Direct torque cooperative control method for SMPMSM drive system based on improved voltage model to realize stator flux observation

Abstract

The present invention proposes a direct torque cooperative control method for an SMPMSM drive system that implements stator flux observation based on an improved voltage model. Compared with the prior art, this method addresses the shortcomings of direct torque control of permanent magnet synchronous motor systems, such as poor stator flux observation accuracy and torque control performance. The present invention includes the following steps: establishing SMPMSM dynamic equations based on stator magnetic field orientation; designing a stator flux observer based on an improved voltage model; implementing SMPMSM direct torque cooperative control based on the improved flux observer; and generating an inverter reference voltage that satisfies voltage constraints. This method overcomes the impact of the DC component inevitably introduced during current sampling on stator flux observation accuracy, achieving simultaneous improvements in both stator flux observation accuracy and torque control accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of direct torque control of permanent magnet synchronous motors, and in particular to a direct torque cooperative control method of an SMPMSM drive system based on an improved voltage model to achieve stator flux observation. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in industry due to their high efficiency, high power density, fast dynamic response, and simple structure. Field-oriented control (FOC) and direct torque control (DTC) are two common control methods for high-performance AC drives. Compared with FOC, DTC not only offers higher torque dynamic response but also boasts a simpler control structure, requiring neither rotational coordinate transformation nor pulse width modulation (PWM) in the inverter. This makes it possible to control PMSMs to achieve wide speed regulation.

[0003] Traditional direct torque control relies on the design of a torque and flux hysteresis comparator, and then selects the switching state of the inverter power switching device required by a lookup table. Although this can fully utilize the inverter DC bus voltage, its inverter switching frequency is unstable and the motor steady-state torque pulsation is large.

[0004] Cooperative control, based on modern mathematics and synergetics, leverages the self-organizing capabilities of open systems far from equilibrium and their nonlinearities to guide system states toward a predefined manifold, achieving global stability. Cooperative control employs continuous dynamic processes to force the system state toward the manifold. By employing a fully continuous control law, it fundamentally eliminates the chattering associated with sliding mode control. Cooperative control shares the advantages of sliding mode control without the chattering issues associated with sliding mode control, and is more amenable to digital control implementation.

[0005] For PMSM drive systems with direct control (DTC), the accuracy of stator flux observation directly impacts system control performance. Current-model-based stator flux observation methods are susceptible to the influence of motor inductance and rotor flux parameters. Voltage-model-based stator flux observation methods obtain stator flux by integrating the motor back-EMF. While this method involves fewer motor parameters, the current measurement signal contains an unnecessary DC component, which can lead to integrator saturation when integrating the motor back-EMF. Furthermore, improper initial value settings can also affect stator flux estimation accuracy. A common solution is to replace a pure integrator with a first-order low-pass filter. However, this can cause offsets in stator flux amplitude and phase angle, particularly when the motor operating frequency is below the filter's cutoff frequency, where distortion becomes more severe. While various distortion compensation strategies have been proposed, their implementation is complex. While second-order generalized integrators and frequency-adaptive observers can eliminate the DC component in stator flux estimation, both require accurate measurement of the motor's synchronous angular velocity.

[0006] Ohtani proposed a stator flux observer based on closed-loop feedback compensation, called a closed-loop (CL) stator flux observer. This observer compensates for the stator flux amplitude and phase by generating a feedback gain based on the error between the designed comparative flux and the estimated stator flux. In the CL model, the phase of the comparative flux is the same as the phase of the stator flux estimate, while the amplitude can be set to a variety of types. The comparative flux amplitude can be calculated based on the current model, or the calculated stator flux can be used as the comparative flux amplitude after being clipped, or obtained using a model reference adaptive system. Alternatively, the stator flux reference value can be used directly as the comparative flux amplitude. Unlike first-order low-pass filters, second-order generalized integrators, and frequency-adaptive observers, the CL stator flux observer does not require the motor's synchronous angular velocity to achieve distortion compensation. However, due to the presence of a DC component in the motor's back-electromotive force, the CL stator flux observer is prone to offset issues, affecting the accuracy of the stator flux estimation. By calculating the average of the maximum and minimum stator flux values ​​detected within a cycle, the offset in the stator flux estimation is obtained and used for compensation, improving the accuracy of the stator flux estimation. However, a closed-loop flux observer based on DC component compensation cannot completely eliminate the impact of the DC component on the stator flux observation accuracy.

[0007] In summary, for the DTC PMSM system, how to comprehensively consider the stator flux observation accuracy and direct torque control performance, while improving the stator flux observation accuracy and reducing the motor torque and stator flux steady-state pulsation, has become a key technical issue that needs to be solved urgently. Summary of the Invention

[0008] The purpose of the present invention is to solve the defects of poor stator flux observation accuracy and torque control performance in the direct torque control of permanent magnet synchronous motor systems in the prior art, and to provide a direct torque cooperative control method of SMPMSM drive system based on an improved voltage model to realize stator flux observation to solve the above problems.

[0009] In order to achieve the above object, the technical solution of the present invention is as follows:

[0010] The direct torque cooperative control method of the SMPMSM drive system based on the improved voltage model to realize stator flux observation includes the following steps:

[0011] Establishing the SMPMSM dynamic equations based on stator flux orientation: Utilizing the transformation relationships between coordinate systems, the torque reference is converted into a load angle reference. This decouples motor torque control and flux linkage control based on stator flux orientation, simplifying the generation of the inverter reference voltage.

[0012] Design of a stator flux observer based on an improved voltage model: This consists of two parts: flux calculation and DC component elimination. A low-pass filter is used in flux calculation instead of a pure integrator, and closed-loop feedback is used to compensate for amplitude and phase.

[0013] The SMPMSM direct torque cooperative control is realized based on the improved flux observer: the torque reference value and the stator flux reference value are input, the stator flux output by the stator flux observer based on the improved voltage model and the rotor position angle obtained by the rotor position sensor are used, and the inverter reference voltage is output based on the proposed direct torque cooperative control;

[0014] Generate an inverter reference voltage that meets voltage constraints: Substitute the inverter reference voltage generated by direct torque cooperative control into the inverter voltage vector hexagonal boundary equation to determine whether the inverter reference voltage exceeds the limit; if the inverter reference voltage does not exceed the hexagonal boundary, then after coordinate transformation and the inverter's SVPWM strategy, six PWM control signals are output to control the inverter's real-time operation; if it exceeds the hexagonal boundary, the constructed Lagrangian function is used, and the optimization method is adopted to adjust the inverter reference voltage to ensure that it meets the voltage constraint.

