A speed control strategy for PMLSM drive system based on RBF adaptive super-twisted sliding mode

Abstract

The present invention provides a PMLSM drive system speed control strategy based on RBF adaptive super-twisted sliding mode, comprising the following steps: first, the relevant motor parameters in the PMLSM dynamic equation are regarded as unknown quantities, and its super-local model is established; secondly, an estimator for estimating the unknown parameters in the super-local model is designed based on an RBF neural network; then, an outer loop AST speed control law is designed based on the RBF neural network estimator; finally, a PI-based vector control method is adopted for the inner loop d-q axis current in the PMLSM drive system to realize the motor stator current tracking its given value. The present invention can ensure high-precision control of the speed of the PMLSM drive system, enhance the robustness of the system to cope with parameter and load disturbances, and has a strong practical engineering value.

Description

Technical Field

[0001] The invention belongs to the technical field of permanent magnet linear synchronous motor control, and relates to a PMLSM drive system speed control strategy based on RBF adaptive super-twisted sliding mode. Background Art

[0002] Due to its advantages of large thrust, high precision, high speed, high power density, fast response and low noise, PMLSM is widely used in precision CNC machine tools, lithography machines, high-speed logistics equipment, ropeless elevators, rail transit equipment and other fields. At the same time, since the ball screw, coupling and other intermediate transmission links are eliminated in the structure, PMLSM can directly drive the load. However, there are uncertainties such as nonlinear friction, thrust fluctuations, load disturbances and perturbations of other parameters during the operation of the motor, which cause the motor performance to deteriorate. Therefore, it is necessary to study an effective control method to enable the PMLSM drive system to overcome the adverse effects of these uncertainties, thereby improving the robustness and steady-state performance of speed control.

[0003] Most PMLSM drive systems adopt a dual-loop control strategy of a speed outer loop and a current inner loop. Its control goal is to make the motor speed quickly and accurately track a given value. Compared with the current inner loop, the control accuracy of the speed outer loop directly affects the overall performance of the drive system. Therefore, the present invention proposes a new adaptive robust speed control method for the speed outer loop.

[0004] At present, the speed control methods widely used in PMLSM drive systems mainly include: PI-based vector control, sliding mode control, model predictive control, and machine learning-based control. Although these methods can control the motor speed, they have the following shortcomings and disadvantages: (1) PI-based vector control can only be used for PMLSM with accurate parameters, but this method is not robust to parameter mismatch or external disturbances; (2) Sliding mode control can enhance the robustness of the PMLSM drive system, but the switching term in the control law of this method causes the system to inevitably vibrate; (3) Model predictive control based on the precise mathematical equations of the system can achieve optimal control of the PMLSM drive system, but this method is not suitable for working conditions such as PMLSM parameter uncertainty or load disturbance; (4) Machine learning-based control methods can flexibly handle nonlinear and difficult-to-model problems in PMLSM drive systems, but most of them currently require offline training, which requires a large amount of motor operation data to be obtained in advance, so this method is time-consuming and labor-intensive.

[0005] The invention patent application "A permanent magnet linear automatic door positioning method based on RBF_PID and nonlinear disturbance observer" (publication number: CN117434826A) is now used as a comparative document of the present invention. It adopts RBF neural network to realize online tuning of PID controller parameters, and simultaneously adopts nonlinear disturbance observer to estimate lumped disturbance, so as to realize the robustness of the system to parameter mismatch or external disturbance.

[0006] The main differences between the present invention and the reference document are:

[0007] ① Regarding the RBF neural network estimator: the present invention estimates the hyperlocal model parameters of the PMLSM online, while the comparative document tunes the PID controller parameters online;

[0008] ② Regarding speed control strategy: the present invention adopts a super-twisted sliding mode strategy based on RBF, while the reference document adopts a PID algorithm based on RBF;

[0009] ③ Regarding lumped disturbance estimation: The present invention adopts RBF neural network estimator based on PMLSM hyperlocal model, while the reference document adopts nonlinear load disturbance observer based on PMLSM mathematical model, but it does not provide any explanation on the specific technical content and implementation method of nonlinear load disturbance observer, so it does not play a role in enlightenment for the present invention;

