CN106208864A - A kind of senseless control system based on SMO - Google Patents

Abstract

The invention discloses a kind of senseless control system based on SMO, including inverter unit, PMSM unit, oneth Clark converter unit, Park converter unit, 2nd Clark converter unit, sliding mode observer unit, first comparator unit, oneth PI regulates unit, second comparator unit, 2nd PI regulates unit, 3rd comparator unit, 3rd PI regulates unit, Park inverse transformation unit and SVPWM unit, position and the spinner velocity of rotor is detected by a kind of sliding mode observer being prone to Project Realization, set up the sliding formwork gain relation with estimation counter electromotive force to reduce system chatter, sliding mode observer in the present invention is in the case of rotating speed sudden change and load changing, rotating speed and the corner change of motor can be followed the tracks of in time and accurately.The present invention has that precise control is high, and dynamic property is good, the feature of strong robustness, additionally, also have that low cost, control algolithm be simple, rotating speed and the estimated speed of position and precision advantages of higher.

Description

SMO-based speed sensorless control system

Technical Field

The invention relates to the technical field of speed measurement without a speed sensor, in particular to a control system without a speed sensor based on SMO (simple message order) and a method thereof.

Background

A Permanent Magnet Synchronous Motor (PMSM for short) has the advantages of high power density, high energy conversion efficiency, wide speed regulation range, small volume, light weight and the like, and is widely applied to the fields of industry, civil use, military and the like.

The control of the permanent magnet synchronous motor needs to obtain the position and speed information of a motor rotor, the position sensor which is commonly applied at present comprises a photoelectric encoder, a rotary transformer and other devices, the use of the devices not only increases the volume and the cost of a system and reduces the reliability of the system, but also limits the application of the permanent magnet synchronous motor in special environments, and in order to solve many defects brought by mechanical sensors, the research of a sensorless control technology becomes a research hotspot at home and abroad and obtains certain results, but also has many problems. Most importantly, there is currently no single sensorless technology that can be adapted to effectively control an electric motor under a variety of operating conditions. In the prior art, the method is suitable for low-speed operation or high-speed operation, or is greatly influenced by motor parameters, or has large calculated amount, complex structure or poor stability.

When the motor runs in a medium-high speed range, the sensorless control method based on the sliding-mode observer is widely applied. The method firstly observes the back electromotive force of the motor by constructing a sliding mode observer, and then directly or indirectly estimates the position and the speed of the rotor from the back electromotive force, and has the characteristics of simple principle, good stability and the like.

Disclosure of Invention

In order to overcome the problems that the principle of the existing method for estimating the rotor angle and the rotating speed of the permanent magnet synchronous motor based on the speed sensorless is complex, the calculated amount is large, the dynamic characteristic of the whole system is reduced due to the slow dynamic characteristic, and even the system is unstable, the speed sensorless control system based on the SMO, which has high dynamic performance and is easy to realize in engineering, is particularly provided.

In order to achieve the above purpose, the technical solution for solving the technical problem is as follows:

a SMO-based speed sensorless control system comprises an inverter unit, a PMSM unit, a first Clark conversion unit, a Park conversion unit, a second Clark conversion unit, a sliding mode observer unit, a first comparator unit, a first PI adjusting unit, a second comparator unit, a second PI adjusting unit, a third comparator unit, a third PI adjusting unit, a Park inverse conversion unit and an SVPWM unit, wherein:

the PMSM unit is used for detecting and outputting three-phase current I_a、I_bAnd I_c；

The first Clark conversion unit is used for converting the three-phase current I output by the PMSM unit_a、I_bAnd I_cOutputting two-phase stator current i under a two-phase static rectangular coordinate system α - β after Clark conversion_αAnd i_β；

The Park conversion unit is used for converting the two-phase stator current i output by the first Clark conversion unit_αAnd i_βAfter being converted by Park, the two-phase current I under the two-phase synchronous rotating coordinate system d-q is output_dAnd I_q；

The second Clark conversion unit is used for converting the three-phase voltage U output by the inverter unit_a、U_bAnd U_cAfter Clark conversion, two-phase stator voltage u under a two-phase static rectangular coordinate system α - β is output_αAnd u_β；

The sliding mode observer unit is used for converting the two-phase stator current i output by the first Clark conversion unit_αAnd i_βAnd the two-phase stator voltage u output by the second Clark conversion unit_αAnd u_βPerforming estimation processing to estimate the estimated value of the rotor speedAnd an estimate of rotor position

