Segmented permanent magnet synchronous linear motor control method based on discretization model

Abstract

The invention provides a segmented permanent magnet synchronous linear motor control method based on a discretization model. The method comprises the following steps: constructing a mathematical model of electrical and mechanical states based on a d-q coordinate system; discretizing the mathematical model to obtain a prediction model; performing optimal prediction on the prediction model through a cost function to obtain an optimal control sequence; based on the optimal control sequence, dynamically adjusting the prediction model through a rolling optimization strategy to obtain an adjustment model; performing dynamic separation on the adjustment model through an improved ADRC algorithm to obtain an active-disturbance-rejection control model; and performing active-disturbance-rejection control on the winding segmented permanent magnet synchronous linear motor through the active-disturbance-rejection control model. According to the method, model predictive control and improved active disturbance rejection control are fused, and strong thrust fluctuation suppression and multi-source disturbance accurate compensation are realized through a layered collaborative architecture.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous linear motor control, and in particular to a segmented permanent magnet synchronous linear motor control method based on a discrete model. Background Art

[0002] As industrial demand for linear drive systems grows, segmented-winding permanent magnet synchronous linear motors (PMSLMs) have become key power devices in fields such as electromagnetic catapults and precision manufacturing, thanks to their high thrust density and modularity. However, their segmented topology results in partially coupled and uncoupled states between the rotor and stator, which can easily lead to nonlinear changes in electromagnetic parameters, strong thrust fluctuations, and multi-source disturbance coupling. Existing control strategies have significant limitations, such as: PID control has poor robustness and is prone to saturation and instability when parameters change; sliding mode control relies on simplified models and is prone to exacerbated vibration under strong WS-PMLSM coupling; traditional ADRC parameter tuning is complex and observation accuracy is insufficient under multiple disturbances; model predictive control (MPC) has a heavy computational burden and is highly dependent on accurate models, resulting in a sharp drop in performance when parameters are mismatched. Therefore, it is necessary to design a segmented permanent magnet synchronous linear motor control method based on a discretized model. Summary of the Invention

[0003] The purpose of the present invention is to provide a segmented permanent magnet synchronous linear motor control method based on a discretized model, so as to accurately compensate for multi-source disturbances while suppressing strong thrust fluctuations by fusing model predictive control and improved active disturbance rejection control.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A segmented permanent magnet synchronous linear motor control method based on a discretization model comprises the following steps:

[0006] Construct mathematical models of electrical and mechanical states based on the dq coordinate system;

[0007] Discretize the mathematical model to obtain the prediction model;

[0008] The cost function is used to make the best prediction of the prediction model and obtain the optimal control sequence;

[0009] Based on the optimal control sequence, the prediction model is dynamically adjusted through the rolling optimization strategy to obtain the adjusted model;

[0010] The improved ADRC algorithm is used to dynamically separate the adjustment model to obtain the active disturbance rejection control model;

[0011] Active disturbance rejection control is performed on the segmented winding permanent magnet linear synchronous motor through the active disturbance rejection control model.

[0012] Optionally, the mathematical model includes: a voltage model, an electromagnetic thrust model, and a dynamic model; the expression of the voltage model is: Among them, u d and u q are the voltage components of the d-axis and q-axis respectively, i d and i q are the current components of the d-axis and q-axis respectively, L d and L q are the inductance components of the d-axis and q-axis respectively, ψ f (x) is the permanent magnet flux, ω e is the electrical angular velocity, R is the stator resistance;

[0013] The expression of the electromagnetic thrust model is: Among them, p n is the number of magnetic pole pairs, τ is the pole pitch;

[0014] The expression of the kinetic model is: Among them, F l is the load thrust, m is the secondary mass, and B is the friction coefficient.

[0015] Optionally, the mathematical model is discretized to obtain a prediction model, including:

[0016] Discretize the mathematical model into a current prediction model;

[0017] The incremental model is introduced into the current prediction model for fusion to obtain the augmented model;

[0018] The augmented model is converted into a prediction model by presetting the prediction step size and control step size.

[0019] Optionally, the prediction model is optimally predicted using a cost function to obtain an optimal control sequence, including:

[0020] The cost function is constructed based on the diagonal matrix of the prediction model; the expression of the cost function is: Where Q and R are both diagonal matrices, Y ref is the given value of current, U I is the optimal control sequence, and Y1 is the output of the prediction model;

[0021] The prediction model is optimized and solved through the cost function to obtain the optimal control sequence.