[0015] The establishment of the SMPMSM dynamic equation based on stator magnetic field orientation includes the following steps:

[0016] Set the relationship between the coordinate systems as follows:

[0017] αβ is a two-phase stationary coordinate system, where the α axis coincides with the axis of the A-phase winding; the dq axis is a two-phase rotating coordinate system based on the rotor permanent magnet flux ψ f Orientation; xy is a synchronous rotating coordinate system based on the stator flux vector ψs Orientation; the angle between the d-axis and the α-axis is θ r The angle δ between the d-axis and the x-axis is defined as the load angle, and the angle between the α-axis and the x-axis is θ. s ; The stator flux vector electric angular velocity is ω s , the rotor electrical angular velocity is ω r ;

[0018] The voltage equation of SMPMSM in the two-phase stationary αβ coordinate system is expressed as:

[0019]

[0020] Among them: U α and U β is the component of the stator voltage on the α and β axes, ψ sα and ψ sβ is the component of the stator flux in the α and β axes, i α and i β is the component of the stator current in the α and β axes, R s is the stator resistance;

[0021] The stator flux equation is:

[0022]

[0023] in:

[0024]

[0025] Among them, ψ fα and ψ fβ is the rotor permanent magnet flux ψ f The components on the α and β axes, L s is the stator inductance, |ψ s | is the stator flux amplitude;

[0026] The electromagnetic torque equation is:

[0027] T e =1.5n p (ψ sα i β -ψ sβ i α ) (34)

[0028] Where: T e is the electromagnetic torque, n p is the number of motor pole pairs;

[0029] In order to simplify the inverter reference voltage generation, based on the stator flux vector ψ s Directed synchronous rotating xy coordinate system, the SMPMSM stator voltage equation is established as:

[0030]

[0031] Among them, u x 、u y is the component of the stator voltage on the x and y axes; i x 、i y is the component of the stator current in the x and y axes, R s is the stator resistance;

[0032] For the synchronously rotating xy coordinate system, we have

[0033] According to formula (5), the dynamic equation of stator flux and load angle of SMPMSM is derived as follows:

[0034]

[0035] In order to convert the torque reference value into the load angle reference value, the electromagnetic torque is rewritten as:

[0036]

[0037] Under the condition that the rotor flux amplitude of the permanent magnet synchronous motor is constant and the stator flux amplitude is constant, the electromagnetic torque is only related to the load angle;

[0038] According to formula (7), the relationship between the electromagnetic torque derivative and the load angle derivative is:

[0039]

[0040] Using forward Euler discretization to discretize equation (8), we have:

[0041]

[0042] Among them, δ * is the load angle reference value, δ(k) is the load angle at time k, T e * is the torque reference value, T e (k) is the torque value at time k, |ψ s (k)| is the stator flux amplitude at time k;

[0043] The load angle reference is calculated based on the torque reference, and:

[0044]

[0045] According to equations (6) and (10), the torque reference value is converted into a load angle reference value, and the decoupling of electromagnetic torque control and stator flux control is achieved based on stator magnetic field orientation, simplifying the generation of inverter reference voltage.

[0046] The design of the stator flux observer based on the improved voltage model includes the following steps:

[0047] The αβ components of the stator flux are expressed as:

[0048]

[0049] Among them, u α and u β is the component of the stator voltage on the α and β axes, ψ sα and ψ sβ is the component of the stator flux in the α and β axes, i α and i β is the component of the stator current in the α and β axes, R s is the stator resistance;

[0050] Based on Laplace transform, Equation (10) can be rewritten as:

[0051]

[0052] The flux estimation based on back-EMF integration has the problem of pure integral saturation. Therefore, LPF is used instead of pure integrator, and then:

[0053]

[0054] Among them, k L is the cutoff frequency coefficient of the low-pass filter, ω e is the cutoff frequency;

[0055] The stator flux observer based on the improved voltage model consists of two parts: flux calculation and DC component elimination. The flux calculation uses LPF to replace the pure integrator to eliminate the disadvantage of the pure integrator's easy saturation. The amplitude and phase are compensated through closed-loop feedback. Its form is:

[0056]

[0057] Where: s is the stator flux, e s is the back electromotive force, ψ sc To compare magnetic linkage;

[0058] Formula (13) is an LPF with variable cutoff frequency, Used to compensate for the error in the stator flux output, so that the comparative flux of feedback compensation ψ sc Phase and ψ s Similarly, the stator flux reference value and the stator flux amplitude calculated based on the current model are combined to design and compare the flux amplitude, and we have:

[0059] ψsc =ψ si ξ+ψ ref (1-ξ) (45)

[0060] in:

[0061]

[0062] Among them, ψ si is the stator flux amplitude calculated based on the current model, ψ ref is the stator flux reference value, ω CB and ω VB is the turning frequency;

[0063] According to formula (15), when ω e ≥ω VB When ψ sc is ψ ref ;

[0064] For the proposed direct torque cooperative control, ψ s |=ψ ref , therefore, ψ s With ψ sc Equal, ψ s =ψ sc Substituting into formula (13) we get:

[0065] e s =sψ s (47)

[0066] The results of Equation (48) are equal to those of Equation (11), indicating that the designed improved voltage model can achieve accurate estimation of stator flux;

[0067] For stator back electromotive force e s There is a problem in which the DC component affects the accuracy of stator flux observation. In order to obtain a stator back electromotive force with unchanged amplitude and phase and completely eliminate the DC component, according to the steady-state integrator transfer function, we have:

[0068]

[0069] Among them, e s =e c +e d represents the stator back electromotive force, e c is the stator back electromotive force e s The sine component, e d represents the DC component of the stator back EMF;

[0070] The signal d, which is proportional to the integrator DC bias, is derived from equation (50):

[0071]

[0072] Where d represents a signal proportional to the integrator DC bias;

[0073] According to the equivalent relationship between the sinusoidal component and the DC component in the back electromotive force:

[0074]

[0075] Among them, k i is the compensation coefficient between d and the DC component;

[0076] Further find the transfer function G of the DC component elimination module c (s) is:

[0077]

[0078] Set s=0, jω e Substitute into G respectively c (s), the steady-state frequency response is:

[0079]

[0080] Simplifying the above equation and projecting it into the αβ coordinate system, we can obtain the extracted sinusoidal component of the stator back electromotive force, and we have:

[0081]

[0082] Among them, v sα 、v sβ are the extracted sinusoidal components of the stator back electromotive force e c The α-axis and β-axis components, e sα 、e sβ They are stator back electromotive force e s The α-axis and β-axis components of

[0083] The stator flux observer designed based on the improved voltage model is composed of a stator back electromotive force sinusoidal component extraction module and a stator flux calculation module. The expression of its αβ axis is:

[0084]

[0085] Among them, ψ scα and ψ scβ To compare the magnetic flux ψ sc Components on the α and β axes.