The first comparator unit is used for estimating the estimated value of the rotor rotating speed in the sliding mode observer unitMultiplying by a constant to obtain an estimated rotor rotationSpeed n, and performing difference operation on the estimated rotor speed n and the actual rotor speed n;

the first PI adjusting unit is used for outputting q-axis reference current after the difference value compared by the first comparator unit is subjected to PI adjustment

The second comparator unit is used for outputting the q-axis reference current after being regulated by the first PI regulation unitAnd the two-phase current I output by the Park conversion unit_qPerforming difference operation;

the second PI regulating unit is used for regulating the difference value compared by the second comparator unit through PI and outputting a q-axis reference voltage

The third comparator unit for referencing a d-axis currentAnd the current I output by the Park conversion unit_dPerforming difference operation;

the third PI regulating unit is used for regulating the difference value compared by the third comparator unit through PI and outputting d-axis reference voltage

The Park inverse transformation unit is used for converting the q-axis reference voltage output by the second PI regulating unitAnd a d-axis reference voltage output by the third PI regulation unitOutputting two-phase control voltage under a two-phase static rectangular coordinate system α - β after Park inverse transformationAnd

the SVPWM unit is used for controlling two phases of voltageAndperforming space vector pulse width modulation, outputting PWM waveform to the inverter unit, and inputting three-phase voltage U to the PMSM unit by the inverter unit_a、U_bAnd U_cThereby controlling the PMSM unit.

Specifically, the sliding-mode observer unit specifically includes an SMO optimization algorithm subunit, a fourth comparator subunit, a switching function calculation subunit, a low-pass filter subunit, a rotation speed estimation subunit, a position compensation subunit, a position estimation subunit, and a summation unit, where: :

the SMO optimization algorithm subunit is used for converting the two-phase stator voltage u output by the second Clark conversion unit_αAnd u_βAnd the back electromotive force e output after being processed by the switching function calculation subunit_αAnd e_βOutput current estimated value calculated by SMO optimization algorithmAnd

the fourth comparator subunit is used for optimizing the SMOEstimation value of current output by legal unitAndand the two-phase stator current i output by the first Clark conversion unit_αAnd i_βPerforming a difference operation to obtain αβ axis current error valueAnd

the switching function calculating subunit is used for calculating the current error value on the αβ axis output by the fourth comparator subunitAndobtaining back electromotive force e after the operation processing of the switching function_αAnd e_β；

The low-pass filter subunit is used for processing the back electromotive force e output by the switching function calculation subunit_αAnd e_βObtaining a back electromotive force estimated value estimated by the sliding mode observer after low-pass filteringAnd

the rotating speed estimation subunit is configured to perform low-pass filtering on the low-pass filter subunit to obtain a low-pass filtered back electromotive force estimation valueAndobtaining an estimate of rotor speed by speed estimation

The position estimation subunit is configured to perform low-pass filtering on the low-pass filter subunit to obtain a low-pass filtered back electromotive force estimation valueAndobtaining estimated value before rotor position uncompensation through position estimation

The position compensation subunit is used for obtaining a phase compensation quantity after Kalman filtering by performing lag compensation on the phase

The summation unit is used for estimating the estimated value of the rotor position obtained by the position estimation subunit before uncompensationAnd the phase compensation quantity obtained by the position compensation subunitSumming to obtain the estimated value of the rotor position

As an embodiment, the SMO optimization algorithm in the SMO optimization algorithm subunit specifically includes the following calculation steps:

firstly, establishing a mathematical model of the alternating current permanent magnet synchronous motor in a two-phase static rectangular coordinate system alpha-beta:

$\stackrel{\·}{i_{\mathrm{\α}}}=-\frac{R_s}{L_s}{i}_{\mathrm{\α}}-\frac{1}{L_s}{e}_{\mathrm{\α}}+\frac{u_{\mathrm{\α}}}{L_s}---\left(1\right)$

$\stackrel{\·}{i_{\mathrm{\β}}}=-\frac{R_s}{L_s}{i}_{\mathrm{\β}}-\frac{1}{L_s}{e}_{\mathrm{\β}}+\frac{u_{\mathrm{\β}}}{L_s}---\left(2\right)$

wherein,is the current value i of the current i on the α axis_αThe derivative of (a) of (b),is the current value i of the current i on the β axis_βDerivative of (A), R_SIs stator winding resistance, Ls is equivalent inductance, e_αBack EMF on α axis for sliding mode observer, e_βFor the back EMF of the sliding-mode observer on the β axis_αIs the voltage value of voltage U on α axis_βIs the voltage value of the voltage U on the β axis;

next, the back emf equation is substituted:

e_α＝-ψ_fω_rsinθ (3)

e_β＝ψ_fω_rcosθ (4)

wherein psi_fFlux linkage, omega, produced for permanent magnets on the rotor_rFor synchronous speed, θ is the rotor angular position;

furthermore, an SMO optimization calculation equation of the alternating current permanent magnet synchronous motor in a two-phase static rectangular coordinate system alpha-beta is as follows:

