Device and method for regulating stator current or stator flux linkage for operating permanent magnet synchronous machine

Abstract

A method for regulating a stator current or a stator flux linkage for operating a permanent magnet synchronous machine using a regulating device (1) according to the claims, in which robust, precise linearization is achieved by means of a non-linear regulating rule such that the regulated non-linear PMSM obtains the performance of a linear PMSM.

Description

Technical Field

[0001] This invention relates to a device for adjusting the stator current or stator flux linkage of a permanent magnet synchronous motor.

[0002] The present invention also relates to a method for regulating the stator current or stator flux linkage for operating a permanent magnet synchronous motor. Background Technology

[0003] Modern drive technology primarily utilizes two types of three-phase motors: asynchronous motors and synchronous motors. These motors either operate on a rigid three-phase power grid or are regulated by a frequency converter. Modern microprocessors, precise current sensing, and fast power electronics provide extensive possibilities for regulating the torque and speed of AC motors.

[0004] Synchronous motors are frequently used in robotics and positioning applications, as well as as generators for energy production. Permanent magnet synchronous motors (PMSMs) offer particular advantages in terms of high power density, excellent efficiency, and high achievable dynamics. These characteristics also make PMSMs especially attractive for applications in the automotive sector.

[0005] In the regulation of permanent magnet synchronous motors, a cascaded regulation structure with lower-level (stator) current regulation is mostly adopted. Current regulation is typically performed in a rotor-fixed coordinate system (d / q coordinate system), and the task is to track the two independent current components along a desired trajectory preset by torque regulation. Alternatively, stator flux linkage can be adjusted to regulate the stator current, since the stator current and stator flux linkage are reversibly and unambiguously related through (non-linear) coordinate transformation.

[0006] Due to their simple structure and the feasibility of calculating regulator parameters by means of simple size design specifications, PI regulators are often used for stator current regulation.

[0007] However, because the PI controller is based on a linear control concept, it is difficult to fully consider the nonlinear characteristics of the system in the controller design.

[0008] Therefore, only limited dynamic tracking performance can be achieved using a PI controller. When the desired current changes rapidly, the PI controller causes overshoot and often introduces unwanted oscillations.

[0009] If the sampling frequency is chosen too low, the PI control loop may even become unstable at higher speeds. These effects are exacerbated when the actual motor parameters deviate from the rated parameters used in the regulator design.

[0010] A regulation scheme is known from WO 2018 089 581 A1, which includes an estimation unit that estimates the position and speed of the synchronous motor before motor startup. The control device uses a field-oriented control vector control routine to control the permanent magnet synchronous motor, the field-oriented control vector control routine including a speed proportional (PI) control loop, a field weakening control, a current PI control loop, and a speed observer.

[0011] Improving synchronous motor control by estimating speed and / or position before motor startup eliminates the need for sensors to measure position and speed.

[0012] Better dynamic tracking performance can, in principle, be achieved through flatness-based tracking adjustment. Here, "flatness-based adjustment" means that, in at least one step of the adjustment algorithm design, an explicit algebraic relationship between the system's state variables and input variables is used, along with an explicit algebraic relationship between the flat output component and its series of time derivatives. In the case of permanent magnet synchronous motors, flatness-based adjustment is particularly simple because the flat output is directly given by the state variables (e.g., optionally stator current or stator flux linkage), which are precisely the quantities to be adjusted.

[0013] However, in practice, the classic flatness-based tracking regulation in PMSM motors results in a rather aggressive regulator due to the decoupling typically implemented in two separate tracking error systems for the two current components. In time-discrete implementations, even a "dead-beat" regulator can occur. The trade-off for better dynamic tracking performance, due to unavoidable measurement noise, is a larger current ripple in steady state.

[0014] DE 10 2021 104 242 A1 Description: Nonlinear effects, such as temperature deviations, can cause imbalances in the resistance values ​​of the three phases. The aforementioned literature is based on a linear model, as can be seen from the use of the transfer function. Transfer functions only exist for linear systems because linear systems rely on the superposition principle, and such considerations in the frequency domain are not feasible for nonlinear systems. The aforementioned literature considers only the three phases individually in order to map and compensate for parameter imbalances.

[0015] In EP 2 626 998 A1, a PI regulator is used for current regulation, and the system is considered linear. Summary of the Invention

[0016] The purpose of this invention is to apply a nonlinear adjustment method suitable for PMSM motors, taking into account the generally nonlinear relationship between stator current and stator flux linkage.

[0017] The objective is achieved by means of a regulating device for the stator current or stator flux linkage of a permanent magnet synchronous motor, which is a nonlinear system. The regulating device has at least one control unit including a software module, a nonlinear regulator for robust and accurate linearization of the system, a feedforward control device, and a disturbance estimator.