[0086] The method for realizing SMPMSM direct torque cooperative control based on the improved flux observer includes the following steps:

[0087] Based on the stator flux observer based on the improved voltage model, the stator flux components on the α and β axes are substituted into formula (3) to obtain the stator flux amplitude and θ s Based on the stator current obtained by the current sensor, the components of the stator current on the α and β axes are obtained through coordinate transformation, and then the electromagnetic torque is obtained through formula (4). Based on the rotor position sensor, the rotor position angle θ is obtained. r , load angle δ=θ s -θ r , then define the stator flux tracking error and load angle tracking error, then:

[0088]

[0089] Among them, ξ1 is the stator flux tracking error, ξ2 is the load angle tracking error, is the stator flux reference value, The stator flux output by the stator flux observer based on the improved voltage model is designed, δ * is the load angle reference value, δ is the load angle;

[0090] In order to achieve the tracking of stator flux and torque to stator flux reference value and torque reference value, macro variables ψ1 and ψ2 are designed, and:

[0091]

[0092] Redesign the dynamic evolution equation, and we have:

[0093]

[0094] Among them, α1>0, β1>0, α2>0, β2>0, α1 and β1 are the proportional coefficient and integral coefficient of the macro variable ψ1, α2 and β2 are the proportional coefficient and integral coefficient of the macro variable ψ2, and T is the time constant of the designed dynamic evolution equation;

[0095] Combining equations (59), (60) and (27), we get:

[0096]

[0097] The solution of equation (28) is:

[0098]

[0099] Among them, C1 and C2 are constants;

[0100] From (29), we can see that no matter the values ​​of C1 and C2, the load angle tracking error and the stator flux tracking error always converge to zero. * and is a constant, so we get:

[0101]

[0102] From this we get:

[0103]

[0104] Substituting formula (31) into (28), we have:

[0105]

[0106] Combining equations (61) and (32), the inverter reference voltage is generated, and:

[0107]

[0108] Among them, u x * and u y * The components of the generated inverter reference voltage on the x-axis and y-axis are: and δ are the stator flux and load angle output by the stator flux observer designed based on the improved voltage model, respectively.

[0109] Generating an inverter reference voltage that satisfies a voltage constraint condition comprises the following steps:

[0110] Considering the maximum output voltage constraint of the inverter, voltage constraint processing is performed to ensure the safe and stable operation of the SMPMSM drive system;

[0111] Assume that the six sides of the inverter voltage vector hexagon are L n (n=1~6), the boundary equation of the hexagonal voltage vector is written as:

[0112]

[0113] in, is the generated inverter reference voltage component on the x-axis and y-axis, h xn , h yn and h cn are all boundary equation coefficients, and the calculation formula is given by formula (35):

[0114]

[0115] Among them, U dc is the inverter DC bus voltage.

[0116]

[0117] Using inequalities to express the boundary equations of the inverter voltage vector hexagon, we have:

[0118]

[0119] Substitute the inverter reference voltage generated by direct torque cooperative control into the boundary equation of the hexagonal voltage vector given by equation (62) to determine whether the generated inverter reference voltage exceeds the limit;

[0120] If the generated inverter reference voltage does not exceed the boundary equation of the hexagon, then after coordinate transformation and the inverter's SVPWM strategy, six PWM control signals are output to control the inverter's real-time operation;

[0121] If the generated inverter reference voltage exceeds the boundary equation of the hexagon, a Lagrangian function is constructed and an optimization method is used to adjust the generated inverter reference voltage so that it meets the voltage constraint. The optimization method is as follows:

[0122] First, taking voltage tracking as the goal, the cost function is designed as:

[0123]

[0124] in: and The components of the inverter reference voltage on the x-axis and y-axis that meet the voltage constraint;

[0125] Then, the boundary equation of the inverter hexagonal voltage vector is used to construct the Lagrangian function:

[0126]

[0127] Finally, according to the optimization conditions of the Lagrangian function: and Combined with the boundary conditions of equation (37), the system of equations is solved simultaneously to obtain the inverter reference voltage that satisfies the voltage constraint, which can be expressed as:

[0128]

[0129] Based on the proposed direct torque cooperative control, the torque reference value, the stator flux reference value, the stator flux output by the stator flux observer based on the improved voltage model, and the rotor position angle θ obtained by the rotor position sensor are used. r , output the inverter reference voltage that meets the voltage constraint conditions, and after coordinate transformation and SVPWM of the inverter, output six PWM control signals to control the real-time operation of the inverter.

[0130] Beneficial effects

[0131] The present invention discloses a direct torque cooperative control method for an SMPMSM drive system that realizes stator flux observation based on an improved voltage model. Compared with the prior art, the present invention establishes a dynamic equation of the SMPMSM based on stator magnetic field orientation, redesigns macro variables and manifolds, and combines them with the designed dynamic evolution equations to generate an inverter reference voltage. At the same time, a stator flux observer design scheme based on an improved voltage model with DC bias elimination is proposed. The proposed scheme improves the stator flux observation accuracy based on the CL-type voltage model. At the same time, based on the ingenious design of the integral steady-state function, it overcomes the influence of the DC component inevitably introduced in the current sampling process on the stator flux observation accuracy, thereby achieving a simultaneous improvement in the stator flux observation accuracy and the torque control accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0132] Figure 1 is a method sequence diagram of the present invention;

[0133] Figure 2 1 is a relationship diagram of each coordinate system of the present invention;

[0134] Figure 3 This is a diagram of a stator flux observer based on an improved voltage model according to the present invention;

[0135] Figure 4 This is a structural diagram of the SMPMSM drive system with direct torque cooperative control proposed in the present invention;

[0136] Figure 5 A diagram showing the experimental bench for the SMPMSM drive system used for experimental verification of the present invention;

[0137] Figure 6 The steady-state waveform of the torque at 100 rpm of the present invention is shown in Figure 1. (a) is sliding mode control, and (b) is cooperative control.

