SMPMSM driving system direct torque cooperative control method for realizing stator flux linkage observation based on improved voltage model

Abstract

The invention discloses an SMPMSM driving system direct torque cooperative control method for realizing stator flux linkage observation based on an improved voltage model. Compared with the prior art, the SMPMSM driving system direct torque cooperative control method solves the defects of poor stator flux linkage observation precision and torque control performance in direct torque control of a permanent magnet synchronous motor system. The method comprises the following steps: establishing an SMPMSM dynamic equation based on stator field orientation; designing a stator flux linkage observer based on an improved voltage model; sMPMSM direct torque cooperative control is realized based on an improved flux observer; and generating an inverter reference voltage meeting the voltage constraint condition. According to the method, the influence of a direct-current component inevitably introduced in the current sampling process on the stator flux linkage observation precision is overcome, and the stator flux linkage observation precision and the torque control precision are improved at the same time.

Description

Technical Field

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

[0002] Permanent Magnet Synchronous Motor (PMSM) has been widely used in the industrial field due to its advantages of high efficiency, high power density, fast dynamic response, simple structure, etc. Field-Oriented Control (FOC) and Direct Torque Control (DTC) are two commonly used control methods for high-performance AC drives. Compared with FOC, DTC not only has a higher torque dynamic response, but also has a simple control structure, does not require rotating coordinate transformation, and the inverter does not need pulse width modulation (PWM), which can control PMSM to achieve its wide speed regulation operation.

[0003] Traditional direct torque control relies on the design of torque and flux hysteresis comparator, and then selects the switching state of the inverter power switch device to be applied by table lookup. Although it can make full use of the inverter DC bus voltage, its inverter switching frequency is unstable and the motor steady-state torque pulsation is large.

[0004] Based on modern mathematics and synergetics, cooperative control uses the self-organizing ability of open systems far from equilibrium and the nonlinearity of the system to guide the system state to converge to a pre-set manifold and achieve global stability of the system. Cooperative control designs a continuous dynamic process to force the system state to approach the manifold. It fundamentally eliminates the chattering of sliding mode control by using a completely continuous control law. Cooperative control has the advantages of sliding mode control, but does not have the chattering problem of sliding mode control, and is more suitable for digital control implementation.

[0005] For the PMSM drive system of DTC, the accuracy of stator flux observation directly affects the control performance of the system. The stator flux observation method based on the current model is easily affected by the motor inductance and rotor flux parameters. The stator flux observation method based on the voltage model obtains the stator flux by integrating the motor back electromotive force. This method involves fewer motor parameters, but because the current measurement signal contains unnecessary DC components, the integrator saturation divergence problem is prone to occur when integrating the motor back electromotive force; in addition, improper setting of the initial value of the integral will also affect the accuracy of the stator flux estimation. The usual solution is to use a first-order low-pass filter instead of a pure integrator, but it will cause an offset in the stator flux amplitude and phase angle, especially when the motor operating frequency is lower than the cutoff frequency of the filter, the distortion will become more serious. Although various strategies for distortion compensation have been studied and proposed, they are relatively complicated to implement. Although the use of a second-order generalized integrator and a frequency adaptive observer can eliminate the DC component in the stator flux estimation, both require accurate acquisition of the motor synchronous angular velocity.

[0006] Ohtani proposed a stator flux observer based on closed-loop feedback compensation, called a closed-loop (CL) stator flux observer, which compensates for the stator flux amplitude and phase by generating feedback gain through the error between the designed comparative flux and the estimated stator flux. The phase of the comparative flux in the CL model is the same as the phase of the stator flux estimate, while the amplitude can be set to multiple types. The comparative flux amplitude can be obtained based on the current model calculation, and the calculated stator flux can be used as the comparative flux amplitude after limiting, or the comparative flux amplitude can be obtained using a model reference adaptive system, and the stator flux reference value can also be directly used as the comparative flux amplitude. Unlike the first-order low-pass filter, the second-order generalized integrator and the frequency adaptive observer, the CL stator flux observer does not need to obtain the synchronous angular velocity of the motor to achieve distortion compensation, but due to the presence of a DC component in the motor back electromotive force, the CL stator flux observation is prone to offset problems, affecting the accuracy of the stator flux estimation. The stator flux estimation error is obtained by calculating the average value of the maximum and minimum stator flux detected in a cycle, and then used for compensation to improve the estimation accuracy of the stator flux. However, the closed-loop flux observer based on DC component compensation cannot completely eliminate the influence of the DC component on the stator flux observation accuracy.

