Independent coil driving type current control method for moving magnet type permanent magnet synchronous linear motor

Abstract

The independent coil driving type current control method of a moving magnet type permanent magnet synchronous linear motor belongs to the technical field of motor driving control, and aims to solve the problems of current tracking precision reduction, multi-channel dynamic consistency deterioration and parameter setting complexity caused by periodic perturbation of inductance parameters and back electromotive force disturbance in the traditional PI controller in the independent coil structure.The independent coil driving type current control method of a moving magnet type permanent magnet synchronous linear motor comprises the following steps: a single coil controlled object state space model is established, inductance variation, back electromotive force and resistance voltage drop are unified and merged into lumped disturbance, and a first-order extended state space expression is constructed; a first-order linear extended state observer is constructed to estimate the lumped disturbance in real time; a proportional-extended state observer control law is constructed to feed forward compensate the disturbance estimation value, and a proportional controller is used for current error feedback; the observer gain and the proportional controller gain are determined according to the inverter switching frequency to complete parameter setting.

Description

Technical Field

[0001] This invention belongs to the field of motor drive control technology, specifically relating to an independent coil drive current control method for a moving magnet permanent magnet synchronous linear motor. Background Technology

[0002] Permanent magnet synchronous linear motors (PMLSMs) with moving magnets are characterized by small thrust fluctuations, high positioning accuracy, and good dynamic performance. They are considered core motion components in intelligent flexible transmission systems and have significant application value in CNC servo systems and flexible conveying applications. The accompanying independent coil drive control system breaks down the traditional "three-phase group" power supply mode into independent single-coil drive, minimizing power supply granularity. The drive system can flexibly switch the switching state of each coil and configure the coil current according to the production line conditions, endowing the flexible transmission system with the ability to adapt to changing operating scenarios from the hardware level.

[0003] However, the independent coil drive architecture also brings new control challenges: traditional dq0 decoupled field-oriented control (FOC) uses three-phase coupled windings as the controlled object, which is no longer suitable for single-coil independent drive mode, requiring a separate current controller for each coil. During motor operation, the mover continuously reciprocates, and the relative position of the coil and mover constantly changes. Due to end effects, the coil inductance changes periodically with the mover displacement. Traditional PI current controller parameters are tuned based on a fixed inductance; fluctuations in the actual inductance value cause zero-pole drift of the controller, system bandwidth shift, and poor consistency of dynamic response among multiple channels. Simultaneously, under heavy load and high-speed conditions, the motor generates high-amplitude AC back EMF disturbances. The PI controller has limited disturbance rejection capability, and the current tracking error is significantly amplified under high-frequency and high-load conditions, directly degrading the motor's thrust characteristics and positioning performance.

[0004] Furthermore, the inherent discrete differences in coil parameters exist in multi-coil independent drive systems. Calibrating the PI parameters for each channel individually would significantly increase the workload of production line debugging and calibration. Most existing disturbance observation and control schemes rely on accurate controlled object models, and inductor drift directly reduces disturbance observation accuracy. While adaptive control can handle parameter perturbations, its computational complexity is high, requiring significant hardware computing power, making it difficult to implement in embedded platforms like FPGAs designed for multi-channel parallel control. Therefore, there is an urgent need for a current control scheme with strong parameter robustness, excellent disturbance rejection capability, low computational overhead, and simple tuning, suitable for the engineering application requirements of independent coil moving magnet permanent magnet synchronous linear motors. Summary of the Invention

[0005] To address the problems of decreased current tracking accuracy, poor dynamic consistency across multiple channels, and cumbersome parameter tuning in traditional PI controllers with independent coil structures due to periodic perturbations of inductor parameters and back EMF disturbances, this invention provides an independent coil-driven current control method for a moving-magnet permanent magnet synchronous linear motor.

[0006] The independent coil drive current control method for a moving magnet permanent magnet synchronous linear motor according to the present invention includes the following steps:

[0007] S1. Establish a state-space model of a single-coil controlled object, and unify the periodic change of coil inductance with position, back electromotive force disturbance and resistance voltage drop into a lumped disturbance, and construct a first-order extended state-space expression that includes current state and lumped disturbance state.

[0008] S2. Construct a first-order linear extended state observer, using the actual sampled current of the coil and the coil control command voltage as the observer input, and observe the estimated value of the coil current and the estimated value of the lumped disturbance.

[0009] S3. Construct a proportional-expanded state observer control law, use a proportional controller for current error feedback, and feed forward the lumped disturbance estimate to the control input to obtain the control command voltage of the coil.

[0010] S4. Determine the observer gain and proportional controller gain based on the inverter switching frequency and the expected bandwidth of the current loop, complete the parameter tuning, and realize current tracking and disturbance suppression of each independent coil.

