , , , , ;

[0101] in, For the natural constant The base is a parameter greater than 0. It is an exponential function of the decay rate.

[0102] In this embodiment, the position reference signal is different for different time periods, specifically set as follows:

[0103] when hour, [deg];

[0104] when hour, [deg];

[0105] when hour, [deg];

[0106] when hour, [deg].

[0107] In this embodiment, the desired torque of the load permanent magnet synchronous motor is: The three neural networks are set as follows: ;

[0108] , , , ;

[0109] , , , ;

[0110] , , , ;

[0111] In the formula, , , This is the input to the radial basis function neural network. , , The center of the radial basis function neural network, , , denoted as the width of the radial basis function neural network.

[0112] In this embodiment, the initial values ​​of all estimators are set to 0. Furthermore, the command filter is: , , , , , .

[0113] Combination Figure 1 This embodiment describes an adaptive integral sliding mode control method for permanent magnet synchronous motors based on a command filter. The steps are as follows:

[0114] Step S1: Based on the fundamental laws of electromagnetics of electric motors, Clarke or Park coordinate transformation, and the principle of rotor field-oriented control, establish a mathematical model of the position, velocity, and current system, i.e., the nonlinear model of the permanent magnet synchronous motor, specifically as follows:

[0115] (twenty one)

[0116] in, For mechanical angles; The derivative of the mechanical angle; It is the mechanical angular velocity; The derivative of the mechanical angular velocity; This is the q-axis current; The derivative of the q-axis current; This refers to the d-axis current. The derivative of the d-axis current; Lumped disturbance for the velocity loop; The lumped interference along the q-axis; The lumped interference along the d-axis; It is a time variable; For containing variables , , as well as augmented variables (e.g.) or , (represents the transpose of a vector). This is the control input voltage for the q-axis; This is the control input voltage for the d-axis; This represents the load torque; the remaining parameters and variables are defined as follows:

[0117] ; ; ;

[0118] ; ; ;

[0119] ; ; ; ;

[0120] In the formula, It is the extreme logarithm; For permanent magnet flux linkage; It is the moment of inertia; It is the coefficient of viscous friction; It is the q-axis inductance; It is the d-axis inductance; Stator resistance; This represents the load torque.

[0121] Step S2, Position tracking error Speed ​​tracking error ,in, For position reference signal, Let be the derivative of the position reference signal, and ;

[0122] Position tracking error is obtained based on the following command filter. The approximate values ​​of the second and third derivatives are as follows:

[0123] (twenty two)

[0124] In the formula, , as well as Parameters that are greater than 0; For position tracking error An approximate value of the first derivative; For position tracking error Approximate value of the second derivative; For position tracking error Approximate value of the third derivative;

[0125] Design position tracking error of permanent magnet synchronous motor Third-order sliding surface :

[0126] (twenty three)

[0127] In the formula, For position tracking error A first integral; For position tracking error The first derivative; , , as well as It is a constant greater than 0.

[0128] Step S3, lumped interference of the velocity loop Decompose into uncertainty and time-varying interference ,definition: q-axis current tracking error ,in, , where is the length contraction coefficient;

[0129] For position tracking error Third-order sliding surface Differentiation yields:

[0130] (twenty four)

[0131] In the formula, Third-order sliding surface The first derivative; , , For the aggregate bounded time-varying disturbance, For interference The estimated quantity, This is to account for the estimation error due to interference.

[0132] in:

[0133] ;

[0134] In the formula, These are the basis functions of a radial basis function neural network. For the ideal weight vector, , For weight estimation error, Let be the approximation error of the radial basis function neural network, and satisfy . , It is a constant greater than 0; and Let be the length contraction factor, and be a constant greater than 0; the virtual control law obtained from the analysis. for:

[0135] (25)

[0136] In the formula, , A constant greater than 0; q-axis current tracking error A first integral; It is a constant greater than 0.

[0137] Step S4: Based on the mathematical model of the q-axis current, the virtual control law, and the measurement output of the q-axis current sensor, design the q-axis current tracking error. First-order sliding surface for:

[0138] (26)

[0139] The virtual control law is obtained based on the following command filter. Approximate values ​​of the first and second derivatives:

[0140] (27)

[0141] In the formula, , as well as Parameters that are greater than 0; For virtual control laws Approximate value; For virtual control laws An approximate value of the first derivative; For virtual control laws Approximate value of the second derivative.

[0142] Step S5, lumped interference on the q-axis Decompose into uncertainty and time-varying interference Then, based on the q-axis current tracking error... First-order sliding surface Differentiation yields:

[0143] (28)

[0144] In the formula, First-order sliding surface The derivative of , For interference The estimated quantity, , This is to account for the estimation error due to interference.