[0007] In summary, for the DTC PMSM system, how to start from the two aspects of stator flux observation accuracy and direct torque control performance, and give a comprehensive consideration, while improving the stator flux observation accuracy, reducing the motor torque and stator flux steady-state pulsation, has become a key technical problem 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] Establish the SMPMSM dynamic equation based on stator field orientation: Use the conversion relationship between the coordinate systems to convert the torque reference value into the load angle reference value, decouple the motor torque control and flux control based on stator field orientation, and simplify the generation of the inverter reference voltage;

[0012] Design of stator flux observer based on improved voltage model: Design of stator flux observer based on improved voltage model, which consists of flux calculation and DC component elimination. The flux calculation uses low-pass filter to replace pure integrator, and compensates amplitude and phase through closed-loop feedback.

[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, the rotor position angle obtained by the rotor position sensor, and the inverter reference voltage is output based on the proposed direct torque cooperative control;

[0014] 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, 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 inverter reference voltage is adjusted by the optimization method to meet the voltage constraint conditions.

[0015] The establishment of the SMPMSM dynamic equation based on stator magnetic field orientation comprises 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 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 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 electrical 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 stator flux in α and β axis, i α and i β is the component of stator current in α and β axis, 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 stator voltage on x and y axis; i x 、i y is the component of stator current in x and y axis, R s is the stator resistance;

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

[0033] According to formula (5), the stator flux and load angle dynamic equation 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 realized based on stator magnetic field orientation, thereby 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 stator flux in α and β axis, i α and i β is the component of stator current in α and β axis, 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 cut-off 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 easy saturation of the pure integrator, and compensates the amplitude and phase 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 ψ of the feedback compensation 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 then 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 sc is ref ;

[0064] For the proposed direct torque cooperative control, ψ s |=ψ ref , so 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 that the DC component affects the accuracy of stator flux observation. In order to obtain a stator back electromotive force with constant 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 is 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 proportional to the integrator DC bias is derived from equation (50):

[0071]

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

[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 c (s), the steady-state frequency response is:

[0079]

[0080] Simplify the above equation and project it into the αβ coordinate system to 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 flux linkage ψ sc Components on the α and β axes.

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

[0087] Based on the stator flux observer based on the improved voltage model, the stator flux in the α and β axes is 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:

[0088]

[0089] Among them, ξ 1 is the stator flux tracking error, ξ 2 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 realize the tracking of stator flux and torque to stator flux reference value and torque reference value, the macro variable ψ is designed. 1 , 2 , and there are:

[0091]

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

[0093]

[0094] Among them, α 1 >0, β 1 >0, α 2 >0, β 2 >0,α 1 , β 1 They are the macro variables ψ 1 The proportional coefficient and integral coefficient, α 2 , β 2 They are the macro variables ψ 2 The proportional coefficient and integral coefficient of , T is the time constant of the designed dynamic evolution equation;

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

[0096]

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

[0098]

[0099] Among them, C 1 and C 2 is a constant;

[0100] From (29), we can see that no matter C 1 and C 2 The load angle tracking error and stator flux tracking error always converge to zero, and then by δ * 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 * are the components of the generated inverter reference voltage on the x-axis and y-axis, and δ are the stator flux and load angle output by the stator flux observer designed based on the improved voltage model.

[0109] The generating of the inverter reference voltage satisfying the 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 x-axis and y-axis components of the generated inverter reference voltage, h xn ,h yn and h cnare 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 represent the boundary equations of the inverter voltage vector hexagon, we have:

[0118]

[0119] Substituting 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 SVPWM strategy of the inverter, six PWM control signals are output to control the real-time operation of the inverter;

[0121] If the generated inverter reference voltage exceeds the boundary equation of the hexagon, a Lagrangian function is constructed, and the generated inverter reference voltage is adjusted by an optimization method to satisfy 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 satisfy the voltage constraint;

[0125] Then, the Lagrangian function is constructed using the boundary equation of the inverter hexagonal voltage vector as:

[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 a 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 simultaneous improvement of 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 It is a relationship diagram of each coordinate system of the present invention;

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

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

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

[0137] Figure 6 The 100rpm torque steady-state waveform diagram of the present invention, (a) is sliding mode control, (b) is cooperative control;

[0138] Figure 7 The 400rpm 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] Fig. 9 The steady-state waveform diagram of the electromagnetic torque of the example of the present invention under the condition of parameter mismatch, (a) is 0.8 times of the nominal permanent magnet flux, (b) is 0.9 times of the nominal stator inductance, and (c) is 1.4 times of the nominal stator resistance;