[0011] Preferably, in step S1, the specific method for establishing the state-space model of the single-coil controlled object includes:

[0012] The single-coil voltage balance equation is used as the basis for the controlled object model. The single-coil voltage balance equation is as follows:

[0013]

[0014] In the formula, The voltage across the coil, The actual sampling current of the coil. For coil resistance, The coil inductance varies with the position of the mover. It is the back electromotive force. Harmonic voltage generated by the modulation of switching devices;

[0015] Define state variables The actual sampling current of the coil , ; For lumped disturbances; The system output corresponds to the actual sampled current of the coil; a state-space model of the single-coil controlled object is established, and the first-order extended state-space expression of the single-coil controlled object state-space model is obtained:

[0016]

[0017] In the formula, , They are respectively , The first derivative;

[0018] The lumped disturbance The expression is:

[0019]

[0020] In the formula, This is the nominal value of the coil inductance. Let be the rate of change of the lumped disturbance.

[0021] Preferably, in step S2, the expression for the first-order linear extended state observer is:

[0022]

[0023] In the formula, For current observation error, The coil control command voltage, , The estimated value output by the observer, where This is an estimated value for the coil current. This is the estimated value of the lumped disturbance. , They are respectively , The first derivative, , This is the observer gain.

[0024] Preferably, in step S3, the proportional-expanded state observer P-ESO control law is:

[0025]

[0026] In the formula, For the proportional controller gain, For coil current reference command, The actual sampling current of the coil. This is the lumped disturbance feedforward compensation term.

[0027] Preferably, in step S4, the observer gain , Set according to the following formula:

[0028]

[0029] In the formula, For the observer's observation bandwidth, Let be the damping coefficient, and satisfy . ;

[0030] The observation bandwidth Satisfying the theoretical constraint interval:

[0031]

[0032] In the formula, For the current loop bandwidth, This refers to the inverter's switching angular frequency.

[0033] Preferably, in step S4, the gain of the proportional controller... Set according to the following formula:

[0034] .

[0035] Preferably, optimal parameters are selected within the theoretical constraint range to make the observation bandwidth... With the bandwidth of the current loop satisfy And the bandwidth of the current loop satisfy ;

[0036] The gain of the proportional controller and the gain of the observer are then adjusted using the following formula:

[0037] .

[0038] The beneficial effects of this invention are:

[0039] To verify the effectiveness of the proportional-extended state observer (P-ESO) control method proposed in this invention, a comparative experiment was conducted under motor load conditions. Given a current amplitude of 4A, tests were performed at two frequency commands: 50Hz and 300Hz, with a switching frequency of 20kHz. Experimental results show that under the 50Hz low-frequency command, the P-ESO controller's output current amplitude is 3.974A, and the total harmonic distortion (THD) is 12.07%, while the traditional PI controller's output amplitude is 3.788A, and the THD is 12.67%. The performance of the two controllers is essentially equivalent, with the P-ESO being slightly superior. Under the 300Hz high-frequency command, the P-ESO controller's output current amplitude is 3.281A, and the THD is 14.45%, while the traditional PI controller's output amplitude decreases to 2.298A, and the THD deteriorates to 20.85%. The experimental data above show that the present invention can maintain current tracking accuracy comparable to that of a PI controller in the low-frequency range, and is significantly better than a PI controller in the high-frequency range, effectively suppressing the impact of back EMF disturbance on current tracking performance.

[0040] Compared with traditional PI control and existing disturbance suppression schemes, the present invention has the following advantages:

[0041] (1) It has strong anti-disturbance capability and overcomes the inherent limitations of PI control.

[0042] This invention decomposes the P-ESO controller into a proportional feedback path and a disturbance feedforward compensation path. The two paths are decoupled from each other and are responsible for current tracking and disturbance suppression, respectively. The proportional path ensures the speed of command tracking, while the disturbance feedforward path estimates and compensates for lumped disturbances in real time, avoiding the performance trade-off caused by a single integrator in traditional PI control that simultaneously undertakes steady-state error elimination and disturbance suppression.

[0043] (2) It is robust to inductance parameter perturbations and does not depend on the resistance model.

[0044] This invention integrates inductance variation, resistance temperature drift, and back electromotive force into a unified lumped disturbance for estimation and compensation, eliminating the need for online inductance parameter identification and precise resistance model establishment. Even with a significant deviation of ±50% between the nominal and actual inductance values, the controller maintains stable current tracking performance, making it suitable for engineering scenarios with large dispersion of multi-coil parameters.

[0045] (3) The parameter setting is simple and directly related to the switching frequency.

[0046] All control parameters (proportional gain, observer gain) of the controller proposed in this invention are only related to the inverter switching frequency and the nominal inductor value. In engineering applications, there is no need to rely on complex tuning tools or trial and error; the controller configuration can be completed simply by inputting the switching frequency, which greatly reduces the debugging workload of multi-channel systems.

[0047] (4) It has a small computational load and is suitable for multi-channel parallel embedded deployment.

[0048] The control law involves only a few multiplication and addition operations, without the need for matrix inversion, coordinate transformation or trigonometric function operations. It has extremely low hardware computing power requirements and can easily run in high sampling rate interrupt service routines of 20kHz and above. It is suitable for implementing multi-channel parallel real-time control on FPGA platforms and has good engineering practicality and portability. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the independent coil type permanent magnet synchronous linear motor drive control hardware scheme of the present invention;

[0050] Figure 2 This is a control block diagram of the current controller for the moving magnet permanent magnet synchronous linear motor with an independent coil structure according to the present invention.