[0145] in:

[0146] ;

[0147] In the formula, These are the basis functions of a radial basis function neural network; For the ideal weight vector, , This represents the weight estimation error. Let be the approximation error of the radial basis function neural network, and satisfy . , It is a constant greater than 0; and is the length contraction factor, and is a constant greater than 0;

[0148] Analysis yields the control input voltage of the q-axis. for:

[0149] (29)

[0150] In the formula, , It is a constant greater than 0.

[0151] Step S6, construct d-axis current tracking error The d-axis current reference signal is 0, and then the d-axis current tracking error is obtained based on the following command filter. Approximate values ​​of the first and second derivatives:

[0152] (30)

[0153] In the formula, , as well as Parameters that are greater than 0; For d-axis current tracking error Approximate value; For d-axis current tracking error An approximate value of the first derivative; For d-axis current tracking error Approximate value of the second derivative;

[0154] Design based on d-axis current tracking error of permanent magnet synchronous motor The second-order sliding surface is:

[0155] ; (31)

[0156] in, For d-axis current tracking error A first integral; For d-axis current tracking error The first derivative; , as well as It is a constant greater than 0.

[0157] Step S7, lumped interference along the d-axis Decompose into uncertainty and time-varying interference And based on the d-axis current tracking error Second-order sliding surface Differentiation yields:

[0158] (32)

[0159] In the formula, Second-order sliding surface The first derivative; , For interference The estimated quantity, , This is to account for the estimation error due to interference.

[0160] in:

[0161] ;

[0162] In the formula, and is the length contraction factor, and is a constant greater than 0; These are the basis functions of a radial basis function neural network. For the ideal weight vector, , For weight estimation error, The approximation error of the radial basis function neural network is and satisfies , It is a constant greater than 0; the control input voltage of the d-axis is obtained through analysis. for:

[0163] (33)

[0164] In the formula, , It is a constant greater than 0.

[0165] Step S8 involves analyzing the interference adaptive law and the radial basis function neural network weight adaptive law using the Lyapunov function, specifically as follows:

[0166] (34)

[0167] In the formula, , and A constant greater than 0 , and They are positive definite symmetric matrices. , and The inverse matrix;

[0168] Analysis yields the interference adaptive law and the radial basis function neural network weight adaptive law for different stages:

[0169] (35)

[0170] (36)

[0171] (37)

[0172] (38)

[0173] (39)

[0174] (40)

[0175] In the formula, , , , , , Estimators , , , , , The first derivative.

[0176] In this embodiment, when controlling the permanent magnet synchronous motor, a desired position reference signal is first given, a tracking position error is designed, and a control voltage is designed based on this tracking position error. ;at the same time, The shaft current reference signal is 0, and the design... Shaft current tracking error, and based on this Shaft current tracking error design control power supply Control voltage and The permanent magnet synchronous motor is controlled by a combination of factors to ensure that its rotor position is consistent with the desired position reference signal.

[0177] Example 2:

[0178] To verify the effectiveness of the proposed adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters, the entire framework was built in Matlab 2024b and Simulink, and the following comparative tests were conducted.

[0179] In this diagram, the red straight line represents the position reference signal, the black short horizontal line represents the second-order or third-order sliding mode controller of the present invention, the blue straight line and the black short horizontal line represent the controller in the present invention, the orange straight line represents the comparison controller, the blue bar chart with black dotted border represents the controller in the present invention, and the magenta bar chart with black straight border represents the comparison controller.

[0180] like Figure 2 and Figure 3 As shown, the third-order sliding mode controller outperforms the second-order sliding mode controller in both transient and steady-state performance. The control parameters of the second-order sliding mode controller... The value is 1800, and other parameters are the same as those of the third-order sliding mode controller; when the control parameters of the second-order sliding mode controller are... When the setting is too low, the control performance will deteriorate.

[0181] like Figure 4 As shown, different length contraction coefficients This will change the performance of the controller, the scaling factor. It cannot be too large or too small; if the length contraction coefficient... If the value is too small, such as 10, the sliding mode controller will not function properly; if the scaling factor is too small... If the value is too large, such as 200, the steady-state and transient performance of the sliding mode controller will be weakened.

[0182] like Figure 5 As shown, when the amplitude of the position reference signal is large, the control performance of the control strategy with and without Radial Basis Function Neural Network (RBFNN) is not significantly different; when the amplitude of the position reference signal is small, the control strategy with RBFNN has a better control effect.