[0018] The stated objective is also achieved by means of a method for adjusting the stator current or stator flux linkage used to operate a permanent magnet synchronous motor using an adjusting device, wherein the concept of robust, precise linearization is represented by the form of The nonlinear adjustment rule achieves precise linearization of the PMSM, making the original nonlinear PMSM... Obtain the characteristics of a linear PMSM.

[0019] The robust, accurate linearization is applied to the time-discretized model that takes into account the sampling time, resulting in a linear, time-discretized system. In fact, it is precisely in the case of nonlinear systems that a clearly more common variation is to derive a regulation rule for time-continuous systems (since accurate discretization of nonlinear systems is often difficult), and then implement the regulation rule "approximately continuously," i.e., simply assuming that the sampling time executed on the processor is short enough.

[0020] In contrast to classical exact linearization (or more generally, classical flatness-based regulator design), robust, exact linearization does not impart the characteristics of a linear, decoupled integrator chain to the system, but rather the characteristics of the original system linearized around a selected operating point. In the context of current PMSM, it is also suitable not to directly choose the system linearized around the operating point as the target system, but rather to use L as the target system. d / γ and L q The inductance is reduced by a factor γ≥1 in the form of / γ. By appropriately selecting this factor, a trade-off can be pre-defined between the fast dynamic response of the regulated system (large γ) on the one hand and robustness against measurement noise (small γ) on the other. This avoids the decoupling of the two current or flux linkage components as in classical exact linearization, where the current or flux linkage components remain coupled according to the natural characteristics of the PMSM.

[0021] Subsequently, feedforward control of the established linear system induces linear and asymptotically stable tracking error dynamics, where the smaller inductance of the selected target system causes a faster decay rate of the tracking error. However, unlike classical flatness-based tracking regulation, the tracking errors of the two components (i.e., the two current or flux components) of the flat output are not decoupled; instead, the tracking error dynamics correspond to the dynamics of a linear PMSM.

[0022] The steady-state regulation deviation between the actual current or flux linkage and the desired current or flux linkage is corrected by estimating the interference voltage and adjusting the input voltage accordingly.

[0023] Interference estimation is achieved using a time delay scheme, where the interference in the previous time step k-1 can be directly calculated using measurements available for the current time step k, with optional low-pass filtering.

[0024] Either the magnetic flux linkage in the stator or the current in the stator is chosen as the state variable for the system model.

[0025] In the design of regulation rules for PMSMs, inductance is typically not a design or tuning parameter, but rather enters the regulation rule simply as a system parameter, such as in feedforward control. That is, nominal or identified values ​​are used for this purpose. To set regulator performance, the system parameters are not changed, but rather, for example, in the case of a PI regulator, the proportional and integral terms are altered.

[0026] Conversely, the regulator design proposed in this application imparts linear target system characteristics to the system through a specific form of precise linearization. A linearized PMSM with a strongly reduced, fictitious inductance value is used as the target system. By altering the position of the target system's eigenvalues ​​through this fictitious, smaller inductance value, the real part of the system's eigenvalues ​​becomes more negative from a time-continuous perspective, thus allowing the system to reach steady state more quickly. Simultaneously, the imaginary part of the eigenvalues ​​remains largely unchanged, and the regulation remains robust against measurement noise. That is, the inductance is used as a design or tuning parameter (or specifically a scaling factor γ), entirely due to the fact that our regulator design is based on the selection of a fictitious PMSM target system.

[0027] The proposed control method has the following advantages:

[0028] The control method combines the excellent dynamic performance of flatness-based tracking regulation with the non-aggressive steady-state characteristics of a PI regulator.

[0029] Compared to PI controllers, the method described above is more robust to both parameter deviations and low sampling frequencies.

[0030] This invention starts with a nonlinear model of the PMSM, which maps the nonlinear relationship between current and flux linkage. Unlike prior art, the three phases are not considered separately because they are assumed to be symmetrical.

[0031] The robust, precise linearization proposed in the application produces linear system characteristics through adjustment, but here the decoupling of the two current or flux components, which is otherwise common in classical precise linearization, is intentionally abandoned.

[0032] A linear system consisting of a decoupled chain of integrators (or a shift chain in the case of time discreteness) is formed through classical exact linearization, which is referred to in the literature as the Brunovsky canonical form. The chain of integrators is then typically tuned individually, meaning that the components of the error dynamics are decoupled.