[0022] Optionally, based on the optimal control sequence, the prediction model is dynamically adjusted through a rolling optimization strategy to obtain an adjusted model, including:

[0023] The first cycle control quantity in the optimal control sequence is extracted through the rolling optimization strategy;

[0024] The optimal input control quantity is obtained by calculating the control quantity of the first cycle;

[0025] The prediction model is dynamically adjusted according to the optimal input control quantity to obtain an adjusted model.

[0026] Optionally, the adjustment model is dynamically separated by an improved ADRC algorithm to obtain an active disturbance rejection control model, including:

[0027] Converting the adjustment model into a current-voltage conversion model;

[0028] Determine the controlled object based on the mathematical model;

[0029] Based on the traditional extended state observer, the known dynamics and unknown disturbances of the traditional extended state observer are separated through the controlled object to obtain the model-compensated extended state observer;

[0030] Based on the model-compensated extended state observer, the estimation error of the adjustment model is compensated by the pole assignment method, and the active disturbance rejection control model is obtained.

[0031] Optionally, the model-compensated extended state observer has a built-in transfer function; the expression of the transfer function is: Where z3 is the estimated value of the model-compensated extended state observer, f0 is the total disturbance, is the parameter estimate of the controlled object, l1 and l3 are the parameter matrix components of the model compensation extended state observer, and s is the complex frequency domain label of the transfer function.

[0032] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: The present invention provides a segmented permanent magnet synchronous linear motor control method based on a discretized model, the method comprising: constructing a mathematical model of electrical and mechanical states based on a dq coordinate system; discretizing the mathematical model to obtain a prediction model; performing optimal prediction on the prediction model through a cost function to obtain an optimal control sequence; based on the optimal control sequence, dynamically adjusting the prediction model through a rolling optimization strategy to obtain an adjustment model; dynamically separating the adjustment model through an improved ADRC algorithm to obtain an auto-disturbance rejection control model; and performing auto-disturbance rejection control on the winding segmented permanent magnet synchronous linear motor through the auto-disturbance rejection control model. This method combines model predictive control with improved auto-disturbance rejection control, and achieves strong thrust fluctuation suppression and precise compensation for multi-source disturbances through a hierarchical collaborative architecture. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0034] Figure 1 This is a flow chart of the improved active disturbance rejection control method of the segmented winding permanent magnet synchronous linear motor of the present invention;

[0035] Figure 2 2 is a control block diagram of the improved ADRC algorithm according to an embodiment of the present invention;

[0036] Figure 3 This is a curve diagram of the actual value response of the simulation experiment current of an embodiment of the present invention;

[0037] Figure 4 This is a current setting value response curve diagram of a simulation experiment according to an embodiment of the present invention;

[0038] Figure 5 This is a curve diagram of the speed response of the mover in the simulation experiment of an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0040] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] like Figure 1 As shown, the present invention provides a segmented permanent magnet synchronous linear motor control method based on a discretization model, comprising the following steps:

[0042] Step 100: Constructing a mathematical model of electrical and mechanical states based on the dq coordinate system;

[0043] Step 200: Discretize the mathematical model to obtain a prediction model;

[0044] Step 300: Optimize the prediction model through the cost function to obtain the optimal control sequence;

[0045] Step 400: Based on the optimal control sequence, dynamically adjust the prediction model through a rolling optimization strategy to obtain an adjusted model;

[0046] Step 500: Dynamically separate the adjustment model using the improved ADRC algorithm to obtain an active disturbance rejection control model;

[0047] Step 600: Performing active disturbance rejection control on the segmented winding permanent magnet linear synchronous motor using an active disturbance rejection control model.

[0048] Specifically, the mathematical model includes a voltage model, an electromagnetic thrust model, and a dynamic model. The WS-PMLSM mathematical model in this embodiment uses a surface-mounted permanent magnet. Ideally, without considering parameter mutations, when the secondary and primary are fully coupled, the motor's electromagnetic parameters are constants. However, when the secondary and primary are partially coupled, some key electromagnetic parameters are time-varying. Assuming that the magnetic field generated by the permanent magnet is sinusoidal, and ignoring the end effects of the linear motor, flux saturation, motor losses, and the effects of temperature on the motor, the stator voltage equation of the WS-PMLSM in the dq coordinate system is:

[0049]

[0050] Among them, u d and u q are the voltage components of the d-axis and q-axis respectively, i d and i q are the current components of the d-axis and q-axis respectively, L d and L q are the inductance components of the d-axis and q-axis respectively, ψ f (x) is the permanent magnet flux, ω e is the electrical angular velocity, R is the stator resistance. The horizontal velocity v is used to describe the linear motion state, which is expressed as:

[0051]

[0052] Where τ is the pole pitch. For surface mounted permanent magnets, L d (x) = L q (x) = L s (x), the WS-PMLSM stator voltage equation is rewritten as:

[0053]

[0054] L d (x), L q (x), L s (x) are the d-axis, q-axis, and total stator inductance components corresponding to the stator position x, and the expression of the electromagnetic thrust equation is derived from this:

[0055]

[0056] Among them, p n is the number of magnetic pole pairs, F e (n-1) and F e (n) is the electromagnetic thrust generated by the primary of the n-1th and nth segments respectively. The expression of the dynamic equation is:

[0057]

[0058] Among them, F l is the load thrust, m is the secondary mass, and B is the friction coefficient.

[0059] Specifically, the steps of discretizing the mathematical model to obtain the prediction model include:

[0060] The current equation of the mathematical model in the dq coordinate system is discretized to obtain the current prediction model of WS-PMLSM, which is expressed as follows:

[0061]

[0062] Among them, i d (k) and i q (k) is the d-axis and q-axis components of the primary current at KT, u d (k) and u q (k) is the d-axis and q-axis components of the primary voltage at KT, i d (k+1) and i q (k+1) is the predicted value of the d-axis and q-axis primary current at (K+1)T. Then rewrite it into the state space equation form:

[0063]

[0064] A, B, and C are the corresponding transfer matrices of the state-space expressions. Then the state-space equations are combined and expressed as:

[0065]

[0066] Among them A s =T s A c +I2,B s =T s B c ,C s =C c In order to eliminate the influence of key electromagnetic parameters such as permanent magnet flux linkage and stator relative position change on the system, an incremental model is introduced:

[0067]

[0068] Among them, x is the state quantity, u is the input, and y is the output.

[0069] Since the electromagnetic time constant of the motor is much smaller than the mechanical time constant, and the digital system control cycle T s Very small, ω at the kth moment and the k+1th moment e They can be approximately considered equal, that is, Δε(k+1)≈0, so the incremental model can be substituted into the merged state space equation to obtain the expression:

[0070]

[0071] By introducing a new set of state variables: And the new input variable: U(k) = Δu(k), further get the augmented model, the expression is: in C=[0 2×2 I2]. This model can select a better vector for model predictive control. At the same time, due to the weight factor between asynchronous, the prediction step size N can be preset. p and control step size N c The augmented model is converted into a prediction model. The conversion process is expressed as:

[0072]

[0073] The expression of the prediction model is: Y1=ΩX(k)+ΓU1, where

[0074]

[0075] It should be noted that compared with the traditional static modeling method, the introduction of incremental modeling eliminates the nonlinear effects caused by the following of electromagnetic parameters such as permanent magnet flux and the change of stator relative position, significantly improving the controller's adaptability to nonlinear changes in the system. Especially in the WS-PMLSM structure where the primary and secondary coupling and decoupling frequently change, the current prediction accuracy and dynamic response stability are effectively improved.

[0076] Specifically, the cost function is used to make the optimal prediction of the prediction model and obtain the optimal control sequence. The specific implementation process is as follows: construct the cost function according to the diagonal matrix of the prediction model. The expression of the cost function is:

[0077]

[0078] Where Q and R are both diagonal matrices, Y ref is the given value of current, U Iis the optimal control sequence, Y1 is the output of the prediction model, Q and R are used as weight factors to evaluate the optimal expectation of the cost function, Q is used to improve the tracking accuracy of the system current, and R is used to prevent the control signal from jumping. Then the prediction model is optimized through the cost function to obtain the optimal control sequence U I , the solution process is: U I =(Γ T QΓ+R) -1 Γ T Q(Y ref -ΩX(k)).

[0079] It should be noted that by introducing the prediction step size N p and control step size N c , and constructs a cost function that combines output error and control variable changes to optimize the control input sequence. The introduction of a multi-step prediction mechanism better balances current control accuracy and control input smoothness, enabling proactive regulation of the motor's acceleration or deceleration phases, improving the system's predictive response and its ability to suppress sudden disturbances.

[0080] Specifically, based on the optimal control sequence, the prediction model is dynamically adjusted through the rolling optimization strategy. The specific implementation process of the adjustment model is as follows: Calculate the optimal control sequence U I After that, according to the rolling optimization strategy, only the control amount of the first cycle is applied to the system, and the control amount of the first cycle is extracted, and the expression is: Δu opt (k)=[I 0 … 0]U I , and then calculate the optimal input control quantity u of the system opt (k)=u opt (k-1)+Δu opt (k), and dynamically adjust the prediction model according to the optimal input control quantity to obtain the adjustment model.

