A deadbeat predictive control method for permanent magnet synchronous motor based on super-spiral sliding mode extended observer

Abstract

The application provides a kind of permanent magnet synchronous motor deadbeat prediction control method based on super-spiral sliding mode extended observer, which first designs a sliding mode observer based on super-spiral theory to estimate unknown disturbances such as parameter perturbation, then designs an extended state observer to estimate disturbances twice, and compensates the estimated values of the two disturbances to the predicted current and output voltage, respectively, to achieve high-precision and robust current control and improve the dynamic and static performance of the control system. Compared with traditional deadbeat prediction control, the application has the advantages of high robustness, low parameter sensitivity, good dynamic performance and no static error.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of surface-mounted permanent magnet synchronous motor dead-beat predictive current control, and particularly relates to a permanent magnet synchronous motor dead-beat predictive control method based on a super-spiral sliding mode extended observer. BACKGROUND

[0002] Since the stator current of the permanent magnet synchronous motor is directly related to the motor torque, great importance is attached to the dynamic and steady-state response of the stator current in motor control. In order to improve the current loop performance, the existing technology mainly adopts hysteresis current control, direct torque control, sliding mode control and current predictive control strategies. The dead-beat predictive control has the advantages of fast response speed and good followability among many strategies, and is more commonly used at present. However, the actual effect is greatly affected by the accuracy of motor parameters, torque, speed, temperature and other factors during motor operation, resulting in poor control precision. Therefore, there is an urgent need in the field for an improved dead-beat current control method which is not sensitive to motor parameters and has high precision. SUMMARY

[0003] Therefore, in view of the technical problems existing in the field, the application provides a permanent magnet synchronous motor dead-beat predictive control method based on a super-spiral sliding mode extended observer, which specifically comprises the following steps:

[0004] Step one, for the surface-mounted permanent magnet synchronous motor, the influence of space harmonics, hysteresis loss, eddy current loss, core loss and temperature frequency factors on motor parameters is ignored, and the d and q axis voltage equations containing disturbances caused by parameter changes are established in the synchronous rotating coordinate system;

[0005] Step two, a super-spiral sliding mode observer is established by using the voltage equation established in step one and combining the super-spiral theory for one-step-ahead prediction and first estimation of disturbances; the actual current is replaced by the observed current in the voltage equation, and the sliding surface, sliding mode control law and sliding mode control function of the super-spiral sliding mode disturbance observer are designed; on this basis, the current of the d and q axes is taken as the state variable, and the control voltage of the d and q axes is taken as the input quantity to obtain the current equation of the super-spiral sliding mode observer; the first-order forward difference discretization processing is performed on the current equation and the sliding mode control function respectively;

[0006] Step three, a double observer is composed of the super-spiral sliding mode observer and the extended observer, and the double observer current equation after the first-order forward difference discretization processing is used to perform second estimation on the d and q axis currents and disturbances;

[0007] Step four, the d and q axis currents obtained by the double observer and the disturbance observation values estimated twice are used to realize one-step-delay feedforward compensation on the control voltage in combination with the sliding mode control function to obtain the final current loop output voltage.

[0008] Further, the d, q-axis voltage equations of the following form are established in step one:

[0009]

[0010] where u d , u q , i d , i q are the d, q-axis voltages and stator currents, R is the stator resistance, L is the d, q-axis stator inductance, ω e is the electrical angular velocity, ψ f is the permanent magnet flux linkage, and the superscript · denotes the differential of the corresponding parameter;

[0011] The voltage equations are extended by considering the disturbances caused by the temperature variation, magnetic saturation, cross-coupling, internal unmodeled and external unknown disturbance factors, to obtain the following voltage equations containing disturbances:

[0012]

[0013] where f d and f q are the d, q-axis disturbances, F d and F q are the rates of change of the disturbances f d and f q .

[0014] Further, the super-spiral sliding mode disturbance observer of the following form is established in step two:

[0015]

[0016] where the superscript o denotes the observed value of the corresponding parameter, U sd and U sq are the d, q-axis sliding mode control functions, g d and g q are the d, q-axis sliding mode control coefficients.

[0017] The d, q-axis currents i d and i q are taken as the control variables, and the linear sliding mode switching surface s = i o -i is designed.