$\stackrel{\·}{\widehat{i_{\mathrm{\α}}}}=-\frac{R_s}{L_s}\widehat{i_{\mathrm{\α}}}+\frac{u_{\mathrm{\α}}}{L_s}-\frac{k}{L_s}sign(\widehat{i_{\mathrm{\α}}}-i_{\mathrm{\α}})---\left(5\right)$

$\stackrel{\·}{\widehat{i_{\mathrm{\β}}}}=-\frac{R_s}{L_s}\widehat{i_{\mathrm{\β}}}+\frac{u_{\mathrm{\β}}}{L_s}-\frac{k}{L_s}sign(\widehat{i_{\mathrm{\β}}}-i_{\mathrm{\β}})---\left(6\right)$

wherein,are respectively i_α、i_βK is the sliding mode switching gain;

finally, from the above available current estimation error equation:

$\stackrel{\·}{\widetilde{i_{\mathrm{\α}}}}=-\frac{R_s}{L_s}\widetilde{i_{\mathrm{\α}}}+\frac{e_{\mathrm{\α}}}{L_s}-\frac{k}{L_s}sat\left(\widetilde{i_{\mathrm{\α}}}\right)---\left(7\right)$

$\stackrel{\·}{\widetilde{i_{\mathrm{\β}}}}=-\frac{R_s}{L_s}\widetilde{i_{\mathrm{\β}}}+\frac{e_{\mathrm{\β}}}{L_s}-\frac{k}{L_s}sign\left(\widetilde{i_{\mathrm{\β}}}\right)---\left(8\right)$

wherein,is the current error value on the α axis,is the current error value on the β axis.

As an embodiment, the current error value in the fourth comparator subunitAndthe calculation equation of (a) is:

$\widetilde{i_{\mathrm{\α}}}={\hat{i}}_{\mathrm{\α}}-i_{\mathrm{\α}}---\left(9\right)$

$\widetilde{i_{\mathrm{\β}}}={\hat{i}}_{\mathrm{\β}}-i_{\mathrm{\β}}---\left(10\right)$

wherein,and i_αFor the current error value on axis α, the current estimate value and the current value,and i_βCurrent error value, current estimate value and current value on axis β.

As an embodiment, the switching function calculates a back electromotive force e in the subcell_αAnd e_βRespectively comprises the following steps:

firstly, a sign switching function is selected to perform switching function operation, namely:

$sign=\left\{\begin{array}{cc}1& x>0\\ -1& x<0\end{array}\right.---\left(11\right)$

secondly, selecting a Lyapunov function:

$V=\frac{1}{2}{\widetilde{i_{\mathrm{\&alpha;}}}}^2+\frac{1}{2}{\widetilde{i_{\mathrm{\&beta;}}}}^2---\left(12\right)$

derivative of V when k>max(|e_α|,|e_βIf | thenV is more than 0, the current sliding mode observer is stable according to the Lyapunov stability theorem, the current error is selected as the sliding mode switching surface, and when the sliding mode enters the sliding modeWhen there isAndwhen the temperature of the water is higher than the set temperature,

$e_{\mathrm{\&alpha;}}=ksign\left(\widetilde{i_{\mathrm{\&alpha;}}}\right)---\left(13\right)$

$e_{\mathrm{\&beta;}}=ksign\left(\widetilde{i_{\mathrm{\&beta;}}}\right)---\left(14\right)$

wherein e is_αAnd e_βIs the back electromotive force of the sliding-mode observer,is the current error value on the α axis,for the current error value on the β axis, k is the sliding mode switching gain.

As an embodiment, theObtaining the back electromotive force estimated value estimated by the sliding mode observer through the low-pass filter in the low-pass filter subunitAndthe calculation process of (2) includes:

using a low-pass filter, the discontinuous switching signal is converted into an equivalent continuous signal, and the corresponding calculation formula is as follows:

${\hat{e}}_{\mathrm{\&alpha;}}=\frac{{\mathrm{\&omega;}}_c}{s+{\mathrm{\&omega;}}_c}{e}_{\mathrm{\&alpha;}}---\left(15\right)$

${\hat{e}}_{\mathrm{\&beta;}}=\frac{{\mathrm{\&omega;}}_c}{s+{\mathrm{\&omega;}}_c}{e}_{\mathrm{\&beta;}}---\left(16\right)$

wherein,andestimated back electromotive force, ω, for sliding mode observer estimation_cIs the cut-off frequency of the low-pass filter, s is the Laplace operator, e_αAnd e_βIs the back electromotive force of the sliding mode observer.