[0138] Figure 7 The 400 rpm torque steady-state waveform diagram of the present invention, (a) is sliding mode control, (b) is cooperative control;

[0139] Figure 8 This is a THD diagram of the a-phase current during steady-state operation of an example of the present invention;

[0140] Figure 9 Figure 2 is a steady-state waveform diagram of the electromagnetic torque of an example of the present invention under parameter mismatch conditions, where (a) is 0.8 times the nominal permanent magnet flux linkage, (b) is 0.9 times the nominal stator inductance, and (c) is 1.4 times the nominal stator resistance.

[0141] Figure 10Figure 2 is a steady-state waveform diagram of the electromagnetic torque of an example of the present invention under parameter mismatch conditions, where (a) is 0.8 times the nominal permanent magnet flux linkage, (b) is 0.9 times the nominal stator inductance, and (c) is 1.4 times the nominal stator resistance.

[0142] Figure 11 Figure 2 is a magnetic flux error diagram of an example of the present invention, where (a) is the α-axis magnetic flux observation error and (b) is the β-axis magnetic flux observation error.

[0143] Figure 12 The torque, flux and current waveforms are shown when the flux observation scheme proposed in the example of the present invention is switched to the traditional scheme. DETAILED DESCRIPTION

[0144] In order to provide a further understanding and appreciation of the structural features and effects achieved by the present invention, a detailed description is provided with reference to preferred embodiments and accompanying drawings as follows:

[0145] like Figure 1 As shown, the present invention provides a direct torque cooperative control method for an SMPMSM drive system based on an improved voltage model to realize stator flux observation, comprising the following steps:

[0146] The first step is to generate the SMPMSM dynamic equations based on stator flux orientation: using the conversion relationship between the various coordinate systems, the torque reference value is converted into a load angle reference value. Based on stator flux orientation, the motor torque control and flux linkage control are decoupled, and the generation of the inverter reference voltage is simplified.

[0147] (1) Figure 2 As shown, the relationship between each coordinate system is set as follows:

[0148] αβ is a two-phase stationary coordinate system, where the α axis coincides with the axis of the A-phase winding; the dq axis is a two-phase rotating coordinate system based on the rotor permanent magnet flux ψ f Orientation; xy is a synchronous rotating coordinate system based on the stator flux vector ψ s Orientation; the angle between the d-axis and the α-axis is θ r The angle δ between the d-axis and the x-axis is defined as the load angle, and the angle between the α-axis and the x-axis is θ. s ; The stator flux vector electric angular velocity is ω s , the rotor electrical angular velocity is ω r .

[0149] (2) Assume that the voltage equation of SMPMSM in the two-phase stationary αβ coordinate system is expressed as:

[0150]

[0151] Among them: U α and U βis the component of the stator voltage on the α and β axes, ψ sα and ψ sβ is the component of the stator flux in the α and β axes, i α and i β is the component of the stator current in the α and β axes, R s is the stator resistance;

[0152] (3) Set the sub-magnetic flux equation as:

[0153]

[0154] in:

[0155]

[0156] Among them, ψ fα and ψ fβ is the rotor permanent magnet flux ψ f The components on the α and β axes, L s is the stator inductance, |ψ s | is the stator flux amplitude;

[0157] (4) Assume that the electromagnetic torque equation is:

[0158] T e =1.5n p (ψ sα i β -ψ sβ i α ) (65)

[0159] Where: T e is the electromagnetic torque, n p is the number of motor pole pairs.

[0160] (5) In order to simplify the inverter reference voltage generation, based on the stator flux vector ψ s Directed synchronous rotating xy coordinate system, the SMPMSM stator voltage equation is established as:

[0161]

[0162] Among them, u x 、u y is the component of the stator voltage on the x and y axes; i x 、i y is the component of the stator current in the x and y axes, R s is the stator resistance;

[0163] For the synchronously rotating xy coordinate system, we have

[0164] According to formula (5), the dynamic equation of stator flux and load angle of SMPMSM is derived as follows:

[0165]

[0166] In order to convert the torque reference value into the load angle reference value, the electromagnetic torque is rewritten as:

[0167]

[0168] Under the condition that the amplitude of the permanent magnet flux linkage of the permanent magnet synchronous motor rotor is constant and the amplitude of the stator flux linkage is constant, the electromagnetic torque is only related to the load angle;

[0169] According to formula (7), the relationship between the electromagnetic torque derivative and the load angle derivative is:

[0170]

[0171] Using forward Euler discretization to discretize equation (8), we have:

[0172]

[0173] Among them, δ * is the load angle reference value, δ(k) is the load angle at time k, T e * is the torque reference value, T e (k) is the torque value at time k, |ψ s (k)| is the stator flux amplitude at time k;

[0174] The load angle reference is calculated based on the torque reference, and:

[0175]

[0176] According to equations (6) and (10), the torque reference value is converted into a load angle reference value, and the decoupling of electromagnetic torque control and stator flux control is achieved based on stator magnetic field orientation, simplifying the generation of inverter reference voltage.

[0177] The second step is to design a stator flux observer based on an improved voltage model. This design consists of two parts: flux calculation and DC component elimination. A low-pass filter (LPF) replaces a pure integrator in the flux calculation to eliminate the saturation drawback of pure integrators. Closed-loop feedback is used to compensate for amplitude and phase. This completely eliminates the influence of the DC component, effectively improving torque control accuracy compared to traditional voltage models.

[0178] (1) The αβ components of the stator flux are expressed as:

[0179]

[0180] Among them, u α and u β is the component of the stator voltage on the α and β axes, ψ sα and ψ sβ is the component of the stator flux in the α and β axes, i α and i β is the component of the stator current in the α and β axes, R s is the stator resistance;

[0181] Based on Laplace transform, Equation (10) can be rewritten as:

[0182]

[0183] The flux estimation based on back-EMF integration has the problem of pure integral saturation. Therefore, LPF is used instead of pure integrator, and then:

[0184]

[0185] Among them, k L is the cutoff frequency coefficient of the low-pass filter, ω e is the cutoff frequency.