[0018] The voltage equations containing disturbances and the super-spiral sliding mode disturbance observer are combined to obtain the following error equations of the permanent magnet synchronous motor system:

[0019]

[0020] Wherein, e1 and e2 are respectively the current observation error of d, q axis, e3 and e4 are respectively the disturbance observation error of d, q axis, each error term is respectively:

[0021]

[0022] On this basis, the d, q axis sliding mode control law is designed as:

[0023]

[0024] In order to compensate the d, q axis disturbance observation error e1 and e2 to make it converge to 0, the sliding mode control function is designed as:

[0025]

[0026] On this basis, the following superhelix sliding mode observer current equation is obtained:

[0027]

[0028] After first-order forward difference, the following discrete form is obtained:

[0029]

[0030] Wherein, The observation value of d, q axis current at the k time and k+1 time is respectively, The observation value of d, q axis disturbance at the k time and k+1 time is respectively;

[0031] The discrete sliding mode control function and current observation error form are as follows:

[0032]

[0033] Further, the specific form of the double observer current equation established in step three is as follows:

[0034]

[0035] Wherein, the superscript ∧ represents the second estimation of the corresponding parameter;

[0036] After first-order forward difference, the following discrete form is obtained:

[0037]

[0038] Wherein, c1 and c2 are respectively the extended observer parameters.

[0039] Further, the d, q axis current and disturbance observation value at the k time obtained by the double observer in step four are combined with the sliding mode control function to calculate the d, q axis voltage at the k+1 time.

[0040]

[0041] The super-helix sliding mode extended observer-based permanent magnet synchronous motor deadbeat predictive control method provided by the application has the advantages of high robustness, low parameter sensitivity, good dynamic performance, no static error and the like. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 A flowchart of the method provided by the application is shown in the figure.

[0043] Figure 2 A comparison chart of the test results of the traditional deadbeat predictive control DPCC modulation and the method provided by the application under the motor parameter mismatch and mismatch working conditions is shown in the figure. DETAILED DESCRIPTION

[0044] The technical solutions of the application will be described clearly and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only some of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the application.

[0045] The super-helix sliding mode extended observer-based permanent magnet synchronous motor deadbeat predictive control method provided by the application has the advantages of high robustness, low parameter sensitivity, good dynamic performance, no static error and the like. Figure 1 As shown in the figure, the method specifically includes the following steps.

[0046] Step 1: For the surface-mounted permanent magnet synchronous motor, the influence of spatial harmonics, hysteresis loss, eddy current loss, core loss and temperature frequency factors on motor parameters is ignored, and d and q axis voltage equations containing disturbances caused by parameter changes are established in the synchronous rotating coordinate system.

[0047] Step 2: The voltage equation established in step 1 is used to establish a super-helix sliding mode observer for one-step prediction and one-time disturbance estimation combined with the super-helix theory. In the voltage equation, the observed current is used to replace the actual current, and the sliding surface, sliding control law and sliding control function of the super-helix sliding mode disturbance observer are designed. On this basis, the currents in the d and q axes are taken as state variables, and the control voltages in the d and q axes are taken as input quantities to obtain the current equation of the super-helix sliding mode observer. The first-order forward difference discretization processing is performed on the current equation and the sliding control function, respectively.

[0048] Step three, on the basis of the super spiral sliding mode observer, a double observer is introduced by introducing an extended observer, and the double observer current equation after first-order forward difference discretization processing is used to estimate the d, q axis currents and the disturbance twice;

[0049] Step four, using the d, q axis currents and the twice estimated disturbance observation values obtained by the double observer, combining the sliding mode control function to realize one beat delay feedforward compensation for the control voltage, and obtaining the final current loop output voltage.

[0050] In a preferred embodiment of the application, the d, q axis voltage equation of the following form is established in step one:

[0051]

[0052] Wherein, u d , u q , i d , i q are the d, q axis voltages and stator currents, R is the stator resistance, L is the d, q axis stator inductance value, ω e is the electrical angular velocity, ψ f is the permanent magnet flux, and the superscript · is the differential of the corresponding parameter.