[0010] ④ Regarding the cost and complexity of the algorithm: the present invention adopts dual-loop control, while the reference document adopts three-loop control. In addition, the present invention only uses one RBF-based estimator, while the reference document uses a total of four estimators, including three RBF-based identifiers and one nonlinear disturbance observer. Therefore, the cost and complexity of the present invention are obviously lower;

[0011] ⑤ The present invention does not require knowledge of motor parameters and is essentially a model-free control strategy, whereas the comparative document is a control method based on an actual motor model, and the two are essentially different. Summary of the invention

[0012] In order to overcome the shortcomings and deficiencies of existing research methods, and ensure that the PMLSM drive system can achieve high-precision speed control under various internal and external disturbance conditions, and has good dynamic and steady-state performance, the present invention proposes a PMLSM drive system speed control strategy based on RBF adaptive super-twisted sliding mode, including: first, the relevant parameters in the PMLSM dynamic equation are regarded as unknown quantities, and its super-local model is established based on the PMLSM dynamic equation; secondly, based on the RBF neural network, an estimator for estimating the unknown parameters in the super-local model is designed; then, based on the RBF neural network estimator, the outer loop AST speed control law is designed to enhance the system robustness, speed up the system response speed and suppress the jitter in conventional sliding mode control; finally, the inner loop dq axis current in the PMLSM drive system is controlled by a PI-based vector control method to achieve the motor stator current tracking its given value. Since there is no need to know the motor parameters, the present invention is essentially a model-free control strategy, which specifically includes the following steps:

[0013] Step 1: Establish a PMLSM hyperlocal model based on the PMLSM dynamic equation;

[0014] The dynamic equation of the hidden-pole PMLSM in the dq-axis rotating coordinate system is:

[0015]

[0016] In the formula, v m is the PMLSM speed; i q is the q-axis stator current; B is the viscous friction coefficient; M is the mover mass; n p is the number of magnetic pole pairs; ψ f is the permanent magnet flux linkage of constant value; F is the pole distance; e is the electromagnetic thrust; F f 、F r 、F d They are nonlinear friction, thrust fluctuation and external load disturbance force respectively;

[0017] The hyperlocal model of PMLSM is established as:

[0018]

[0019] In the formula, u represents i q , that is, the speed outer loop control signal; the expressions of g and f are:

[0020]

[0021] Since the PMLSM parameters include B, M, ψ f , 、F f 、Fr 、F d is unknown, so g and f are also unknown.

[0022] Step 2: Based on the PMLSM hyperlocal model of step 1, a RBF neural network estimator for estimating unknown parameters is designed; the RBF neural network estimator is used to estimate the unknown parameters g and f in the hyperlocal model;

[0023] The input of the RBF neural network estimator is:

[0024]

[0025] In the formula, v mref Give speed to PMLSM; v m With v mref difference;

[0026] The output of the RBF neural network estimator is:

[0027]

[0028]

[0029] In the formula, are the estimated values ​​of the PMLSM hyperlocal model parameters f and g respectively; w fj 、w gj are the weights of the jth hidden layer node of RBF with respect to f and g respectively; h fj With h gj are the outputs of the jth hidden layer node of the RBF neural network about f and g respectively; c fj With c gj are the radial basis function center values ​​of the jth hidden layer node of the RBF neural network with respect to f and g respectively; b fj With b gj are the radial basis function widths of the jth hidden layer nodes of the RBF neural network with respect to f and g respectively; H f With H g are the hidden layer matrices of f and g respectively; W f With W g are the weight matrices for f and g respectively.

[0030] Step 3: Based on the RBF neural network estimator in step 2, an online adaptive law for the weight matrix is ​​designed, and an online iteration method for the central value of the radial basis function is proposed;

[0031] The RBF neural network weight update method, that is, the online adaptive law of the weight matrix is:

[0032]

[0033] Where l(t) is the super-twisted sliding mode gain;

[0034] The iterative method for the (k+1)th sampling time of the radial basis function center value is:

[0035]

[0036] In the formula, k 1 and k 2 are the RBF radial basis function center value learning rates with respect to f and g, respectively, both of which are positive real numbers.

[0037] Step 4: Based on the RBF neural network estimator in step 3, design the outer loop AST speed control law;

[0038] Select the sliding surface s as:

[0039]

[0040] Therefore, the outer loop AST speed control law based on RBF is:

[0041]

[0042] The adaptive law of l(t) in the RBF-based outer loop AST speed control law is:

[0043]

[0044] In the formula, k 3 and l are positive real numbers, and the initial value l(0) of l(t) is set to a positive real number.