[0051] Figure 3 This is a comparison graph of the actual output current and the reference current of the proportional-extended state observer control method of the present invention under a 50 Hz command, wherein... Figure 3 (a) is the reference current waveform. Figure 3 (b) is the actual output current waveform of the proportional-expanded state observer control method;

[0052] Figure 4 This is a comparison graph of the actual output current and the reference current under a 50 Hz command using the traditional proportional-integral control method. Figure 4 (a) is the reference current waveform. Figure 4 (b) is the actual output current waveform of the proportional-integral control method;

[0053] Figure 5 This is a comparison graph of the actual output current and the reference current of the proportional-extended state observer control method of the present invention under a 300 Hz command, wherein... Figure 5 (a) is the reference current waveform. Figure 5 (b) is the actual output current waveform of the proportional-expanded state observer control method;

[0054] Figure 6 This is a comparison graph of the actual output current and the reference current under a 300 Hz command using the traditional proportional-integral control method. Figure 6 (a) is the reference current waveform. Figure 6 (b) is the actual output current waveform of the proportional-integral control method. Detailed Implementation

[0055] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0056] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0057] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; and the term "one embodiment" means "at least one embodiment". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0058] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0059] The names of the messages or information exchanged between the multiple devices in the embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of these messages or information.

[0060] In related technologies, the independent coil structure of the moving magnet permanent magnet synchronous linear motor drive control scheme decomposes the traditional "three-phase group" power supply mode into a single coil independent drive, minimizing the power supply granularity. This allows the drive system to flexibly switch the switching state of each coil and configure the coil current according to the production line conditions, endowing the flexible transmission system with the ability to adapt to changing operating scenarios from the hardware level. However, the independent coil drive architecture also brings new technical challenges to current loop control.

[0061] From the perspective of control principles, traditional field-oriented control methods use three-phase coupled windings as the controlled object. They decompose the three-phase AC current into direct-axis and quadrature-axis currents through Clark and Park transformations, achieving static decoupling control of the current. However, in an independent coil structure, the currents in each coil are not orthogonally distributed in space, making the aforementioned coordinate transformation impossible. Therefore, a separate current controller must be configured for each coil.

[0062] From the perspective of the controlled object's parameter characteristics, there is no fixed coupling relationship between the coil and the mover in a moving-magnet permanent magnet synchronous linear motor. During motor operation, the mover continuously reciprocates along the track, and the relative position of the coil and the mover constantly changes. Due to end effect, the coil inductance changes periodically with the mover displacement, and the inductance value fluctuates around the nominal value. Traditional proportional-integral current controllers are based on fixed nominal inductance values ​​for proportional and integral gain tuning. When the actual inductance value deviates from the set value, the zero and pole positions of the controller drift, the system bandwidth shifts accordingly, and the consistency of dynamic response across channels deteriorates.

[0063] From the perspective of disturbance characteristics, under heavy load or high-speed operation, the magnetic field of the mover permanent magnet cutting the coil windings generates a high-amplitude AC back electromotive force (EMF). This back EMF has the same frequency as the coil current, and its amplitude is proportional to the motor's operating speed. Traditional proportional-integral (PI) controllers are essentially phase lag correction networks, and their gain for AC disturbances decreases as the frequency increases, resulting in limited suppression capabilities. When the back EMF frequency rises to several hundred hertz, the PPI controller struggles to maintain sufficient disturbance suppression gain, significantly amplifying the current tracking error and directly degrading the motor's thrust characteristics and positioning accuracy.

[0064] From an engineering implementation perspective, in multi-coil independent drive systems, the actual resistance and inductance values ​​of each coil exhibit inherent discrete differences due to manufacturing processes and assembly tolerances. If a proportional-integral (PI) control scheme is used, parameter calibration is required for each channel individually, significantly increasing the workload of production line debugging and calibration. Existing disturbance observation control schemes mostly rely on the accurate transfer function model of the controlled object; inductance parameter perturbations directly reduce disturbance observation accuracy, leading to compensation failure. While adaptive control can theoretically handle parameter perturbations, it requires online parameter identification, involves large algorithm computations, and demands high hardware computing power, making it difficult to implement in engineering on embedded platforms like field-programmable gate arrays (FPGAs) designed for multi-channel parallel control.

[0065] To address the aforementioned technical problems, this invention provides an independent coil-driven current control method for a moving-magnet permanent magnet synchronous linear motor. By unifying inductance changes, back EMF disturbances, and resistance voltage drops into a lumped disturbance, and utilizing a linear extended state observer to estimate and feed forward compensate for the lumped disturbance in real time, the controlled object is approximately equivalent to a nominal inductance model in the control model. Only a proportional controller is needed to achieve zero steady-state error current tracking, fundamentally overcoming the performance degradation problem of proportional-integral control under inductance perturbations and back EMF disturbances. Furthermore, the control parameters are directly related to the inverter switching frequency, simplifying tuning, reducing computational complexity, and making it suitable for multi-channel parallel deployment.