[0183] like Figure 6 As shown, the integral of absolute error (IAE), integral of squared error (ISE), time-weighted integral of absolute error (ITAE), and time-weighted integral of squared error (ITSE) are displayed. It can also be seen that the control strategy with RBFNN has a better control effect.

[0184] In summary, the method of this invention outperforms the existing solutions in terms of both transient and steady-state performance, as well as various error indices.

[0185] 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. An adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters, characterized in that, The integral sliding mode control method includes the following steps: S1. Construct a mathematical model of the position, speed and current system of a permanent magnet synchronous motor with uncertainties and time-varying disturbances. S2, calculate the position and velocity tracking errors, and construct a command filter based on the measurement output of the velocity and q-axis current sensors. Obtain an approximate value of the second derivative of the position tracking error through the command filter, and design a third-order sliding surface based on the position tracking error. S3 uses a radial basis function neural network based on the length contraction factor to approximate the uncertainty in the velocity loop, estimates the time-varying disturbance based on the disturbance adaptive law of the length contraction factor, and obtains the virtual control law through analysis. S4. Design the first-order sliding surface for q-axis current tracking error, and obtain an approximate value of the first-order derivative of the virtual control law based on the virtual control law and the command filter. S5 uses a radial basis function neural network based on the length contraction factor to approximate the uncertainty in the q-axis of the current loop, estimates the time-varying disturbance based on the length contraction factor-based adaptive disturbance law, and designs the control input voltage for the q-axis. ; S6. Construct the d-axis current tracking error, design a command filter based on the measurement output of the d-axis current sensor, and then design the second-order sliding surface of the d-axis current tracking error based on the first integral of the d-axis current tracking error, the d-axis current tracking error and the approximate value of the first derivative of the d-axis current tracking error obtained by the command filter. S7, using a radial basis function neural network based on a scale factor to approximate the uncertainty in the current loop d-axis, a disturbance adaptive law based on a scale factor to estimate the time-varying disturbance in the d-axis, and redesigning the control input voltage U d ; S8 combines the third-order sliding surface of position tracking error, the axis errors of velocity loop and current loop, the neural network weight error and the disturbance estimation error to construct a Lyapunov function, analyze the disturbance adaptive law and the radial basis function neural network weight adaptive law in each link, design a controller based on this adaptive law, and use the controller to control the permanent magnet synchronous motor.

2. The adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters as described in claim 1, characterized in that, In step S1, based on the fundamental electromagnetic laws of motors, Clarke or Park coordinate transformation, and the rotor field-oriented control principle, a mathematical model of the position, velocity, and current system is established, namely, the nonlinear model of the permanent magnet synchronous motor, specifically: ； in, For mechanical angles; The derivative of the mechanical angle; It is the mechanical angular velocity; The derivative of the mechanical angular velocity; This is the q-axis current; The derivative of the q-axis current; This refers to the d-axis current. The derivative of the d-axis current; Lumped disturbance for the velocity loop; The lumped interference along the q-axis; The lumped interference along the d-axis; It is a time variable; For containing variables , , as well as augmented variables; This is the control input voltage for the q-axis; This is the control input voltage for the d-axis; This represents the load torque; the remaining parameters and variables are defined as follows: ； ； ； ； ； ； ； ； ； ； In the formula, It is the extreme logarithm; For permanent magnet flux linkage; It is the moment of inertia; It is the coefficient of viscous friction; It is the q-axis inductance; It is the d-axis inductance; Stator resistance; This represents the load torque.

3. The adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters as described in claim 1, characterized in that, Step S2 specifically includes the following steps: S21, Position tracking error and speed tracking error ,in, For position reference signal, Let be the derivative of the position reference signal, and ; S22, obtain the position tracking error based on the following command filter. Approximate values ​​of the second and third derivatives: ； In the formula, , as well as Parameters that are greater than 0; For position tracking error An approximate value of the first derivative; For position tracking error Approximate value of the second derivative; For position tracking error Approximate value of the third derivative; S23, Design of position tracking error of permanent magnet synchronous motor Third-order sliding surface : ； In the formula, For position tracking error A first integral; For position tracking error The first derivative; , , as well as It is a constant greater than 0.