[0186] (2) A stator flux observer based on the improved voltage model is designed. It consists of two parts: flux calculation and DC component elimination. The flux calculation uses LPF to replace the pure integrator to eliminate the disadvantage of the pure integrator being easily saturated. The amplitude and phase are compensated through closed-loop feedback. Its form is:

[0187]

[0188] Where: s is the stator flux, e s is the back electromotive force, ψ sc To compare magnetic linkage;

[0189] Formula (13) is an LPF with variable cutoff frequency, Used to compensate for the error in the stator flux output, so that the comparative flux of feedback compensation ψ sc Phase and ψ s Similarly, the stator flux reference value and the stator flux amplitude calculated based on the current model are combined to design and compare the flux amplitude, and we have:

[0190] ψ sc =ψ si ξ+ψ ref (1-ξ) (76)

[0191] in:

[0192]

[0193] Among them, ψ si is the stator flux amplitude calculated based on the current model, ψ ref is the stator flux reference value, ω CB and ω VB is the turning frequency;

[0194] According to formula (15), when ω e ≥ω VB When ψ sc Set to ψ ref ;

[0195] For the proposed direct torque cooperative control, |ψ s |=ψ ref , therefore, ψ s With ψ sc Equal, ψ s =ψ sc Substituting into formula (13) we get:

[0196] e s =sψ s (78)

[0197] The results of Equation (79) are equal to those of Equation (11), indicating that the designed improved voltage model can achieve accurate estimation of the stator flux.

[0198] (3) Regarding the stator back electromotive force e s There is a problem in which the DC component affects the accuracy of stator flux observation. In order to obtain a stator back electromotive force with unchanged amplitude and phase and completely eliminate the DC component, according to the steady-state integrator transfer function, we have:

[0199]

[0200] Among them, e s =e c +e d represents the stator back electromotive force, e c is the stator back electromotive force e s The sine component, e d represents the DC component of the stator back EMF;

[0201] The signal d, which is proportional to the integrator DC bias, is derived from equation (81):

[0202]

[0203] Where d represents a signal proportional to the integrator DC bias;

[0204] According to the equivalent relationship between the sinusoidal component and the DC component in the back electromotive force:

[0205]

[0206] Among them, k i is the compensation coefficient between d and the DC component;

[0207] Further find the transfer function G of the DC component elimination module c (s) is:

[0208]

[0209] Set s=0, jω e Substitute into G respectively c (s), the steady-state frequency response is:

[0210]

[0211] Simplifying the above equation and projecting it into the αβ coordinate system, we can obtain the extracted sinusoidal component of the stator back electromotive force, and we have:

[0212]

[0213] Among them, v sα 、v sβ are the extracted sinusoidal components of the stator back electromotive force e c The α-axis and β-axis components, e sα 、e sβ They are stator back electromotive force e s The α-axis and β-axis components of .

[0214] (4) The stator flux observer designed based on the improved voltage model is obtained as follows Figure 3 As shown in the figure, it consists of a stator back electromotive force sinusoidal component extraction module and a stator flux calculation module. The expression of its αβ axis is:

[0215]

[0216] Among them, ψ scα and ψ scβ To compare the magnetic flux ψ sc Components on the α and β axes.

[0217] The third step is to realize the direct torque cooperative control of SMPMSM based on the improved flux observer, such as Figure 4 As shown in the figure, the torque reference value and the stator flux reference value are input, the stator flux is output by the stator flux observer based on the improved voltage model, and the rotor position angle is obtained by the rotor position sensor. Based on the proposed direct torque cooperative control, the inverter reference voltage is output.

[0218] (1) Based on the stator flux observer based on the improved voltage model, the stator flux components on the α and β axes are substituted into equation (3) to obtain the stator flux amplitude and θ s Based on the stator current obtained by the current sensor, the components of the stator current on the α and β axes are obtained through coordinate transformation. Then, the electromagnetic torque can be obtained through formula (4). Based on the rotor position sensor, the rotor position angle θ is obtained. r , load angle δ=θ s -θ r , then define the stator flux tracking error and load angle tracking error, then:

[0219]

[0220] Among them, ξ1 is the stator flux tracking error, ξ2 is the load angle tracking error, is the stator flux reference value, The stator flux output by the stator flux observer based on the improved voltage model is designed, δ * is the load angle reference value, and δ is the load angle.

[0221] (2) In order to achieve the tracking of stator flux and torque with respect to stator flux reference value and torque reference value, macro variables ψ1 and ψ2 are designed, and:

[0222]

[0223] Redesign the dynamic evolution equation, and we have:

[0224]

[0225] Among them, α1>0, β1>0, α2>0, β2>0, α1 and β1 are the proportional coefficient and integral coefficient of the macro variable ψ1, α2 and β2 are the proportional coefficient and integral coefficient of the macro variable ψ2, and T is the time constant of the designed dynamic evolution equation;

[0226] Combining equations (90), (91) and (27), we get:

[0227]

[0228] The solution of equation (28) is:

[0229]

[0230] Among them, C1 and C2 are constants;

[0231] From (29), we can see that no matter the values ​​of C1 and C2, the load angle tracking error and the stator flux tracking error always converge to zero. * and is a constant, so we get:

[0232]

[0233] From this we get:

[0234]

[0235] Substituting formula (31) into (28), we have:

[0236]

[0237] Combining equations (92) and (32), the inverter reference voltage is generated, and:

[0238]

[0239] Among them, u x * and u y * The components of the generated inverter reference voltage on the x-axis and y-axis are: and δ are the stator flux and load angle output by the stator flux observer designed based on the improved voltage model, respectively.

[0240] The fourth step is to generate an inverter reference voltage that meets the voltage constraint conditions: the inverter reference voltage generated by direct torque cooperative control is substituted into the inverter voltage vector hexagonal boundary equation to determine whether the inverter reference voltage exceeds the limit; if the inverter reference voltage does not exceed the hexagonal boundary, then after coordinate transformation and the inverter's SVPWM strategy, six PWM control signals are output to control the real-time operation of the inverter; if it exceeds the hexagonal boundary, the constructed Lagrangian function is used, and the optimization method is adopted to adjust the inverter reference voltage to meet the voltage constraint conditions.

[0241] (1) Considering the maximum output voltage constraint of the inverter, voltage constraint processing is performed to ensure the safe and stable operation of the SMPMSM drive system;

[0242] Assume that the six sides of the inverter voltage vector hexagon are L n (n=1~6), the boundary equation of the hexagonal voltage vector is written as:

[0243]

[0244] in, is the generated inverter reference voltage component on the x-axis and y-axis, h xn , h yn and h cn are all boundary equation coefficients, and the calculation formula is given by formula (35):

[0245]

[0246] Among them, U dc is the inverter DC bus voltage.