[0066] This invention provides an independent coil drive-type current control method for a moving-magnet permanent magnet synchronous linear motor. This method is used in hardware solutions for the drive control of independent coil permanent magnet synchronous linear motors, such as... Figure 1 As shown, each independent coil of the motor is equipped with an inverter unit and a single-channel current controller. The n independent coils correspond to n inverter units and n single-channel current controllers. All single-channel current controllers are integrated into the field programmable gate array (FPGA). The current reference commands for each coil are sent from the upper-level controller to the FPGA, and the closed-loop control of the current of the n coils is completed in parallel through the multi-channel current control module inside the FPGA.

[0067] The control method of the present invention includes the following steps:

[0068] S1. Establish a state-space model of a single-coil controlled object, and unify the periodic change of coil inductance with position, back electromotive force disturbance and resistance voltage drop into a lumped disturbance, and construct a first-order extended state-space expression that includes current state and lumped disturbance state.

[0069] Specifically, the moving-magnet permanent magnet synchronous linear motor with an independent coil structure adopts a single-coil independent drive architecture. The electrical characteristics of each coil can be described by a voltage balance equation. This equation reflects the physical constraints between the applied voltage across the coil and the coil current, resistance voltage drop, inductance voltage drop, and back electromotive force. The pulse width modulation harmonic voltage is an additional voltage component generated during the modulation process of the switching device. The coil inductance has nonlinear time-varying characteristics, changing periodically with the displacement of the mover, which belongs to the internal uncertainty of the system; the amplitude of the back electromotive force increases with the increase of the running speed, which belongs to the external disturbance; the resistance voltage drop is affected by temperature and drifts, which belongs to the parameter perturbation. All three factors affect the current tracking accuracy.

[0070] This step uses the single-coil voltage balance equation as the basis for the controlled object model, rewriting the original voltage balance equation into a first-order state-space form by defining state variables. During this process, all non-ideal factors, except for the nominal coil inductance, are uniformly grouped into a lumped disturbance variable. This lumped disturbance includes both internal system parameter perturbations and external voltage disturbances, which do not require separate modeling.

[0071] Through the above processing, the mathematical model of the controlled object is simplified from the original differential equation containing time-varying parameters to a first-order linear system plus an unknown disturbance term. The derivative of the current state consists of two parts: one is the input voltage divided by the nominal value of the coil inductance, and the other is the lumped disturbance. The advantage of this state-space expression is that it concentrates all uncertainties into a single state variable, requiring only estimation and compensation of this variable subsequently, without separately dealing with different physical factors such as inductance changes, back electromotive force, and resistance voltage drop.

[0072] This step ultimately generates a first-order extended state-space expression for a single-coil controlled object, which includes measurable current states and indirect lumped disturbance states, providing a mathematical model foundation for the next step of building an observer.

[0073] S2. Construct a first-order linear extended state observer (ESO), using the actual sampled current of the coil and the coil control command voltage as the observer input, to observe the estimated value of the coil current and the estimated value of the lumped disturbance.

[0074] Specifically, step S1 has established a first-order extended state-space expression containing the lumped disturbance state, where the lumped disturbance is a state variable that cannot be directly measured. To obtain the real-time value of the lumped disturbance, a state observer needs to be constructed to estimate it.

[0075] This step designs a first-order linear extended state observer, using the system output (actual sampled coil current) and control input (coil control command voltage) as the observer's input information. The observer operates through an error-driven mechanism: the error between the observer's output coil current estimate and the actual sampled current is used as a correction signal and fed back to the current estimation channel and the disturbance estimation channel, respectively.

[0076] In the observer, the expression for the current estimation channel consists of three parts: an error feedback term (derived from the observer gain) and an error feedback term. The weighted average, lumped disturbance estimate, and coil control command voltage divided by the nominal coil inductance are used. The expression for the disturbance estimation channel is the integral of the error feedback term (derived from the observer gain). (Weighted), this structure allows the perturbation estimate to asymptotically track the actual lumped perturbation.

[0077] Through real-time estimation by a linearly extended state observer, two state variables are observed simultaneously: one is the coil current estimate, used to monitor the observer's convergence state; the other is the lumped disturbance estimate, used for subsequent feedforward compensation. The advantage of this observer lies in its simple structure, involving only the configuration of two gain parameters, requiring no precise mathematical model of the controlled object, and being insensitive to parameter perturbations.

[0078] This step ultimately generates two estimates: a coil current estimate and a lumped disturbance estimate, where the lumped disturbance estimate will be used for feedforward compensation in step S3.

[0079] S3. Construct a proportional-extensional state observer P-ESO control law, use a proportional controller for current error feedback, and feed forward the lumped disturbance estimate to the control input to obtain the control command voltage of the coil.