[0045] Stability analysis ideas of the outer loop AST speed control law based on RBF:

[0046] Because there is an ideal weight matrix W fideal and W gideal So that the following is true:

[0047]

[0048] In the formula,

[0049]

[0050] Therefore, the difference between the actual weight matrix of RBF and the ideal weight matrix is ​​expressed as:

[0051]

[0052] To make the description concise, l is used instead of l(t) in the following text, and the auxiliary variable p is set to:

[0053]

[0054] Select the state variable as:

[0055] x 1 =s,x 2 =r (13)

[0056] Substituting equation (8) into equation (2), and considering equations (12) and (13) at the same time, the state equation of PMLSM is expressed as:

[0057]

[0058] The stability analysis of the outer loop AST speed control law based on RBF is essentially to prove the stability of system (14). The Lyapunov method can be used for analysis, including the following steps: first, define the Lyapunov function; second, calculate its derivative; then, prove the negative definiteness of its derivative; finally, draw the conclusion that the control law is stable; specifically:

[0059] First, define the Lyapunov function as follows:

[0060] V(x)=V 1 (x)+V 2 (x)+V 3 (x) (15)

[0061] In the formula,

[0062]

[0063] Next, find the derivative of V(x) The result is:

[0064]

[0065] In the formula,

[0066]

[0067] The proposed RBF weight matrix adaptive law and the adaptive law in AST Substituting into formula (17), we get:

[0068]

[0069] In the formula,

[0070] e=-(e g u+e f ) (20)

[0071] Next, prove Negative definiteness;

[0072] Formula (19) can be written as:

[0073]

[0074] In the formula, λ min (Q) and λ max (Q) are the minimum and maximum eigenvalues ​​of Q, respectively;

[0075] From formula (21), we can see that as long as k 3 ≥|e|, then

[0076]

[0077] Since Q is a positive definite matrix, λ min (Q)>0;

[0078] Next, we discuss k 3 ≥|e|, substituting formula (8) into (20) yields:

[0079]

[0080] From formula (10), we can see that when W f and W g When taking the ideal weight matrix, and are close to the true values ​​f and g respectively, so it can be considered that e g →0,e f →0, and |e| is also a number close to 0, so there must be a number that satisfies the condition k 3 k ≥|e| 3 , so that It is negatively determined.

[0081] Finally, the above analysis shows that the AST speed control law based on RBF can ensure the stability of the system.

[0082] Step 5: Use PI-based vector control to design the inner loop dq axis current control law:

[0083] The inner loop dq axis PI current control law is:

[0084]

[0085] In the formula, i dref 、i qref are the dq axis reference currents respectively, the former is taken as 0, and the latter is the output of the speed outer loop controller; pd (k pq ), k id (k iq) are the proportional gain and integral gain of the d-axis (q-axis) respectively, both of which are positive real numbers.

[0086] The beneficial effects of the present invention are:

[0087] 1. Since there is no need to know the motor parameters, the present invention provides a control method based on a super-local model, which is essentially a model-free advanced control strategy;

[0088] 2. The present invention does not need to obtain sample data in advance, thus eliminating the need for an offline training process. The online training process of the RBF-based estimator in the present invention will be directly integrated into the system adaptive control, which is easy to implement and execute;

[0089] 3. The present invention adopts the outer loop AST speed control strategy, which can eliminate the system chattering phenomenon and make the PMLSM drive system have strong robustness;

[0090] 4. On the one hand, the present invention adopts an RBF-based estimator to estimate the actual parameters of the PMLSM super-local model in real time online. On the other hand, the AST control method with strong robustness can combine the two to construct an RBF-based AST control strategy, which can greatly enhance the ability to resist various internal and external interferences, thereby significantly improving the dynamic and steady-state performance of the PMLSM drive system, providing a new method for permanent magnet synchronous linear motor speed control, and has strong practical engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 Schematic diagram of an RBF-based estimator in the present invention;

[0092] Figure 2 It is the AST speed control block diagram of the PMLSM drive system based on RBF in the present invention;