[0247]

[0248] Using inequalities to express the boundary equations of the inverter voltage vector hexagon, we have:

[0249]

[0250] (2) Substituting the inverter reference voltage generated by direct torque cooperative control into the boundary equation of the hexagonal voltage vector given by equation (93) to determine whether the generated inverter reference voltage exceeds the limit;

[0251] If the generated inverter reference voltage does not exceed the boundary equation of the hexagon, then after coordinate transformation and the inverter's SVPWM strategy, six PWM control signals are output to control the inverter's real-time operation;

[0252] If the generated inverter reference voltage exceeds the boundary equation of the hexagon, a Lagrangian function is constructed and an optimization method is used to adjust the generated inverter reference voltage so that it meets the voltage constraint. The optimization method is as follows:

[0253] First, taking voltage tracking as the goal, the cost function is designed as:

[0254]

[0255] in: and The components of the inverter reference voltage on the x-axis and y-axis that meet the voltage constraint.

[0256] Then, the boundary equation of the inverter hexagonal voltage vector is used to construct the Lagrangian function:

[0257]

[0258] Finally, according to the optimization conditions of the Lagrangian function: and Combined with the boundary conditions of equation (37), the system of equations is solved simultaneously to obtain the inverter reference voltage that satisfies the voltage constraint, which can be expressed as:

[0259]

[0260] (3) Based on the proposed direct torque cooperative control, the torque reference value, the stator flux reference value, the stator flux output by the stator flux observer based on the improved voltage model, and the rotor position angle θ obtained by the rotor position sensor are used. r , output the inverter reference voltage that meets the voltage constraint conditions, and after coordinate transformation and SVPWM of the inverter, output six PWM control signals to control the real-time operation of the inverter.

[0261] In order to verify the effectiveness of the proposed scheme, an experimental platform for SMPMSM drive system was built based on dSPACE / DS1007. Figure 5 The motor under test is a 900W surface-mount permanent magnet synchronous motor, with nominal parameters listed in Table 1. A programmable DC power supply was used to power the inverter, which consisted of MOSFET modules. The current sensor was a LEM LA25-P, and the rotor position sensor was a single-pole resolver. The three-phase asynchronous motor had a power of 2.2kW and was driven by an ABB ACS800 series inverter, capable of four-quadrant operation, as the dynamometer for the motor under test. During the experiment, the SMPMSM operated in torque control mode, while the dynamometer operated in speed control mode.

[0262] Table 1 Parameters of the tested SMPMSM

[0263]

[0264] Experimental parameters such as DC bus voltage, maximum allowable current for safe operation, dead time, and other parameters that need to be adjusted during the experiment are shown in Table 2.

[0265] Table 2 Test parameters

[0266]

[0267]

[0268] The proposed direct torque coordinated control (SDTC) method, based on an improved voltage model for stator flux observation, was experimentally tested for system speed step response and load torque step response. Under the same experimental conditions, the control performance of the SMPMSM drive system was compared with that of a sliding mode direct torque control (SMDTC). The experimental results and analysis are discussed below.

[0269] (1) Comparison of torque steady-state tracking performance

[0270] In order to test the steady-state tracking performance of SDTC compared with SMDTC, torque tracking experiments were performed at 100 rpm and 400 rpm respectively.

[0271] The controlled SMPMSM is driven to 100 rpm using a dynamometer. The initial value of the torque reference is set to 0 N.m and then stepped to 5 N.m in 1 second. The torque steady-state waveform is as follows: Figure 6 As shown, Figure 6 (a) is the 100rpm torque steady-state waveform of SMDTC, Figure 6 (b) is the 100 rpm torque steady-state waveform of SDTC.

[0272] The controlled SMPMSM is dragged to 400rpm using a dynamometer. The initial value of the torque reference is set to 0N.m, and then stepped to 10N.m in 1s. The torque steady-state waveform is as follows: Figure 7 As shown, Figure 7 (a) is the 400rpm torque steady-state waveform of SMDTC, Figure 7 (b) is the 400rpm torque steady-state waveform of SDTC. Figure 8 As shown, Figure 8 (a) is the THD of the a-phase current during steady-state operation of SDTC. Figure 8 (b) shows the phase a power THD of the SMDTC during steady-state operation. Experimental results show that direct torque cooperative control based on the improved voltage model to achieve stator flux observation does not suffer from the chattering problem of sliding mode control, and has lower steady-state torque ripple and lower steady-state current THD.

[0273] (2) Parameter robustness experiment

[0274] In order to test the robustness of direct torque cooperative control based on stator flux observation using an improved voltage model, mismatch experiments of stator resistance, permanent magnet flux, and stator inductance were conducted. The experiments did not actually change the motor parameters, but rather made corresponding parameter changes in the controller. The controlled SMPMSM was dragged to 100rpm using a dynamometer, and the initial value of the torque reference was set to 0N.m, which was stepped to 5N.m at 1s. The steady-state waveform of the electromagnetic torque under parameter mismatch conditions is shown below. Figure 9 ,in Figure 9 (a) is the steady-state waveform of the electromagnetic torque when the nominal permanent magnet flux is 0.8 times. Figure 9 (b) is the steady-state waveform of the electromagnetic torque when the nominal stator inductance is 0.9 times. Figure 9 (c) is the steady-state waveform of the electromagnetic torque when the nominal stator resistance is 1.4 times.

[0275] The controlled SMPMSM is dragged to 400rpm using a dynamometer. The initial value of the torque reference is set to 0N.m and then stepped to 10N.m in 1s. The steady-state waveform of the electromagnetic torque under parameter mismatch is as follows: Figure 10 ,in Figure 10(a) is the steady-state waveform of the electromagnetic torque when the nominal permanent magnet flux is 0.8 times. Figure 10 (b) is the steady-state waveform of the electromagnetic torque when the nominal stator inductance is 0.9 times. Figure 10 (c) shows the steady-state electromagnetic torque waveform when the stator resistance is 1.4 times the nominal stator resistance. Based on the experimental waveforms, the direct torque cooperative control using the improved voltage model to implement stator flux observation does not exhibit significant shifts in the steady-state torque waveform when parameters change, demonstrating robustness. Furthermore, the steady-state torque ripple is lower than that of the sliding-mode direct torque control using nominal parameters.

[0276] (3) Stator flux observer performance verification

[0277] Based on the stator flux observer output of the current model, the proposed improved voltage model is used to implement the stator flux observation scheme and the traditional scheme to observe the stator flux. The stator flux error is as follows: Figure 11 As shown, Figure 11 (a) is the α-axis stator flux observation error of different stator flux observation schemes, Figure 11 (b) β-axis stator flux observation errors for different stator flux observation schemes. This shows that the proposed improved voltage model achieves more accurate stator flux observation. The traditional scheme is based on the 2015 IEEE paper "Improved stator flux estimator for speed sensorless induction motor drives" ("Improved stator flux estimator for speed sensorless induction motor drives" - IEEE Journal of Power Electronics, 2015).