[0080] Specifically, step S2 has already obtained the lumped disturbance estimate through the observer. This step uses this estimate to construct a control law, achieving decoupled control of current tracking and disturbance suppression.

[0081] The design concept of the P-ESO control law is to feed forward the lumped disturbance estimate to the input to offset the influence of the actual lumped disturbance on the system. When the lumped disturbance estimate approaches the actual lumped disturbance, the lumped disturbance term and the feedforward compensation term in the state-space expression cancel each other out. The controlled object is equivalent to a nominal inductance model in the control model. At this time, the controlled object is approximately a first-order integral element, and zero steady-state error tracking can be achieved with only a proportional controller.

[0082] The control law consists of two parts: the first is the proportional control voltage, generated by multiplying the proportional controller gain by the current error (the difference between the coil current reference command and the actual sampled coil current), which is responsible for current command tracking; the second is the feedforward compensation voltage, generated by multiplying the nominal coil inductance by the lumped disturbance estimate, which is responsible for disturbance suppression. These two parts are independent of each other; the proportional channel is responsible for response speed, and the feedforward channel is responsible for disturbance suppression, thus they are decoupled.

[0083] This step ultimately generates the coil control command voltage, which serves as the input command for the inverter. After pulse width modulation, it is applied to both ends of the coil to achieve closed-loop current control.

[0084] S4. Determine the observer gain and proportional controller gain based on the inverter switching frequency and the expected bandwidth of the current loop, complete the parameter tuning, and realize current tracking and disturbance suppression of each independent coil.

[0085] Specifically, the P-ESO control law in step S3 includes three parameters to be tuned: one proportional controller gain and two observer gains. This step provides the quantization tuning rules for these parameters.

[0086] The observer gain is tuned according to the standard form of a second-order system, with the observation bandwidth as the design parameter. The damping coefficient is typically set to 0.707, balancing the observer's response speed and overshoot. The selection of the observation bandwidth must meet three constraints: First, it must be at least three times greater than the frequency of the controlled object's disturbance to ensure effective estimation of major disturbances such as back EMF; second, it must be less than one-tenth of the inverter's switching angular frequency to meet the discrete system stability constraints; third, it must have sufficient amplitude attenuation at the switching frequency to suppress current harmonics introduced by the pulse width modulation switching process.

[0087] The proportional controller gain tuning must satisfy the stability condition of the closed-loop transfer function. Through derivation, the upper limit of the proportional controller gain is determined by both the inverter switching angular frequency and the nominal value of the coil inductance. When selecting optimal parameters, if the observation bandwidth is set to 3.5 times the current loop bandwidth, and the current loop bandwidth is taken as one-fortieth of the inverter switching angular frequency, then all control parameters can be expressed as explicit functions of the switching angular frequency and the nominal value of the coil inductance.

[0088] The core advantage of the above tuning rules is that all controller parameters are only related to the inverter switching frequency and the nominal value of the coil inductance, eliminating the need for trial and error based on experience or complex tuning tools. In engineering applications, batch parameter configuration of multi-channel controllers can be completed simply by inputting the switching frequency, significantly reducing the workload of debugging.

[0089] This step ultimately completes the tuning of all control parameters, enabling each independent coil current controller to simultaneously possess excellent command tracking and disturbance suppression capabilities.

[0090] Furthermore, in step S1, the specific method for establishing the state-space model of the single-coil controlled object includes:

[0091] The single-coil voltage balance equation is used as the basis for the controlled object model. The single-coil voltage balance equation is as follows:

[0092]

[0093] In the formula, The voltage across the coil, The actual sampling current of the coil. For coil resistance, The coil inductance varies with the position of the mover. It is the back electromotive force. Harmonic voltage generated by the modulation of switching devices;

[0094] Define state variables The actual sampling current of the coil , ; For lumped disturbances; The system output corresponds to the actual sampled current of the coil; a state-space model of the single-coil controlled object is established, and the first-order extended state-space expression of the single-coil controlled object state-space model is obtained:

[0095]

[0096] In the formula, , They are respectively , The first derivative;

[0097] The lumped disturbance The expression is:

[0098]

[0099] In the formula, This is the nominal value of the coil inductance. Let be the rate of change of the lumped disturbance.

[0100] Specifically, specifically, lumped disturbances The three terms on the right-hand side of the expression correspond to: the resistance voltage drop disturbance term, the back electromotive force disturbance term, and the input voltage disturbance term caused by the deviation between the actual inductance value and the nominal coil inductance value. The physical meanings of these three terms are clear, achieving a unified representation of all non-ideal factors. Through the above definition, the resistance parameter does not need to appear in the observer or control law, and the model mismatch caused by resistance temperature drift is automatically included in the lumped disturbance for compensation. Furthermore, this method only requires the nominal coil inductance value. It can participate in calculations without the need for online inductance identification or table lookup correction.

[0101] Further, in step S2, the expression for the first-order linear extended state observer is:

[0102]

[0103] In the formula, For current observation error, The coil control command voltage, , The estimated value output by the observer, where This is an estimated value for the coil current. This is the estimated value of the lumped disturbance. , They are respectively , The first derivative, , This is the observer gain.