[0053] Considering the disturbance caused by the change of motor parameters with temperature, magnetic saturation, cross coupling, internal unmodeled and external unknown interference factors, the voltage equation is extended to obtain the following voltage equation containing disturbance:

[0054]

[0055] Wherein, f d and f q are the d, q axis disturbances, F d and F q are the change rates of the disturbances f d and f q .

[0056] In a preferred embodiment of the application, the super spiral sliding mode disturbance observer of the following form is established in step two:

[0057]

[0058] Wherein, the superscript o represents the observation value of the corresponding parameter, U sd and U sq are the d, q axis sliding mode control functions, g d and g q are the d, q axis sliding mode control coefficients.

[0059] The d, q axis currents i dand i q As a control variable, a linear sliding mode switching surface s = i o -i;

[0060] The voltage equation containing disturbance and the super-spiral sliding mode disturbance observer are combined to obtain the following error equation of the permanent magnet synchronous motor system:

[0061]

[0062] Wherein, e1 and e2 are the current observation errors of d and q axes respectively, e3 and e4 are the disturbance observation errors of d and q axes respectively, and each error term is:

[0063]

[0064] The super-spiral sliding mode observer can reduce the high-frequency oscillation of the output signal and suppress the chattering effect, so the sliding mode control law of d and q axes is designed respectively based on this:

[0065]

[0066] In order to compensate the disturbance observation errors e1 and e2 of d and q axes to make them converge to 0, the sliding mode control function is designed as:

[0067]

[0068] On this basis, the following current equation of the super-spiral sliding mode observer is obtained:

[0069]

[0070] After first-order forward difference, the following discrete form is obtained:

[0071]

[0072] Wherein, e1(k) and e2(k) are the observation values of d and q axes currents at the kth moment respectively, e3(k) and e4(k) are the observation values of d and q axes disturbances at the kth moment respectively;

[0073] The discrete sliding mode control function and the current observation error form are as follows:

[0074]

[0075] In one preferred embodiment of the present application, the double-observer current equation established in step three has the following specific form:

[0076]

[0077] Wherein, the superscript ∧ represents the second estimation of the corresponding parameter;

[0078] The first-order forward difference thereof obtains the following discrete form:

[0079]

[0080] Wherein, c1 and c2 are respectively expansion observer parameters.

[0081] In a preferred embodiment of the present application, the d-axis and q-axis currents and disturbance observation values at the kth moment obtained by the double observer in step four are combined with the sliding mode control function to calculate the d-axis and q-axis voltages at the k+1th moment:

[0082]

[0083] In a specific example of the present application, simulation tests are carried out based on the control framework shown in Figure 1 Under the condition that the speed reference is 1500 rpm and a load jump disturbance is suddenly added at 0.05 seconds, the traditional deadbeat predictive current control method and the method provided by the present application are respectively used for control simulation, and finally the comparison results are as follows:

[0084] Please see Figure 2 (a) and Figure 2 (b), which respectively show the d-axis and q-axis currents of the two control methods under the condition that the motor parameters (including inductance, resistance, flux linkage) and control parameters exist 1.5 times mismatch. It can be seen that the q-axis current using the traditional deadbeat predictive control method appears overshoot, and there is a steady-state error with the target current; the q-axis current using the deadbeat predictive control method based on the cascaded disturbance state observer has no overshoot phenomenon, and there is no static error between the d-axis and q-axis currents and the target current; the q-axis current of the method of the present application has better followability to the target current, the control strategy has lower sensitivity to the motor model parameters, and has better robustness.