[0141] Fig.10 The steady-state waveform diagram of the electromagnetic torque of the example of the present invention under the condition of parameter mismatch, (a) is 0.8 times of the nominal permanent magnet flux, (b) is 0.9 times of the nominal stator inductance, and (c) is 1.4 times of the nominal stator resistance;

[0142] Fig.11 1 is a diagram of flux error of an example of the present invention, (a) is the α-axis flux observation error, (b) is the β-axis flux observation error;

[0143] Fig.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 have a further understanding and recognition of the structural features and the effects achieved by the present invention, a preferred embodiment and accompanying drawings are used for detailed description as follows:

[0145] like Figure 1 As shown, the present invention discloses a direct torque cooperative control method for a 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 equation based on stator field orientation: using the conversion relationship between the coordinate systems, the torque reference value is converted into the load angle reference value, the decoupling of motor torque control and flux control is realized based on stator field orientation, and the generation of 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 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 electrical angular velocity is ω s , the rotor electrical angular velocity is ω r .

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

[0150]

[0151] 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 stator flux in α and β axis, i α and i β is the component of stator current in α and β axis, R s is the stator resistance;

[0152] (3) Set the sub-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 stator voltage on x and y axis; i x 、i yis the component of stator current in x and y axis, R s is the stator resistance;

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

[0164] According to formula (5), the stator flux and load angle dynamic equation 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 magnetic flux amplitude of the permanent magnet of the permanent magnet synchronous motor rotor remains unchanged, and the magnetic flux amplitude of the stator remains unchanged, 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 realized based on stator magnetic field orientation, thereby simplifying the generation of inverter reference voltage.

[0177] The second step is to design a stator flux observer based on an improved voltage model: The stator flux observer based on an improved voltage model is designed, which consists of two parts: flux calculation and DC component elimination. The flux calculation uses a low-pass filter LPF to replace the pure integrator to eliminate the disadvantage of the pure integrator being easy to saturate, and compensates the amplitude and phase through closed-loop feedback. The influence of the DC component can be completely eliminated, and the torque control accuracy is effectively improved compared to the traditional voltage model.

[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 stator flux in α and β axis, i α and i β is the component of stator current in α and β axis, 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 cut-off frequency.

[0186] (2) The stator flux observer based on the improved voltage model is designed, which 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 easy to saturate, and 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 ψ of the feedback compensation 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 then 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 ref ;

[0195] For the proposed direct torque cooperative control, |ψ s |=ψ ref , so 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 stator flux.

[0198] (3) Regarding the stator back electromotive force e s There is a problem that the DC component affects the accuracy of stator flux observation. In order to obtain a stator back electromotive force with constant 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 is the stator back electromotive force, e cis 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 proportional to the integrator DC bias is derived from equation (81):

[0202]

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

[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 c (s), the steady-state frequency response is:

[0210]

[0211] Simplify the above equation and project it into the αβ coordinate system to 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 designed stator flux observer based on the improved voltage model is obtained as follows Figure 3 As shown, it consists of a stator back electromotive force sinusoidal component extraction module and a stator flux calculation module, and its αβ axis expression is:

[0215]

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

[0217] The third step is to realize the SMPMSM direct torque cooperative control 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 output by the stator flux observer based on the improved voltage model, the rotor position angle obtained by the rotor position sensor, and the inverter reference voltage is output based on the proposed direct torque cooperative control.

[0218] (1) Based on the stator flux observer based on the improved voltage model, the components of the stator flux 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, ξ 1 is the stator flux tracking error, ξ 2 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, the macro variable ψ is designed. 1 , 2 , and there are:

[0222]

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

[0224]

[0225] Among them, α 1 >0, β 1 >0, α 2 >0, β 2 >0,α 1 , β 1 They are the macro variables ψ 1The proportional coefficient and integral coefficient, α 2 , β 2 They are the macro variables ψ 2 The proportional coefficient and integral coefficient of , T is the time constant of the designed dynamic evolution equation;

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

[0227]

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

[0229]

[0230] Among them, C 1 and C 2 is a constant;

[0231] From (29), we can see that no matter C 1 and C 2 The load angle tracking error and stator flux tracking error always converge to zero, and then by δ * 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 * are the components of the generated inverter reference voltage on the x-axis and y-axis, and δ are the stator flux and load angle output by the stator flux observer designed based on the improved voltage model.