[0033] This application avoids such decoupling because the regulator becomes highly sensitive to measurement noise through decoupling. Instead of decoupling, the invention linearizes the PMSM characteristics of the system through regulation. To achieve faster steady-state characteristics, the inductance in the linear target system is significantly reduced by means of a scaling factor, which causes a shift of the eigenvalues ​​in the complex plane. In the case of a time-continuous system, the real part of the eigenvalues ​​becomes more negative, while the imaginary part remains largely unchanged. In the case of a time-discrete system, the eigenvalues ​​shift towards the origin of the complex plane.

[0034] The disturbance estimator used in this application estimates voltage errors generated by deviations between the nominal (nonlinear) system model and the actual system, as well as other disturbances acting on the system. Therefore, the disturbance estimator does not require a desired current, but rather a measured current; that is, the disturbance estimator does not operate "open-loop". By taking the estimated voltage error into account in the control of the PMSM, steady-state regulation deviations can be compensated for or avoided.

[0035] The system model according to the invention considers the nonlinear relationship between stator current and stator flux linkage; therefore, the system model is nonlinear. The proposed regulator design can be implemented using a system model with stator flux linkage as the state variable, as well as a system model with stator current as the state variable. However, the design based on the flux linkage representation is advantageous because the equations are simplified. Attached Figure Description

[0036] Figure 1 Explain the proposed control method. Detailed Implementation

[0037] With the help of a regulator for robust, precise linearization 1, the regulated nonlinear PMSM 4 behaves like a linear system 2.

[0038] Linear (time-discrete) system 2 with the help of Description, where A and B represent matrices of the selected linear target system, the matrices having states and input The meanings of the reference numerals in the attached figures are listed in the table below.

[0039]

[0040] For linear system 2, the expected trajectory based on expectation The application form is Feedforward control 3 yields linear tracking error dynamics. The tracking error is dynamically determined by the dynamic matrix A of the linear system.

[0041] To avoid steady-state control deviations caused by factors such as parameter bias, the adjustment scheme is supplemented by disturbance estimator 5. Each module is described in detail below.

[0042] Nonlinear Systems 4

[0043] The system equations of the nonlinear PMSM 4 in the rotor-fixed d / q coordinate system can be written as a state representation.

[0044]

[0045] The two-dimensional state x is chosen as follows: (Stator flux linkage).

[0046] Here, the input is given by the stator voltage in the d / q coordinate system where the rotor is stationary: .

[0047] With flux linkage as the selected state variable, the equations of the nonlinear system are:

[0048]

[0049] Where R is the ohmic resistance, and ω el ω is the electric angular velocity.

[0050] The proposed control method is based on time-discrete system representation.

[0051] ,

[0052] The system representation can be derived from a time-continuous system using a suitable discretization method, such as simple Euler discretization, or through more advanced methods. The more precise the discretization method, the better the achievable control performance.

[0053] Regulator for robust, precise linearization

[0054] The basic idea of ​​robust, accurate linearization 1 is that it applies in the form of The nonlinear adjustment rule makes the adjusted nonlinear system Achieving linear performance

[0055]

[0056] Where A and B are the system at the selected steady-state points. The surrounding linearized matrix, i.e. and .

[0057] That is, the regulator only eliminates the nonlinearity of the system, thus applying very mild, less aggressive regulatory intervention. As in classic exact linearization or classic flatness-based regulator designs, decoupling is omitted in the independent integrator chain. This results in very good robustness relative to measurement noise or parameter deviation.

[0058] For the aforementioned time-continuous nonlinear PMSM model with stator flux linkage as the state variable, around the steady-state point... Using approximation

[0059]

[0060] and inductors

[0061] and

[0062] The linearization yields the system equations

[0063] .

[0064] In PMSM, the system dynamics are quite fast compared to the typical sampling frequency of the control loop. Furthermore, it has proven advantageous to apply robust exact linearization¹ to the discretized model considering the sampling time. This applies not only to nonlinear systems¹ but also to linear target systems. All are discretized appropriately. This yields the form: The linear-time discrete-time system is taken as the target system. It is important to note that matrices A and B are usually different from the time-continuous system matrices that form its basis.

[0065]

[0066] Discretized nonlinear systems Solving the system of equations on the right side, we get the following system of equations.

[0067] ,

[0068] From this, through solving The form obtained is The adjustment rule transforms the nonlinear system into the desired linear system 2.

[0069] To achieve faster dynamic characteristics, it is advantageous not to precisely select a linearized PMSM, but rather to choose one with a significantly smaller inductance L. d / γ and L q The PMSM with / γ is used as a linear target system. The quotient γ ≥ 1 between the actual inductance and the selected "virtual" inductance allows the regulator to be adjusted in a trade-off between fast dynamic response (large γ) on the one hand and robustness against measurement noise (small γ) on the other. The linear target system with the adjustment parameter γ achieves optimal setting. However, this avoids decoupling that is detrimental to robustness.