[0093] Figure 3 It is the flow chart of AST speed control of PMLSM drive system based on RBF in the present invention;

[0094] Figure 4 It is a schematic diagram of the lumped load applied to the motor in the Matlab / Simulink simulation;

[0095] Figure 5 It is a schematic diagram of speed comparison and speed error comparison under three outer loop control strategies;

[0096] Figure 6 It is a comparison diagram of the q-axis stator current under three outer loop control strategies;

[0097] Figure 7 is the three-phase stator current i under the three outer loop control strategies abc Simulation result diagram;

[0098] Figure 8 This is a schematic diagram comparing electromagnetic thrust under three outer loop control strategies. DETAILED DESCRIPTION

[0099] The technical solution of the present invention is described below in conjunction with the accompanying drawings and implementation methods.

[0100] A speed control strategy of a PMLSM drive system based on RBF adaptive super-twisted sliding mode includes the following steps:

[0101] Step 1: Establish a PMLSM hyperlocal model based on the PMLSM dynamic equation;

[0102] The dynamic equation of the hidden-pole PMLSM in the dq-axis rotating coordinate system is:

[0103]

[0104] In the formula, v m is the PMLSM speed; i q is the q-axis stator current; B is the viscous friction coefficient; M is the mover mass; n p is the number of magnetic pole pairs; ψ f is the permanent magnet flux linkage of constant value; F is the pole distance; e is the electromagnetic thrust; F f 、F r 、F d They are nonlinear friction, thrust fluctuation and external load disturbance force respectively;

[0105] The hyperlocal model of PMLSM is established as:

[0106]

[0107] In the formula, u represents i q , that is, the speed outer loop control signal; the expressions of g and f are:

[0108]

[0109] Since the PMLSM parameters include B, M, ψ f , 、F f 、F r 、F d is unknown, so g and f are also unknown.

[0110] Step 2: Based on the PMLSM hyperlocal model in step 1, design an RBF neural network estimator for estimating unknown parameters; Figure 1 As shown, the RBF neural network estimator is used to estimate the unknown parameters g and f in the hyperlocal model;

[0111] The input of the RBF neural network estimator is:

[0112]

[0113] In the formula, v mref Give speed to PMLSM; v m With v mref difference;

[0114] The output of the RBF neural network estimator is:

[0115]

[0116] In the formula, are the estimated values ​​of the PMLSM hyperlocal model parameters f and g respectively; w fj 、w gj are the weights of the jth hidden layer node of RBF with respect to f and g respectively; h fj With h gj are the outputs of the jth hidden layer node of the RBF neural network about f and g respectively; c fj With c gj are the radial basis function center values ​​of the jth hidden layer node of the RBF neural network with respect to f and g respectively; b fj With b gj are the radial basis function widths of the jth hidden layer nodes of the RBF neural network with respect to f and g respectively; H f With H g are the hidden layer matrices of f and g respectively; W f With W g are the weight matrices of f and g respectively.

[0117] Step 3: Based on the RBF neural network estimator in step 2, an online adaptive law for the weight matrix is ​​designed, and an online iteration method for the central value of the radial basis function is proposed;

[0118] The RBF neural network weight update method, that is, the online adaptive law of the weight matrix is:

[0119]

[0120] Where l(t) is the super-twisted sliding mode gain;

[0121] The iterative method for the (k+1)th sampling time of the radial basis function center value is:

[0122]

[0123] In the formula, k 1 and k2 are the RBF radial basis function center value learning rates with respect to f and g, respectively, both of which are positive real numbers.

[0124] Step 4: Based on the RBF neural network estimator in step 3, design the outer loop AST speed control law;

[0125] Select the sliding surface s as:

[0126]

[0127] Therefore, the outer loop AST speed control law based on RBF is:

[0128]

[0129] The adaptive law of l(t) in the RBF-based outer loop AST speed control law is:

[0130]

[0131] In the formula, k 3 and is a positive real number, and the initial value l(0) of l(t) is set to a positive real number.