[0104] Specifically, the core working principle of the observer is: current observation error Drive the update of the two estimated channels, Includes The term represents the current estimation error through the observer gain. Feedback correction Includes The term represents the perturbation estimation error through the observer gain. Feedback correction. When Approaching the actual sampling current of the coil hour, Approaching zero Approaching the actual lumped disturbance The observer converges.

[0105] Further, in step S3, the control law of the proportional-expanded state observer P-ESO is:

[0106]

[0107] In the formula, For the proportional controller gain, For coil current reference command, The actual sampling current of the coil. This is the lumped disturbance feedforward compensation term.

[0108] Specifically, in the P-ESO control law, the current error... Gain via proportional controller After being amplified, it is superimposed with the feedforward compensation term, and the feedforward compensation term... Real-time tracking of lumped disturbance changes and their inverse superposition into the coil control command voltage in advance. This allows disturbances to be canceled out before they affect the current, thus achieving advance compensation. Since the feedforward compensation term already includes the effects of resistor voltage drop, back electromotive force, and inductance deviation, the proportional controller only needs to adjust the residual error, reducing the tuning requirements for the proportional gain.

[0109] Further, in step S4, the observer gain , Set according to the following formula:

[0110]

[0111] In the formula, For the observer's observation bandwidth, Let be the damping coefficient, and satisfy . ;

[0112] The observation bandwidth Satisfying the theoretical constraint interval:

[0113]

[0114] In the formula, For the current loop bandwidth, This refers to the inverter's switching angular frequency.

[0115] Specifically, in order to effectively suppress lumped disturbances, It should be at least three times greater than the disturbance frequency of the controlled object. The back electromotive force generated during motor operation constitutes the main part of the lumped disturbance, and its frequency is the same as the coil current. Let the current loop bandwidth be... ,but The minimum should be three times that. This is to satisfy the stability constraints of discrete systems. It should satisfy 0 < <1. Furthermore, to satisfy the observer's requirement for suppressing current harmonics introduced during the switching process, the transfer function Gob(s) should have an amplitude gain of -40dB at the switching frequency, approximately converted to... .because In conclusion, Should satisfy the formula .

[0116] The observer's estimation characteristics for lumped disturbances can be further described by the transfer function. (Lumped disturbance) (Actual value) and the lumped disturbance estimate output by the observer The transfer function between them is:

[0117]

[0118] In the formula, Let be the observer's estimated transfer function for lumped disturbances. Estimated value of lumped disturbance Laplace transform, Actual value of lumped disturbance Laplace transform. Adjust the observer gain. , Substituting into the above equation, the observer transfer function is rewritten using the observation bandwidth. The standard form of a second-order low-pass filter:

[0119]

[0120] The transfer function shows that the observer's estimation of the lumped disturbance is equivalent to a standard second-order low-pass filter, the bandwidth of which is determined by... Determine the damping coefficient Determine the overshoot of the estimated response. When At this time, the observer balances response speed and convergence stability. Therefore, the observation bandwidth... The choice of bandwidth determines the speed at which the observer tracks lumped disturbances: the larger the bandwidth, the faster the estimated value tracks the actual disturbance, but the sensitivity to high-frequency noise also increases accordingly.

[0121] Further, in step S4, the gain of the proportional controller Set according to the following formula:

[0122] .

[0123] Specifically, the proportional controller gain The upper limit is determined by the inverter switching angular frequency. and nominal inductance value Together, we determine that this constraint ensures the poles of the closed-loop transfer function lie within the unit circle, guaranteeing system stability. The derivation of this constraint is based on the following: When the observer fully compensates for lumped disturbances, the controlled object is approximately equivalent to a nominal inductor model. At this point, the transfer function of the current closed-loop control loop is:

[0124]

[0125] In the formula, Let be the current closed-loop transfer function. For the Laplace operator, The actual sampling current of the coil Laplace transform, Reference command for coil current Laplace transform, This refers to the normalized proportional gain, i.e., the proportional controller gain. Divide by the nominal value of the coil inductance The resulting equivalent gain, For the inverter switching cycle, the denominator contains The term represents the combined delay coefficient of pulse width modulation update delay and inverter power device switching delay. The denominator of the closed-loop transfer function is a second-order polynomial. To ensure that the system response does not oscillate and has a good stability margin, the normalized proportional gain is... Should meet At this point, the bandwidth of the control loop can be expressed as Combining the above formulas, we can derive... .at the same time Ultimately, the gain of the proportional controller can be derived. The tuning constraints are .

[0126] Furthermore, within the theoretically constrained range, optimal parameters are selected to make the observation bandwidth... With the bandwidth of the current loop satisfy And the bandwidth of the current loop satisfy ;

[0127] The gain of the proportional controller and the gain of the observer are then adjusted using the following formula:

[0128] .