4. The adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters as described in claim 2, characterized in that, Step S3 specifically includes the following steps: S31, lumped interference in the speed loop Decompose into uncertainty and time-varying interference ,definition: q-axis current tracking error ,in, , where is the length contraction coefficient; S32, for position tracking error Third-order sliding surface Differentiation yields: ； In the formula, Third-order sliding surface The first derivative; , , For the aggregate bounded time-varying disturbance, For interference The estimated quantity, , This is to account for the estimation error due to interference. in: ； In the formula, These are the basis functions of a radial basis function neural network. For the ideal weight vector, , For weight estimation error, Let be the approximation error of the radial basis function neural network, and satisfy . , It is a constant greater than 0; Represents the transpose of a vector; and is the length contraction factor, and is a constant greater than 0; S33, the virtual control law obtained from the analysis for: ； In the formula, , A constant greater than 0; q-axis current tracking error A first integral; It is a constant greater than 0.

5. The adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters as described in claim 1, characterized in that, Step S4 specifically includes the following steps: S41, based on the mathematical model of the q-axis current, the virtual control law, and the measurement output of the q-axis current sensor, the q-axis current tracking error is analyzed. First-order sliding surface for: ； S42, Obtain the virtual control law based on the following command filter. Approximate values ​​of the first and second derivatives: ； In the formula, , as well as Parameters that are greater than 0; For virtual control laws Approximate value; For virtual control laws An approximate value of the first derivative; For virtual control laws Approximate value of the second derivative.

6. The adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters as described in claim 1, characterized in that, Step S5 specifically includes the following steps: S51, lumped interference on the q-axis Decompose into uncertainty and time-varying interference Then, based on the q-axis current tracking error... First-order sliding surface Differentiation yields: ； In the formula, First-order sliding surface The derivative of , For interference The estimated quantity, , This is to account for the estimation error due to interference. in: ； In the formula, These are the basis functions of a radial basis function neural network; For the ideal weight vector, , This represents the weight estimation error. Let be the approximation error of the radial basis function neural network, and satisfy . , It is a constant greater than 0; and is the length contraction factor, and is a constant greater than 0; S52, analysis yields the control input voltage of the q-axis. for: ； In the formula, , It is a constant greater than 0.

7. The adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters as described in claim 1, characterized in that, Step S6 specifically includes the following steps: S61, Construct d-axis current tracking error The d-axis current reference signal is 0, and then the d-axis current tracking error is obtained based on the following command filter. Approximate values ​​of the first and second derivatives: ； In the formula, , as well as Parameters that are greater than 0; For d-axis current tracking error Approximate value; For d-axis current tracking error An approximate value of the first derivative; For d-axis current tracking error Approximate value of the second derivative; S62, Design based on d-axis current tracking error of permanent magnet synchronous motor The second-order sliding surface is: ； in, For d-axis current tracking error A first integral; For d-axis current tracking error The first derivative; , as well as It is a constant greater than 0.

8. The adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters as described in claim 2, characterized in that, Step S7 specifically includes the following steps: S71, lumped interference along the d-axis Decompose into uncertainty and time-varying interference And based on the d-axis current tracking error Second-order sliding surface Differentiation yields: ； In the formula, Second-order sliding surface The first derivative; , For interference The estimated quantity, , This is to account for the estimation error due to interference. in: ； In the formula, and is the length contraction factor, and is a constant greater than 0; These are the basis functions of a radial basis function neural network. For the ideal weight vector, , For weight estimation error, Let be the approximation error of the radial basis function neural network, and satisfy . , It is a constant greater than 0; S72, analysis yields the control input voltage of the d-axis. for: ； In the formula, , It is a constant greater than 0.

9. The adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters as described in claim 1, characterized in that, The position tracking error third-order sliding surface, velocity loop and current loop axis errors, neural network weight errors and disturbance estimation errors in step S8 specifically include: velocity loop radial basis function neural network weight estimation error, velocity loop disturbance adaptive estimation error, current loop q-axis current tracking error first-order sliding surface, current loop q-axis radial basis function neural network weight estimation error, current loop q-axis disturbance adaptive estimation error, current loop d-axis current tracking error second-order sliding surface, current loop d-axis radial basis function neural network weight estimation error, and current loop d-axis disturbance adaptive estimation error.

10. The adaptive integral sliding mode control method for permanent magnet synchronous motors based on command filters as described in claim 1, characterized in that, Step S8 specifically includes the following steps: S81 analyzes the interference adaptive law and the radial basis function neural network weight adaptive law using Lyapunov functions, specifically as follows: ； In the formula, , and A constant greater than 0 , and They are positive definite symmetric matrices. , and The inverse matrix; S82, the interference adaptive law and the weight adaptive law of the radial basis function neural network at different stages are obtained through analysis: ； ； ； ； ； ； In the formula, , , , , , Estimators , , , , , The first derivative.

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