[0132] Stability analysis ideas of the outer loop AST speed control law based on RBF:

[0133] Because there is an ideal weight matrix W fideal and W gideal So that the following is true:

[0134]

[0135] In the formula,

[0136]

[0137] Therefore, the difference between the actual weight matrix of RBF and the ideal weight matrix is ​​expressed as:

[0138]

[0139] To make the description concise, l is used instead of l(t) in the following text, and the auxiliary variable p is set to:

[0140]

[0141] Select the state variable as:

[0142] x 1 =s,x 2 =r (13)

[0143] Substituting equation (8) into equation (2), and considering equations (12) and (13) at the same time, the state equation of PMLSM is expressed as:

[0144]

[0145] The stability analysis of the outer loop AST speed control law based on RBF is essentially to prove the stability of system (14). The Lyapunov method can be used for analysis, including the following steps: first, define the Lyapunov function; second, calculate its derivative; then, prove the negative definiteness of its derivative; finally, draw the conclusion that the control law is stable; specifically:

[0146] First, define the Lyapunov function as follows:

[0147] V(x)=V 1 (x)+V 2 (x)+V 3 (x) (15)

[0148] In the formula,

[0149]

[0150] Next, find the derivative of V(x) The result is:

[0151]

[0152] In the formula,

[0153]

[0154] The proposed RBF weight matrix adaptive law and the adaptive law in AST Substituting into formula (17), we get:

[0155]

[0156] In the formula,

[0157] e=-(e g u+e f ) (20)

[0158] Next, prove Negative definiteness;

[0159] Formula (19) can be written as:

[0160]

[0161] In the formula, λ min (Q) and λ max(Q) are the minimum and maximum eigenvalues ​​of Q, respectively;

[0162] From formula (21), we can see that as long as k 3 ≥|e|, then

[0163]

[0164] Since Q is a positive definite matrix, λ min (Q)>0;

[0165] Next, we discuss k 3 ≥|e|, substituting formula (8) into (20) yields:

[0166]

[0167] From formula (10), we can see that when W f and W g When taking the ideal weight matrix, and are close to the true values ​​f and g respectively, so it can be considered that e g →0,e f →0, and |e| is also a number close to 0, so there must be a number that satisfies the condition k 3 k ≥|e| 3 , so that It is negatively determined.

[0168] Finally, the above analysis shows that the AST speed control law based on RBF can ensure the stability of the system.

[0169] Step 5: Use PI-based vector control to design the inner loop dq axis current control law:

[0170] The inner loop dq axis PI current control law is:

[0171]

[0172] In the formula, i dref 、i qref are the dq axis reference currents respectively, the former is taken as 0, and the latter is the output of the speed outer loop controller; pd (k pq ), k id (k iq ) are the proportional gain and integral gain of the d-axis (q-axis) respectively, both of which are positive real numbers.

[0173] Example

[0174] In order to verify the effectiveness and feasibility of the method proposed in the present invention, a PMLSM drive system simulation model under three outer-loop control strategies based on MATLAB / Simulink was built for verification. The three outer-loop control strategies include PI algorithm, super-twisted sliding mode control method STC and RBF-AST of the present invention. The inner-loop dq-axis currents in the three adopt exactly the same PI-based vector control method, and the parameters involved are shown in Table 1.

[0175] Table 1MATLAB / Simulink simulation parameter settings

[0176]

[0177]

[0178] The test conditions of this embodiment are: simulation time t = 0 ~ 1.95s, given speed is 1.5m / s, the lumped load applied to the motor is F l =F f +F r +F d , its waveform is as follows Figure 4 shown.

[0179] Depend on Figure 5 It can be seen that compared with the PI algorithm and STC, the present invention can significantly speed up the system response speed, reduce overshoot and weaken speed fluctuation, enable the system to adapt to load mutation conditions, enhance robustness and improve speed control accuracy.

[0180] Depend on Figure 6 It can be seen that, compared with PI and super-twisted sliding mode control method STC, the present invention can significantly reduce current fluctuations and enable the system to adapt to sudden load changes.

[0181] Depend on Figure 7 It can be seen that, compared with PI and super-twisted sliding mode control method STC, the present invention can make the actual three-phase stator current of the system better approach the standard sinusoidal three-phase current waveform.

[0182] Depend on Figure 8 It can be seen that compared with PI and super-twisted sliding mode control method STC, the present invention can significantly reduce the electromagnetic thrust fluctuation of the system, so that the system can adapt to the load mutation condition, and its electromagnetic thrust fluctuation is significantly smaller than PI and super-twisted sliding mode control method STC.