[0129] Specifically, in the above tuning formula, all parameters are based on the inverter switching angular frequency. As the independent variable, , The inverter switching frequency is used. The tuning process only requires inputting the inverter switching frequency and the nominal coil inductance value, eliminating the need for individual tuning for each channel and greatly simplifying the engineering deployment process for multi-coil systems. The lumped disturbance estimated by the observer includes at least inductance parameter perturbation disturbance, back EMF disturbance, and coil resistance voltage drop disturbance. The observer does not need to input coil resistance parameters; model mismatch caused by resistance temperature drift is automatically included in the lumped disturbance for compensation. This method allows for a ±50% deviation between the nominal coil inductance value and the actual coil inductance without requiring online inductance identification or table lookup correction.

[0130] Combination Figure 2 As shown, Figure 2 This is a control block diagram of the current controller for the moving magnet permanent magnet synchronous linear motor with an independent coil structure in this invention, constituting a P-ESO controller. The diagram shows the current control structure of a single coil channel, including a proportional controller channel, a linear expansion state observer channel, a feedforward compensation channel, and a pulse width modulation and inverter link. The following provides a complete description of each channel and link.

[0131] like Figure 2 As shown, the coil current reference command Laplace transform With the actual sampling current of the coil Laplace transform The Laplace transform of the current error signal is obtained by subtracting the first comparison node. The current error signal is sent to the proportional controller, and the gain of the proportional controller is... The proportional controller output is The output is the Laplace transform of the proportional control voltage, which is the control command voltage. Laplace transform One of the components.

[0132] Actual sampling current of the coil Laplace transform Simultaneously, the Laplace transform serves as an input parameter for the linearly extended state observer. , and the observer current estimate Laplace transform The current observation error is obtained by performing a subtraction operation within the observer. Laplace transform . Gain via observer respectively , Feedback is sent to the observer's internal circuitry. Simultaneously, the coil controls the command voltage. Laplace transform It also serves as the input to the observer, via the nominal value of the coil inductance. reciprocal After calibration, the data is fed into the observer. The observer output is an estimated value of the coil current. Laplace transform and lumped disturbance estimate Laplace transform ,in nominal value of coil inductance After calibration, the Laplace transform of the feedforward compensation voltage is obtained. The feedforward compensation voltage is superimposed on the output of the proportional controller via the second comparator node.

[0133] The output of the proportional controller and the feedforward compensation voltage are superimposed at the second comparator node to obtain the coil control command voltage. Laplace transform The signal is processed by pulse width modulation and an approximate transfer function of the inverter link. The delay effect of pulse width modulation and the inverter link is approximated by a first-order inertial element. This indicates that this stage characterizes the combined effect of pulse width modulation update delay and inverter power device switching delay. The delayed voltage is applied to the controlled object, and this voltage interacts with the lumped disturbance at the input. The Laplace transforms are superimposed at the third comparison node. The transfer function of the controlled object is... It consists of coil inductance and resistance, and the controlled object is within the nominal value of the coil inductance. With aggregate disturbance Laplace transform The actual output current is due to the combined effect of the two. Laplace transform . After being sampled by the current sampling circuit, the signal is fed back to the input terminal to form a closed-loop control.

[0134] The control block diagram has three comparison nodes: the first comparison node is located at the input of the proportional controller, which compares the current reference command with the actual sampled current to generate a current error signal; the second comparison node is located between the output of the proportional controller and the input of the pulse width modulation (PWM) circuit, which superimposes the proportional control voltage and the feedforward compensation voltage to generate the control command voltage; the third comparison node is located between the output of the PWM circuit and the inverter link and the input of the controlled object, which superimposes the PWM output voltage and the lumped disturbance, with the lumped disturbance acting on the controlled object in a superimposed form. The proportional controller constitutes the main controller of the feedforward path, responsible for generating the proportional control voltage based on the current error; the linear extended state observer constitutes the disturbance observation path, responsible for estimating the lumped disturbance in real time and feeding the estimated value forward to the input; the two paths converge at the second comparison node, jointly determining the coil control command voltage. Laplace transform .

[0135] Example: To verify the effectiveness of the proportional-extended state observer control method proposed in this invention, a comparative experiment was conducted under motor load conditions. A given current amplitude of 4 amps was used to test two frequency commands: 50 Hz and 300 Hz. The inverter switching frequency was 20 kHz.

[0136] Figure 3 A comparison of the actual output current and the reference current of the proportional-extended state observer control method of this invention under a 50 Hz command is presented. Figure 3 (a) is the reference current waveform. Figure 3 (b) shows the actual output current waveform of the proportional-extended state observer control method. The output current amplitude is 3.974 amperes, and the total harmonic distortion is 12.07%.

[0137] Figure 4 A comparison of the actual output current and the reference current under a 50 Hz command using the traditional proportional-integral (PI) control method is presented. Figure 4 (a) is the reference current waveform. Figure 4 (b) shows the actual output current waveform of the proportional-integral control method. The output current amplitude is 3.788 amperes, and the total harmonic distortion is 12.67%.