[0081] It should be noted that, in order to obtain the best current control effect, this embodiment selects the difference between the expected current and the predicted current to construct the cost function. d and i q They are the same type of physical quantities obtained through coordinate transformation, and their relative importance is the same, so the design of weights is omitted.

[0082] Specifically, if Figure 2As shown in the figure, the dynamic separation of the adjustment model through the improved ADRC algorithm to obtain the specific implementation process of the active disturbance rejection control model includes: improving the extended state observer in ADRC to obtain the model-compensated extended state observer (MESO). By introducing the known model information of the controlled object on the basis of the traditional extended state observer (ESO), the known model dynamics are separated from the unknown disturbance to improve the observer's estimation accuracy and dynamic response speed. MESO combines model information to more accurately distinguish between the system's internal dynamics and external disturbances, reducing disturbance estimation errors and improving the system's control performance. NLSEF is the nonlinear state error feedback controller in ADRC, LinearHall is the linear Hall position sensor, and PMLSM is the permanent magnet synchronous linear motor.

[0083] More specifically, the current-voltage conversion equation of WS-PMLSM is expressed as: q =K u u. According to the electromagnetic thrust equation in the WS-PMLSM mathematical model, the controlled object of the speed loop is obtained as follows:

[0084]

[0085] in represents the estimated value of parameter a1. In addition, Represents the total disturbance, including modeling error and uncertain disturbance to the WS-PMSLM servo system. The traditional ESO is improved to MESO and the controlled object model dynamics are introduced to separate the known system dynamics from the unknown disturbances, thus improving the observation accuracy. In this embodiment, considering the disturbance to the controlled object, the state variable x1=y is selected. And the extended state x3 = f0, assuming that the total disturbance f0 is derivable and bounded, the extended state equation can be obtained:

[0086]

[0087] The expression of MESO is: where Z = [z1z2z3] T Represents the state matrix The estimated value matrix, L = [l1l2 l3] T The MESO parameter matrix L is represented by the parameter values of the matrix L, which determines the estimation speed and accuracy of the MESO. The pole assignment method is then used to solve the problem to ensure accurate and fast estimation of the MESO. The transfer function from input u and y to output z3 in the MESO is expressed as:

[0088]

[0089] After solving, we get the transfer function of the estimated value z3 to the total interference f0:

[0090]

[0091] Where z3 is the estimated value of the model-compensated extended state observer, f0 is the total disturbance, is the parameter estimate of the controlled object, l1 and l3 are the parameter matrix components of the model compensation extended state observer, and s is the complex frequency domain label of the transfer function.

[0092] It should be noted that the model expression of the nonlinear state error feedback controller (NLSEF) in MESO is:

[0093]

[0094] in is the final output reference control signal, i qd is the output of the nonlinear error feedback control link, and k is the error gain coefficient. The model expression of the tracking differentiator (TD) in MESO is:

[0095]

[0096] where ω * The improved MESO effectively overcomes the estimation error problem of the traditional ESO under strong nonlinear and strongly coupled disturbances. It partially compensates for the hysteresis defect of the ESO itself by using the known system model. It can still achieve accurate disturbance observation under severe dynamic changes such as instantaneous acceleration of the actuator or sudden load increase, thus enhancing the robustness of the system.

[0097] This example uses MATLAB and Simulink software to simulate the WS-PMLSM collaborative control architecture. The parameter settings of WS-PMLSM are shown in Table 1:

[0098] Table 1 Simulation parameter setting table

[0099] symbol Parameter Type value <![CDATA[P n ]]> Pole 5 M Mover mass 5kg B Viscous friction coefficient 0.3 τ Polar distance 20mm <![CDATA[L s ]]> Synchronous Inductor 4.68mH <![CDATA[Ψ f ]]> Permanent magnet flux 0.02Wb v Initial speed of mover 2m / s

[0100] After completing the motor parameter setting, the mover enters the stator at an initial speed of 2m / s in the simulation; at 0.1s, the set speed is adjusted to 3m / s to simulate the acceleration process of the mover; at 0.2s, the load is introduced to simulate the load disturbance on the stator; at 0.3s, the set speed is adjusted back to 2m / s to simulate the deceleration process of the mover. The response curve of the simulation result is shown as follows: Figure 3 and Figure 4As shown in the figure, it can be seen that the cooperative control strategy of this embodiment shows excellent current tracking performance under the working conditions of rotor acceleration, load disturbance and deceleration. There is no obvious current fluctuation when facing external disturbances, and it can achieve high-precision tracking of the given current command. The rotor speed response curve is shown in Figure 5 shown.