[0278] Figure 12 Experimental waveforms of torque, flux, and current are presented when switching from the proposed stator flux observer to the traditional scheme with the addition of a 0.5V DC component. The experimental results show a significant change in torque ripple before and after the switch, demonstrating that the proposed direct torque coordinated control using an improved voltage model to implement stator flux observation can better eliminate the impact of the DC component inevitably introduced during current sampling on the stator flux observation accuracy, thereby improving torque control accuracy.

[0279] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions merely illustrate the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A direct torque cooperative control method for SMPMSM drive system based on an improved voltage model to realize stator flux observation, characterized in that: The following steps are involved: 11) Establish the dynamic equations of the SMPMSM based on stator field orientation: Utilize the conversion relationship between various coordinate systems to convert the torque reference value into the load angle reference value. Based on stator field orientation, the motor torque control and flux linkage control are decoupled, simplifying the generation of the inverter reference voltage. 12) Design of a stator flux observer based on an improved voltage model: A stator flux observer based on an improved voltage model is designed. The observer consists of two parts: flux calculation and DC component elimination. A low-pass filter is used in the flux calculation to replace a pure integrator, and amplitude and phase compensation are performed through closed-loop feedback. 13) Implementing SMPMSM direct torque cooperative control based on an improved flux observer: Input torque reference value, stator flux reference value, stator flux output by the stator flux observer based on the improved voltage model, rotor position angle obtained by the rotor position sensor, and output inverter reference voltage based on the proposed direct torque cooperative control; 14) Generate an inverter reference voltage that meets the voltage constraint conditions: Substitute the inverter reference voltage generated by direct torque cooperative control into the inverter voltage vector hexagonal boundary equation to determine whether the inverter reference voltage exceeds the limit; if the inverter reference voltage does not exceed the hexagonal boundary, then after coordinate transformation and the inverter's SVPWM strategy, output six PWM control signals to control the real-time operation of the inverter; if it exceeds the hexagonal boundary, use the constructed Lagrangian function and adopt the optimization method to adjust the inverter reference voltage to make it meet the voltage constraint conditions.

2. The direct torque cooperative control method of the SMPMSM drive system based on the improved voltage model to realize stator flux observation according to claim 1 is characterized in that: The establishment of the SMPMSM dynamic equation based on stator magnetic field orientation includes the following steps: 21) Set the relationship between the coordinate systems as follows: αβ is a two-phase stationary coordinate system, where the α axis coincides with the A-phase winding axis; the dq axis is a two-phase rotating coordinate system based on the rotor permanent magnet flux ψ f Orientation; xy is a synchronous rotating coordinate system based on the stator flux vector ψ s Orientation; the angle between the d-axis and the α-axis is θ r The angle δ between the d-axis and the x-axis is defined as the load angle, and the angle between the α-axis and the x-axis is θ. s ; The stator flux vector electric angular velocity is ω s , the rotor electrical angular velocity is ω r ; 22) The voltage equation of the SMPMSM in the two-phase stationary αβ coordinate system is expressed as: Among them: U α and U β is the component of the stator voltage on the α and β axes, ψ sα and ψ sβ is the component of the stator flux in the α and β axes, i α and i β is the component of the stator current in the α and β axes, R s is the stator resistance; 23) The stator flux equation is: in: Among them, ψ fα and ψ fβ is the rotor permanent magnet flux ψ f The components on the α and β axes, L s is the stator inductance, |ψ s | is the stator flux amplitude; 24) The electromagnetic torque equation is: T e =1.5n p (ψ sα I β -ψ sβ I α ) (3 Where: T e is the electromagnetic torque, n p is the number of motor pole pairs; 25) In order to simplify the inverter reference voltage generation, based on the stator flux vector ψ s Directed synchronous rotating xy coordinate system, the SMPMSM stator voltage equation is established as: Among them, u x 、u y is the component of the stator voltage on the x and y axes; i x 、i y is the component of the stator current in the x and y axes, R s is the stator resistance; For the synchronously rotating xy coordinate system, we have According to formula (5), the dynamic equation of stator flux and load angle of SMPMSM is derived as follows: In order to convert the torque reference value into the load angle reference value, the electromagnetic torque is rewritten as: Under the condition that the rotor flux amplitude of the permanent magnet synchronous motor is constant and the stator flux amplitude is constant, the electromagnetic torque is only related to the load angle; According to formula (7), the relationship between the electromagnetic torque derivative and the load angle derivative is: Using forward Euler discretization to discretize equation (8), we have: Among them, δ * is the load angle reference value, δ(k) is the load angle at time k, T e * is the torque reference value, T e (k) is the torque value at time k, |ψ s (k)| is the stator flux amplitude at time k; The load angle reference is calculated based on the torque reference, and: According to equations (6) and (10), the torque reference value is converted into a load angle reference value, and the decoupling of electromagnetic torque control and stator flux control is achieved based on stator magnetic field orientation, simplifying the generation of inverter reference voltage.