[0240] The fourth step is to 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 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 x-axis and y-axis components of the generated inverter reference voltage, h xn ,h yn and h cn are 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 represent 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 SVPWM strategy of the inverter, six PWM control signals are output to control the real-time operation of the inverter;

[0252] If the generated inverter reference voltage exceeds the boundary equation of the hexagon, a Lagrangian function is constructed, and the generated inverter reference voltage is adjusted by an optimization method to satisfy 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 satisfy the voltage constraint.

[0256] Then, the Lagrangian function is constructed using the boundary equation of the inverter hexagonal voltage vector as:

[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 of SMPMSM drive system was built based on dSPACE / DS1007. Figure 5 The motor under test is a 900W surface-mount permanent magnet synchronous motor, and its nominal parameters are shown in Table 1. The experiment uses a programmable DC power supply to power the inverter composed of MOSFET modules. The current sensor is LEM LA25-P, and the rotor position sensor is a single-pole rotary transformer. The power of the three-phase asynchronous motor is 2.2kW. As the dynamometer of the motor under test, it is driven by an ABB ACS800 series inverter and can operate in four quadrants. During the experiment, the SMPMSM works in torque control mode and the dynamometer runs 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 in the experiment are shown in Table 2.

[0265] Table 2 Test parameters

[0266]

[0267]

[0268] The proposed direct torque cooperative control (SDTC) method based on the improved voltage model to realize stator flux observation is experimentally tested for system speed step response and load torque step. Under the same experimental conditions, a comparative study on the control performance of the SMPMSM drive system with the sliding mode direct torque control (SMDTC) is carried out. The system experimental results and analysis are discussed as follows.

[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 100rpm by a dynamometer. The initial value of the torque reference is set to 0N.m, and then it is stepped to 5N.m in 1s. 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 100rpm torque steady-state waveform of SDTC.

[0272] The controlled SMPMSM is driven 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 phase a current during steady-state operation of SDTC. Figure 8 (b) is the a-phase power THD of SMDTC during steady-state operation. The experimental results show that the direct torque cooperative control based on the improved voltage model to realize stator flux observation does not have the jitter problem of sliding mode control, has lower steady-state torque ripple and enjoys lower steady-state current THD.

[0273] (2) Parameter robustness experiment

[0274] In order to test the robustness of direct torque cooperative control based on improved voltage model to realize stator flux observation, mismatch experiments of stator resistance, permanent magnet flux and stator inductance were carried out respectively. The experiment does not actually change the motor parameters, but makes corresponding parameter changes in the controller. The controlled SMPMSM is dragged to 100rpm by a dynamometer, and the initial value of the torque reference value is set to 0N.m, and it is stepped to 5N.m at 1s. The steady-state waveform of the electromagnetic torque under parameter mismatch is as follows Fig. 9 ,in Fig. 9 (a) is the steady-state waveform of the electromagnetic torque when the nominal permanent magnet flux is 0.8 times. Fig. 9 (b) is the steady-state waveform of the electromagnetic torque when the nominal stator inductance is 0.9 times. Fig. 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 driven to 400rpm by 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: Fig.10 ,in Fig.10 (a) is the steady-state waveform of the electromagnetic torque when the nominal permanent magnet flux is 0.8 times. Fig.10 (b) is the steady-state waveform of the electromagnetic torque when the nominal stator inductance is 0.9 times. Fig.10 (c) is the steady-state waveform of the electromagnetic torque when the nominal stator resistance is 1.4 times. According to the experimental waveform, the steady-state torque waveform of the direct torque cooperative control based on the improved voltage model to realize stator flux observation does not have a significant offset when the parameters change, and has a certain parameter robustness, and the steady-state torque pulsation is lower than that of the sliding mode direct torque control under nominal parameters.

[0276] (3) Stator flux observer performance verification

[0277] Based on the output of the stator flux observer 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: Fig.11 As shown, Fig.11 (a) is the α-axis stator flux observation error of different stator flux observation schemes, Fig.11(b) is the β-axis stator flux observation error of different stator flux observation schemes. It can be seen that the stator flux observation accuracy of the stator flux observation scheme realized by the proposed improved voltage model is more accurate. The traditional scheme is the 2015 IEEE document "Improved stator flux estimator for speed sensorless induction motor drives" ("Speed ​​sensorless control of asynchronous motors based on improved flux observer" - 2015 IEEE Journal of Power Electronics).