Claims

1. A speed control strategy for a PMLSM drive system based on an RBF adaptive super-twisted sliding mode, characterized in that: The following steps are involved: Step 1: Establish a PMLSM hyperlocal model based on the PMLSM dynamic equation; The dynamic equation of the hidden pole PMLSM in the dq axis rotating coordinate system in step 1 is: In the formula, v m is the PMLSM speed; i q is the q-axis stator current; B is the viscous friction coefficient, M is the mover mass; n p is the number of magnetic pole pairs; ψ f is the permanent magnet flux linkage of constant value; F is the pole distance; e is the electromagnetic thrust; F f 、F r 、F d They are nonlinear friction, thrust fluctuation and external load disturbance force; The PMLSM super-local model in step 1 is: In the formula, u represents i q , that is, the speed outer loop control signal; the expressions of g and f are: Since the parameters B, M, ψ in the PMLSM dynamic equation f , 、F f 、F r 、F d are all unknown, so g and f are also unknown; Step 2: Based on the PMLSM hyperlocal model in step 1, a RBF neural network estimator is designed for estimating unknown parameters; In step 2, the RBF neural network estimator is used to estimate the unknown parameters g and f in the PMLSM hyperlocal model; The input of the RBF neural network estimator is: In the formula, v mref Give speed to PMLSM; v m With v mref difference; The output of the RBF neural network estimator is: IN f =[in f1 In f2 In f3 In f4 In f5 ] T ,IN g =[in g1 In g2 In g3 In g4 In g5 ] T H f =[h f1 h f2 h f3 h f4 h f5 ] T ,H g =[h g1 h g2 h g3 h g4 h g5 ] T In the formula, are the estimated values ​​of the PMLSM hyperlocal model parameters f and g respectively; w fj 、w gj are the weights of the jth hidden layer node of RBF with respect to f and g respectively; h fj With h gj are the outputs of the jth hidden layer node of the RBF neural network about f and g respectively; c fj With c gj are the radial basis function center values ​​of the jth hidden layer node of the RBF neural network with respect to f and g respectively; b fj With b gj are the radial basis function widths of the jth hidden layer nodes of the RBF neural network with respect to f and g respectively; H f With H g are the hidden layer matrices of f and g respectively; W f With W g are the weight matrices about f and g respectively; Step 3: Based on the RBF neural network estimator in step 2, an online adaptive law for the weight matrix is ​​designed, and an online iteration method for the central value of the radial basis function is proposed; Step 4: Based on the RBF neural network estimator in step 3, design the outer loop AST speed control law; Step 5: Use PI-based vector control to design the inner loop dq axis current control law.

2. According to claim 1, a PMLSM drive system speed control strategy based on RBF adaptive super-twisted sliding mode is characterized in that: The adaptive law of the RBF weight matrix in step 3 is: Where l(t) is the super-twisted sliding mode gain.

3. According to claim 1, a PMLSM drive system speed control strategy based on RBF adaptive super-twisted sliding mode is characterized in that: The iterative method for the (k+1)th sampling time of the radial basis function center value in step 3 is: Where k1 and k2 are the RBF radial basis function center value learning rates with respect to f and g, respectively, and both are positive real numbers.

4. According to claim 1, a PMLSM drive system speed control strategy based on RBF adaptive super-twisted sliding mode is characterized in that: In step 4, the sliding surface s is selected as: Therefore, the outer loop AST speed control law based on RBF in step 4 is: The adaptive law of l(t) in the outer loop AST speed control law in step 4 is: In the formula, k3 and is a positive real number, and the initial value l(0) of l(t) is set to a positive real number.

5. The speed control strategy of a PMLSM drive system based on RBF adaptive super-twisted sliding mode according to claim 1 is characterized in that: In step 5, the inner loop dq axis PI current control law is: u dref =k pd (i dref -i d )+k id ∫(i dref -i d )dt u qref =k pq (i qref -i q )+k iq ∫(i qref -i q )dt In the formula, i dref 、i qref are the dq axis reference currents respectively, the former is taken as 0, and the latter is the output of the speed outer loop controller; pd , k id are the proportional gain and integral gain of the d-axis, both of which are positive real numbers; k pq , k iq They are the proportional gain and integral gain of the q-axis respectively, both of which are positive real numbers.

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