3. The direct torque cooperative control method of the SMPMSM drive system based on the improved voltage model to realize stator flux observation according to claim 1 is characterized in that: The design of the stator flux observer based on the improved voltage model includes the following steps: 31) The αβ components of the stator flux are expressed as: Among them, u α and u β is the component of the stator voltage on the α and β axes, ψ sα and ψ sβ is the component of the stator flux in the α and β axes, i α and i β is the component of the stator current in the α and β axes, R s is the stator resistance; Based on Laplace transform, Equation (10) can be rewritten as: The flux estimation based on back-EMF integration has the problem of pure integral saturation. Therefore, LPF is used instead of pure integrator, and then: Among them, k L is the cutoff frequency coefficient of the low-pass filter, ω e is the cutoff frequency; 32) The stator flux observer based on the improved voltage model consists of two parts: flux calculation and DC component elimination. The flux calculation uses LPF to replace the pure integrator to eliminate the disadvantage of the pure integrator's easy saturation, and the amplitude and phase are compensated through closed-loop feedback. Its form is: Where: s is the stator flux, e s is the back electromotive force, ψ sc To compare magnetic linkage; Formula (13) is an LPF with variable cutoff frequency, Used to compensate for the error in the stator flux output, so that the comparative flux of feedback compensation ψ sc Phase and ψ s Similarly, the stator flux reference value and the stator flux amplitude calculated based on the current model are combined to design and compare the flux amplitude, and we have: ψ sc =ψ si x+ψ ref (1-ξ) (14) in: Among them, ψ si is the stator flux amplitude calculated based on the current model, ψ ref is the stator flux reference value, ω CB and ω VB is the turning frequency; According to formula (15), when ω e ≥ω VB When ψ sc is ψ ref ; For the proposed direct torque cooperative control, |ψ s |=ψ ref , therefore, ψ s With ψ sc Equal, ψ s =ψ sc Substituting into formula (13) we get: And s =sψ s (16) The results of formula (17) are equal to those of formula (11), which shows that the designed improved voltage model can achieve accurate estimation of stator flux; 33) For stator back electromotive force e s There is a problem in which the DC component affects the accuracy of stator flux observation. In order to obtain a stator back electromotive force with unchanged amplitude and phase and completely eliminate the DC component, according to the steady-state integrator transfer function, we have: Among them, e s =e c +e d represents the stator back electromotive force, e c is the stator back electromotive force e s The sine component, e d represents the DC component of the stator back EMF; The signal d, which is proportional to the integrator DC bias, is derived from equation (19): Where d represents a signal proportional to the integrator DC bias; According to the equivalent relationship between the sinusoidal component and the DC component in the back electromotive force: Among them, k i is the compensation coefficient between d and the DC component; Find the transfer function G of the DC component elimination module c (s) is: Set s=0, jω e Substitute into G respectively c (s), the steady-state frequency response is: Simplifying the above equation and projecting it into the αβ coordinate system, we can obtain the extracted sinusoidal component of the stator back electromotive force, and we have: Among them, v sα 、v sβ are the extracted sinusoidal components of the stator back electromotive force e c The α-axis and β-axis components, e sα 、e sβ They are stator back electromotive force e s The α-axis and β-axis components of 34) The stator flux observer based on the improved voltage model is designed, which consists of a stator back electromotive force sinusoidal component extraction module and a stator flux calculation module. The expression of its αβ axis is: Among them, ψ scα and ψ scβ To compare the magnetic flux ψ sc Components on the α and β axes.

4. The direct torque cooperative control method of the SMPMSM drive system based on the improved voltage model to realize stator flux observation according to claim 1 is characterized in that: The method for realizing SMPMSM direct torque cooperative control based on the improved flux observer includes the following steps: 41) Based on the stator flux observer based on the improved voltage model, the stator flux components on the α and β axes are substituted into equation (3) to obtain the stator flux amplitude and θ s Based on the stator current obtained by the current sensor, the components of the stator current on the α and β axes are obtained through coordinate transformation, and then the electromagnetic torque is obtained through formula (4). Based on the rotor position sensor, the rotor position angle θ is obtained. r , load angle δ=θ s -θ r , then define the stator flux tracking error and load angle tracking error, then: Among them, ξ1 is the stator flux tracking error, ξ2 is the load angle tracking error, is the stator flux reference value, The stator flux output by the stator flux observer based on the improved voltage model is designed, δ * is the load angle reference value, δ is the load angle; 42) In order to achieve the tracking of stator flux and torque with respect to stator flux reference value and torque reference value, macro variables ψ1 and ψ2 are designed, and: Redesign the dynamic evolution equation, and we have: Among them, α1>0, β1>0, α2>0, β2>0, α1 and β1 are the proportional coefficient and integral coefficient of the macro variable ψ1, α2 and β2 are the proportional coefficient and integral coefficient of the macro variable ψ2, and T is the time constant of the designed dynamic evolution equation; Combining equations (28), (29) and (27), we get: The solution of equation (28) is: Among them, C1 and C2 are constants; From (29), we can see that no matter the values ​​of C1 and C2, the load angle tracking error and the stator flux tracking error always converge to zero. * and As a constant, we get: From this we get: Substituting formula (31) into (28), we have: Combining equations (30) and (32), the inverter reference voltage is generated, and: Among them, u x * and u y * The components of the generated inverter reference voltage on the x-axis and y-axis are: and δ are the stator flux and load angle output by the stator flux observer designed based on the improved voltage model, respectively.

5. The direct torque cooperative control method of the SMPMSM drive system based on the improved voltage model to realize stator flux observation according to claim 1 is characterized in that: The inverter reference voltage generated to meet the voltage constraint condition The following steps are involved: 51) Considering the maximum output voltage constraint of the inverter, voltage constraint processing is performed to ensure the safe and stable operation of the SMPMSM drive system; Assume that the six sides of the inverter voltage vector hexagon are L n (n=1~6), the boundary equation of the hexagonal voltage vector is written as: in, is the generated inverter reference voltage component on the x-axis and y-axis, h xn , h yn and h cn are all boundary equation coefficients, and the calculation formula is given by formula (35): Among them, U dc is the inverter DC bus voltage, Using inequalities to express the boundary equations of the inverter voltage vector hexagon, we have: 52) Substitute the inverter reference voltage generated by direct torque cooperative control into the boundary equation of the hexagonal voltage vector given by equation (31) to determine whether the generated inverter reference voltage exceeds the limit; If the generated inverter reference voltage does not exceed the boundary equation of the hexagon, then after coordinate transformation and the inverter's SVPWM strategy, six PWM control signals are output to control the inverter's real-time operation; If the generated inverter reference voltage exceeds the boundary equation of the hexagon, a Lagrangian function is constructed and an optimization method is used to adjust the generated inverter reference voltage so that it meets the voltage constraint. The optimization method is as follows: First, taking voltage tracking as the goal, the cost function is designed as: in: and The components of the inverter reference voltage on the x-axis and y-axis that meet the voltage constraint; Then, the boundary equation of the inverter hexagonal voltage vector is used to construct the Lagrangian function: Finally, according to the optimization conditions of the Lagrangian function: and Combined with the boundary conditions of equation (37), the system of equations is solved simultaneously to obtain the inverter reference voltage that satisfies the voltage constraint, which can be expressed as: 53) Based on the proposed direct torque cooperative control, the torque reference value, the stator flux reference value, the stator flux output by the stator flux observer based on the improved voltage model, and the rotor position angle θ obtained by the rotor position sensor are used. r , output the inverter reference voltage that meets the voltage constraint conditions, and after coordinate transformation and SVPWM of the inverter, output six PWM control signals to control the real-time operation of the inverter.

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