[0138] Figure 5 A comparison of the actual output current and the reference current of the proportional-extended state observer control method of this invention under a 300 Hz command is presented. Figure 5 (a) is the reference current waveform. Figure 5 (b) shows the actual output current waveform of the proportional-extended state observer control method. The output current amplitude is 3.281 amperes, and the total harmonic distortion is 14.45%.

[0139] Figure 6A comparison of the actual output current and the reference current using the traditional proportional-integral (PI) control method under a 300 Hz command is presented. Figure 6 (a) is the reference current waveform. Figure 6 (b) shows the actual output current waveform of the proportional-integral control method. The output current amplitude is 2.298 amperes, and the total harmonic distortion is 20.85%.

[0140] Experimental results show that, under a low-frequency command of 50 Hz, the current tracking performance of the proposed proportional-extended state observer control method is basically equivalent to that of the proportional-integral control method, with the proportional-extended state observer showing slight advantages in amplitude preservation and total harmonic distortion (THD). Under a high-frequency command of 300 Hz, the back EMF amplitude increases with increasing frequency, and the current output amplitude of the proportional-integral controller decays to 2.298 amperes, while the THD deteriorates to 20.85%. In contrast, the output amplitude of the proportional-extended state observer control method remains at 3.281 amperes, with a THD of 14.45%, significantly better than the proportional-integral control method. These experimental data verify the effective suppression capability of the proposed method against back EMF disturbances under high-frequency conditions, and the parameter robustness of the proportional-extended state observer control method over a wide frequency range.

[0141] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. An independent coil-driven current control method for a moving-magnet permanent magnet synchronous linear motor, characterized in that, Includes the following steps: S1. Establish a state-space model of a single-coil controlled object, and unify the periodic change of coil inductance with position, back electromotive force disturbance and resistance voltage drop into a lumped disturbance, and construct a first-order extended state-space expression that includes current state and lumped disturbance state. S2. Construct a first-order linear extended state observer, using the actual sampled current of the coil and the coil control command voltage as the observer input, and observe the estimated value of the coil current and the estimated value of the lumped disturbance. S3. Construct a proportional-expanded state observer control law, use a proportional controller for current error feedback, and feed forward the lumped disturbance estimate to the control input to obtain the control command voltage of the coil. S4. Determine the observer gain and proportional controller gain based on the inverter switching frequency and the expected bandwidth of the current loop, complete the parameter tuning, and realize current tracking and disturbance suppression of each independent coil.

2. The independent coil drive current control method for a moving magnet permanent magnet synchronous linear motor according to claim 1, characterized in that, In step S1, the specific method for establishing the state-space model of the single-coil controlled object includes: The single-coil voltage balance equation is used as the basis for the controlled object model. The single-coil voltage balance equation is as follows: In the formula, The voltage across the coil, The actual sampling current of the coil. For coil resistance, The coil inductance varies with the position of the mover. It is the back electromotive force. Harmonic voltage generated by the modulation of switching devices; Define state variables The actual sampling current of the coil , ; For lumped disturbances; The system output corresponds to the actual sampled current of the coil; a state-space model of the single-coil controlled object is established, and the first-order extended state-space expression of the single-coil controlled object state-space model is obtained: In the formula, , They are respectively , The first derivative; The lumped disturbance The expression is: In the formula, This is the nominal value of the coil inductance. Let be the rate of change of the lumped disturbance.

3. The independent coil drive current control method for a moving magnet permanent magnet synchronous linear motor according to claim 2, characterized in that, In step S2, the expression for the first-order linear extended state observer is: In the formula, For current observation error, The coil control command voltage, , The estimated value output by the observer, where This is an estimated value for the coil current. This is the estimated value of the lumped disturbance. , They are respectively , The first derivative, , This is the observer gain.

4. The independent coil drive current control method for a moving magnet permanent magnet synchronous linear motor according to claim 3, characterized in that, In step S3, the control law of the proportional-expanded state observer P-ESO is: In the formula, For the proportional controller gain, For coil current reference command, The actual sampling current of the coil. This is the lumped disturbance feedforward compensation term.

5. The independent coil drive current control method for a moving magnet permanent magnet synchronous linear motor according to claim 4, characterized in that, In step S4, the observer gain , Set according to the following formula: In the formula, For the observer's observation bandwidth, Let be the damping coefficient, and satisfy . ; The observation bandwidth Satisfying the theoretical constraint interval: In the formula, For the current loop bandwidth, This refers to the inverter's switching angular frequency.

6. The independent coil drive current control method for a moving magnet permanent magnet synchronous linear motor according to claim 5, characterized in that, In step S4, the gain of the proportional controller Set according to the following formula: 。 7. The independent coil drive current control method for a moving magnet permanent magnet synchronous linear motor according to claim 6, characterized in that, Selecting optimal parameters within the theoretical constraint range, and setting the observation bandwidth... With the bandwidth of the current loop satisfy And the bandwidth of the current loop satisfy ; The gain of the proportional controller and the gain of the observer are then adjusted using the following formula: 。

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