[0070] Feedforward control

[0071] The expected trajectory of the state variables for a nonlinear system ,use The desired trajectory of the state variables for linear system 2 is obtained directly. Since the 2x2 matrix B is always invertible in the case of PMSM, it can be derived from the system equations of linear system 2.

[0072]

[0073] Immediately calculate the feedforward control 3 for linear system 2:

[0074] .

[0075] Using the aforementioned feedforward control, a linear tracking error dynamic is obtained.

[0076] .

[0077] Therefore, tracking error The attenuation rate is determined by the dynamic matrix A of the selected linear target PMSM. Choosing a linear target PMSM with smaller inductance affects the location of the eigenvalues ​​of matrix A and causes a faster attenuation rate for the tracking error.

[0078] Interference estimator 5

[0079] If the nominal system parameters of a nonlinear PMSM are inconsistent with the actual system parameters, or if other disturbances occur to the system, a steady-state regulation deviation is maintained between the actual and desired current or flux linkage using the aforementioned regulation rules. This is because, for example, unlike a PI controller, the regulation rules do not have an integral term. To account for this disturbance, the system model...

[0080]

[0081] Extended into the following forms of interference voltage :

[0082] .

[0083] Interference With input voltage The same approach applies to this system (selectively using the opposite notation here). The purpose of interference estimator 5 is now to obtain the interference... estimated value This allows for subsequent compensation of the interference. Let the voltage calculated using the above adjustment rules be denoted as... Then, the alternative is to use only Also applied .

[0084] Simple and effective for obtaining estimates The method is the so-called time delay scheme. Using the measurements available for the current time step k, it can be solved by solving the following... The equation directly calculates the disturbance in the earlier time step k-1:

[0085] .

[0086] However, due to both measurement noise and time delay, directly using the earlier value as an estimate is problematic. That's problematic. A better approach is to use the low-pass filtered version, which can be obtained, for example, through update rules of the following form:

[0087] .

[0088] parameter The interference estimator can be tuned in a way that strikes a balance between a fast response to changing interference (α close to 1) and robustness against measurement noise (α close to 0).

[0089] The proposed control design can be executed in the same way using current as a state variable: .

[0090] This invention optimizes the regulation and control of PMSM by leveraging the concept of robust and precise linearization and its combination with an interference estimator.

[0091] Furthermore, the regulator design is based on a discretized motor model to account for the sampling time of the control loop.

[0092] As a linear target system, it is not necessary to use the linearized PMSM itself, but to use a linear PMSM with a suitably selected smaller inductance so as to achieve fast dynamics without the need for other regulators.

Claims

1. A regulating device for stator current or stator flux linkage of a permanent magnet synchronous motor, the synchronous motor being a nonlinear system (4), the regulating device having at least one control unit including a software module, a regulator (1) for robust, accurate linearization to establish a linear system (2), a feedforward control device (3), and a disturbance estimator (5).

2. A method for adjusting the stator current or stator flux linkage for operating a permanent magnet synchronous motor using the adjustment device according to claim 1, wherein robust and precise linearization of the PMSM is achieved through a nonlinear adjustment rule, such that the adjusted nonlinear system acquires the characteristics of the linear PMSM.

3. The method for adjustment according to claim 2, wherein, The robust, accurate linearization is applied to a time-discrete model that takes into account sampling time in order to achieve a linear, time-discrete system.

4. The method for regulation according to claim 2 or 3, wherein the linear target system need not necessarily correspond precisely to the linearized PMSM, but is selected to have a smaller inductance (L). d / γ and L q The target system is defined as γ, where a quotient (γ≥1) is preset to coordinate a fast dynamic response (large γ) on the one hand with robustness against measurement noise (small γ) on the other hand.

5. The method for regulation according to any one of claims 2 to 4, wherein feedforward control of the established linear system causes linear tracking error dynamics, wherein a smaller inductance of the selected linear target system produces a faster decay rate of the tracking error.

6. The method for adjustment according to any one of claims 2 to 5, wherein, By estimating the interference voltage ( ) and correspondingly adjust the input voltage ( This is used to correct the steady-state regulation deviation between the actual current or flux and the desired current or flux.

7. The method for regulation according to any one of claims 2 to 6, wherein the interference estimation is achieved by means of a time delay scheme, wherein the interference in the previous time step (k-1) can be directly calculated by means of measurements available for the current time step (k), wherein low-pass filtering is optionally performed.

8. The method for regulation according to any one of claims 2 to 7, wherein either the stator flux linkage or the stator current (in a d / q coordinate system with the rotor fixed) is selected as a state variable for the system model.

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