[0101] The beneficial effects of the present invention are as follows:

[0102] 1) The special topology of the WS-PMLSM coupled with the stator and rotor effectively suppresses thrust fluctuations caused by nonlinear changes in electromagnetic parameters, significantly improving anti-interference capabilities.

[0103] 2) The system response time is significantly shortened by combining multi-step prediction with MESO’s rapid disturbance observation;

[0104] 3) The incremental model eliminates the drift influence of position-related parameters and enhances the robustness of the model.

[0105] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0106] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A segmented permanent magnet synchronous linear motor control method based on a discretization model, characterized in that: The steps include: Construct mathematical models of electrical and mechanical states based on the dq coordinate system; Discretizing the mathematical model to obtain a prediction model; Performing optimal prediction on the prediction model through a cost function to obtain an optimal control sequence; Based on the optimal control sequence, dynamically adjusting the prediction model through a rolling optimization strategy to obtain an adjusted model; Dynamically separating the adjustment model through an improved ADRC algorithm to obtain an active disturbance rejection control model; Active disturbance rejection control is performed on a segmented winding permanent magnet linear synchronous motor using the active disturbance rejection control model.

2. The control method of a segmented permanent magnet synchronous linear motor based on a discretization model according to claim 1, characterized in that: The mathematical model includes: a voltage model, an electromagnetic thrust model and a dynamic model; the expression of the voltage model is: Among them, u d and u q are the voltage components of the d-axis and q-axis respectively, i d and i q are the current components of the d-axis and q-axis respectively, L d and L q are the inductance components of the d-axis and q-axis respectively, ψ f (x) is the permanent magnet flux, ω e is the electrical angular velocity, R is the stator resistance; The expression of the electromagnetic thrust model is: Among them, p n is the number of magnetic pole pairs, τ is the pole pitch; The expression of the kinetic model is: Among them, F l is the load thrust, m is the secondary mass, and B is the friction coefficient.

3. The control method of a segmented permanent magnet synchronous linear motor based on a discretization model according to claim 1, characterized in that: Discretizing the mathematical model to obtain a prediction model includes: discretizing the mathematical model into a current prediction model; Introducing an incremental model into the current prediction model for fusion to obtain an augmented model; The augmented model is converted into the prediction model through a preset prediction step size and a control step size.

4. The control method of a segmented permanent magnet linear synchronous motor based on a discretization model according to claim 1, characterized in that: The optimal prediction of the prediction model is performed using a cost function to obtain an optimal control sequence, including: The cost function is constructed according to the diagonal matrix of the prediction model; the expression of the cost function is: J1=(Y ref -Y I ) T Q(Y ref -Y I )+U I T RU I ; where Q and R are both diagonal matrices, Y ref is the given value of current, U I is the optimal control sequence, and Y1 is the output of the prediction model; The prediction model is optimized and solved using the cost function to obtain the optimal control sequence.

5. The control method of a segmented permanent magnet synchronous linear motor based on a discretization model according to claim 1, characterized in that: Based on the optimal control sequence, the prediction model is dynamically adjusted through a rolling optimization strategy to obtain an adjusted model, including: Extracting the first cycle control quantity in the optimal control sequence by the rolling optimization strategy; Obtaining the optimal input control amount by calculating the first period control amount; The prediction model is dynamically adjusted according to the optimal input control amount to obtain the adjustment model.

6. The control method of a segmented permanent magnet linear synchronous motor based on a discretization model according to claim 1, characterized in that: The adjustment model is dynamically separated by an improved ADRC algorithm to obtain an active disturbance rejection control model, including: converting the adjustment model into a current-voltage conversion model; determining a controlled object according to the mathematical model; Based on a traditional extended state observer, the known dynamics and unknown disturbances of the traditional extended state observer are separated through the controlled object to obtain a model-compensated extended state observer; Based on the model-compensated extended state observer, the adjustment model is estimated error compensated by a pole assignment method to obtain the active disturbance rejection control model.

7. The control method of a segmented permanent magnet linear synchronous motor based on a discretization model according to claim 6, characterized in that: The model-compensated extended state observer has a built-in transfer function; the expression of the transfer function is: Where z3 is the estimated value of the model-compensated extended state observer, f0 is the total disturbance, is the parameter estimate of the controlled object, l1 and l3 are the parameter matrix components of the model compensation extended state observer, and s is the complex frequency domain label of the transfer function.

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