[0278] Fig.12 The torque, flux and current experimental waveforms are given when the proposed stator flux observer scheme is switched to the traditional scheme with the addition of a 0.5V DC component. From the experimental results, it can be found that the torque pulsation changes significantly before and after the switch, proving that the proposed direct torque cooperative control based on the improved voltage model to realize stator flux observation can better eliminate the influence of the DC component inevitably introduced in the current sampling process on the stator flux observation accuracy, and improve the 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 only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached 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 SMPMSM dynamic equation based on stator field orientation: Use the conversion relationship between the coordinate systems to convert the torque reference value into the load angle reference value, realize the decoupling of motor torque control and flux control based on stator field orientation, and simplify the generation of inverter reference voltage; 12) Design of stator flux observer based on improved voltage model: Design of stator flux observer based on improved voltage model, which consists of flux calculation and DC component elimination. The flux calculation uses low-pass filter to replace pure integrator, and compensates amplitude and phase through closed-loop feedback. 13) SMPMSM direct torque cooperative control based on improved flux observer: input torque reference value, stator flux reference value, stator flux output by stator flux observer based on improved voltage model, rotor position angle obtained by 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: 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 meet the voltage constraint.

2. According to claim 1, the direct torque cooperative control method of the SMPMSM drive system based on the improved voltage model to realize stator flux observation is characterized in that: The establishment of the SMPMSM dynamic equation based on stator magnetic field orientation comprises 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 electrical angular velocity is ω s , the rotor electrical angular velocity is ω r ; 22) The voltage equation of 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 stator flux in α and β axis, i α and i β is the component of stator current in α and β axis, 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 stator voltage on x and y axis; i x 、i y is the component of stator current in x and y axis, R s is the stator resistance; For a synchronously rotating xy coordinate system, we have According to formula (5), the stator flux and load angle dynamic equation 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 realized based on stator magnetic field orientation, thereby simplifying the generation of inverter reference voltage.

3. The direct torque cooperative control method of SMPMSM drive system based on 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 stator flux in α and β axis, i α and i β is the component of stator current in α and β axis, 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 cut-off 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 easy saturation of the pure integrator, and compensates the amplitude and phase 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 ψ of the feedback compensation 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 then 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 sc is ref ; For the proposed direct torque cooperative control, |ψ s |=ψ ref , so ψ s With ψ sc Equal, ψ s =ψ sc Substituting into formula (13) we get: And s =sψ s (16) The results of equation (17) are equal to those of equation (11), indicating that the designed improved voltage model can achieve accurate estimation of stator flux; 33) For the stator back electromotive force e s There is a problem that the DC component affects the accuracy of stator flux observation. In order to obtain a stator back electromotive force with constant 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 is 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 proportional to the integrator DC bias is derived from equation (19): Where d represents a signal proportional to the DC bias of the integrator; 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 c (s), the steady-state frequency response is: Simplify the above equation and project it into the αβ coordinate system to 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 designed stator flux observer 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: Among them, ψ scα and ψ scβ To compare the flux linkage ψ sc Components on the α and β axes.

4. The direct torque cooperative control method of SMPMSM drive system based on improved voltage model to realize stator flux observation according to claim 1 is characterized in that: The method of realizing SMPMSM direct torque cooperative control based on improved flux observer includes the following steps: 41) Based on the stator flux observer based on the improved voltage model, the components of the stator flux 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 δ * is the load angle reference value, δ is the load angle; 42) In order to realize the tracking of stator flux and torque for 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 macro variable ψ1, α2 and β2 are the proportional coefficient and integral coefficient of macro variable ψ2, and T is the time constant of the designed dynamic evolution equation; Combining equation (28), equation (29) and equation (27), we get: The solution of equation (28) is: Among them, C1 and C2 are constants; From (29), we can see that no matter what the values ​​of C1 and C2 are, 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 * are the components of the generated inverter reference voltage on the x-axis and y-axis, and δ are the stator flux and load angle output by the stator flux observer designed based on the improved voltage model.

5. The direct torque cooperative control method of SMPMSM drive system based on 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 on the x-axis and y-axis components, h xn ,h yn and h cn are 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 represent the boundary equations of the inverter voltage vector hexagon, we have: 52) Substituting 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 SVPWM strategy of the inverter, six PWM control signals are output to control the real-time operation of the inverter; If the generated inverter reference voltage exceeds the boundary equation of the hexagon, a Lagrangian function is constructed, and the generated inverter reference voltage is adjusted by an optimization method to satisfy 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 satisfy the voltage constraint; Then, the Lagrangian function is constructed using the boundary equation of the inverter hexagonal voltage vector as: 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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