[0085] It should be understood that the size of the serial number of each step in the embodiments of the present application does not mean the order of execution, and the execution order of each process should be determined according to its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0086] Although the embodiments of the present application have been shown and described, it can be understood by those of ordinary skill in the art that various changes, modifications, replacements and variations can be made to these embodiments without departing from the principles and spirits of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A deadbeat predictive control method for permanent magnet synchronous motors based on a superspiral sliding mode expansion observer, characterized in that: Specifically, it includes the following steps; Step 1: Ignoring the effects of spatial harmonics, hysteresis loss, eddy current loss, core loss, and temperature and frequency factors on the parameters of the surface-mounted permanent magnet synchronous motor, establish the d-axis and q-axis voltage equations in the synchronous rotating coordinate system, which include the disturbances caused by parameter changes. Step 2: Using the voltage equation established in Step 1 and combined with the superhelical theory, a superhelical sliding mode observer is established for leading-one-beat prediction and first-order estimation of disturbances. The observed current is replaced with the actual current in the voltage equation, and the sliding surface, sliding mode control law, and sliding mode control function of the superhelical sliding mode disturbance observer are designed. Based on this, the current equation of the superhelical sliding mode observer is obtained with the d-axis and q-axis currents as state variables and the d-axis and q-axis control voltages as inputs. The current equation and the sliding mode control function are respectively subjected to first-order forward differential discretization. Step 3: Based on the superhelical sliding mode observer, an extended observer is introduced to form a dual observer. The specific form of the current equation for the dual observer is as follows: Among them, u d u q i d i q These represent the voltage and stator current along the d and q axes, respectively; R is the stator resistance; L is the stator inductance along the d and q axes; and ω... e It is the electric angular velocity, ψ f For permanent magnet flux linkage, f d and f q Let U represent the perturbations along the d and q axes, respectively. The superscript · indicates the derivative of the corresponding parameter, the superscript ∧ indicates the quadratic estimate of the corresponding parameter, and the superscript o indicates the observed value of the corresponding parameter. sd and U sq c1 and c2 are the sliding mode control functions for the d and q axes, respectively, and the extended observer parameters are c1 and c2, respectively. The d-axis current and disturbance are estimated twice using the dual-observer current equation after first-order forward differential discretization. Step 4: Using the d-axis and q-axis currents obtained from the dual observers and the two estimated disturbance observations, the control voltage is compensated for with a one-step delay feedforward using the sliding mode control function to obtain the final current loop output voltage.

2. The method as described in claim 1, characterized in that: In step one, the following forms of d-axis and q-axis voltage equations are established: Among them, u d u q i d i q These represent the voltage and stator current along the d and q axes, respectively; R is the stator resistance; L is the stator inductance along the d and q axes; and ω... e It is the electric angular velocity, ψ f For permanent magnet flux linkage, the superscript · indicates the derivative of the corresponding parameter; Considering the disturbances to motor parameters caused by temperature changes, magnetic saturation, cross-coupling, unmodeled internal components, and unknown external interference factors, the voltage equations are extended to obtain the following voltage equations that include the disturbances: Among them, f d and f q The disturbances on the d and q axes are respectively, F d and F q The disturbances f are respectively d and f q The rate of change.

3. The method as described in claim 2, characterized in that: Step two specifically establishes the following type of superhelical sliding mode perturbation observer: Where the superscript o represents the observed value of the corresponding parameter, U sd and U sq The sliding mode control functions for the d and q axes are respectively, g d and g q These are the sliding mode control coefficients for the d and q axes, respectively; The d-axis and q-axis currents i d and i q As a control variable, design a linear sliding mode switching surface: s = i o -i; By combining the voltage equations containing the disturbance with the super-helical sliding mode disturbance observer, the following error equations for the permanent magnet synchronous motor system are obtained: Where e1 and e2 are the current observation errors of the d and q axes, respectively, and e3 and e4 are the disturbance observation errors of the d and q axes, respectively. The error terms are as follows: Based on this, the sliding mode control laws for the d and q axes are designed as follows: To compensate for the disturbance observation errors e1 and e2 along the d and q axes and bring them to converge to zero, the sliding mode control function is designed as follows: Based on this, the following current equation for the superspiral sliding mode observer is obtained: After its first-order forward difference, we obtain the following discretized form: in, These are the observed values ​​of the d-axis and q-axis currents at time k and time (k+1), respectively. These are the observed values ​​of the d-axis and q-axis perturbations at time k and time k+1, respectively. The discretized sliding mode control function and the current observation error are in the following forms:

4. The method as described in claim 3, characterized in that: In step three, the dual-observer current equations are discretized using a first-order forward difference to obtain the following discretized form: Where c1 and c2 are the extended observer parameters, respectively.

5. The method as described in claim 4, characterized in that: In step four, the d-axis and q-axis currents at time k obtained from the dual observers, along with the disturbance observations, are combined with the sliding mode control function to calculate the d-axis and q-axis voltages at time k+1.

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