As an embodiment, the estimation value of the low-pass filtered rotor speed in the speed estimation subunit is obtained by the following formula:

$\widehat{\mathrm{\&omega;}}=\frac{\sqrt{{\widehat{e_{\mathrm{\&alpha;}}}}^2+{\widehat{e_{\mathrm{\&beta;}}}}^2}}{{\mathrm{\&psi;}}_f}---\left(17\right)$

wherein,in order to estimate the rotational speed of the rotor,andback electromotive force, psi, estimated for sliding mode observer_fThe flux linkage generated by the permanent magnets on the rotor.

As an embodiment, the estimate of the low-pass filtered rotor position in the position estimation subunit is obtained by the following formula:

$\widehat{{\mathrm{\&theta;}}_c}=-\arctan \left(\frac{\widehat{e_{\mathrm{\&alpha;}}}}{\widehat{e_{\mathrm{\&beta;}}}}\right)---\left(18\right)$

wherein,for the estimation of the position of the rotor,andback emf estimated for a sliding mode observer.

As an embodiment, in the position compensation subunit, because of the use of the low-pass filter, the phase has a certain hysteresis, and the phase needs to be compensated for with the hysteresis, and the phase compensation amount after kalman filtering is:

$\mathrm{\&Delta;}\widehat{\mathrm{\&theta;}}=-\arctan \left(\frac{\mathrm{\&omega;}}{{\mathrm{\&omega;}}_c}\right)---\left(19\right)$

wherein,is the phase compensation quantity, omega is the rotation speed at steady state, omega_cThe cut-off frequency of the low-pass filter.

Due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages and positive effects:

1. the SMO-based speed sensorless control system has robustness to uncertain factors such as system disturbance, parameter perturbation and the like, so that sensorless control of the permanent magnet synchronous motor can be better realized;

2. the sliding mode observer can timely and accurately track the rotation speed and the rotation angle change of the motor under the conditions of rotation speed mutation and load mutation, has the characteristics of high control accuracy, good dynamic performance and strong robustness, is relatively convenient to implement on hardware and software, and has certain practicability;

3. according to the invention, the state estimation is realized by adopting the sliding-mode observer, so that the estimation accuracy of the position and the speed of the rotor is obviously improved;

4. the invention has the advantages of low cost, simple control algorithm, high speed and precision of estimation of the rotating speed and the position, and the like.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. In the drawings:

FIG. 1 is a movement process diagram of a sliding mode variable structure control system in an SMO-based speed sensorless control system according to the invention;

FIG. 2 is a block diagram of a non-speed sensor control system based on SMO according to the present invention;

FIG. 3 is a structure diagram of a sliding mode observer in a SMO-based speed sensorless control system according to the present invention;

FIG. 4 is a diagram of a sliding mode observer package subunit in an SMO-based non-speed sensor control system according to the present invention;

FIG. 5 is a system simulation diagram corresponding to an SMO-based speed sensorless control system of the present invention;

FIG. 6 is a diagram of a sudden change in rotational speed waveform in an SMO-based sensorless control system of the present invention;

FIG. 7 is a plot of a speed flare waveform in an SMO-based speed sensorless control system of the present invention;

FIG. 8 is a torque ramp speed waveform in an SMO based speed sensorless control system of the present invention;

fig. 9 is a waveform of a torque jump angle in an SMO based speed sensorless control system of the present invention.

[ Main symbol Mark ]

1-an inverter unit;

2-PMSM unit;

3-a first Clark transformation unit;

4-Park transformation unit;

5-a second Clark transformation unit;

6-sliding mode observer unit;

7-a first comparator unit;

8-a first PI regulation unit;

9-a second comparator unit;

10-a second PI regulation unit;

11-a third comparator unit;

12-a third PI regulation unit;

13-Park inverse transformation unit;

14-SVPWM unit;

61-SMO optimization algorithm subunit;

62-a fourth comparator subunit;

63-a switch function calculation subunit;

64-a low-pass filter subunit;

65-a rotational speed estimation subunit;

66-a position compensation subunit;

67-a location estimation subunit;

68-summing unit.

Detailed Description

While the embodiments of the present invention will be described and illustrated in detail with reference to the accompanying drawings, it is to be understood that the invention is not limited to the specific embodiments disclosed, but is intended to cover various modifications, equivalents, and alternatives falling within the scope of the invention as defined by the appended claims.

Referring to fig. 1, considering now the general situation in the present patent, there is a switching plane s (x)₁,x₂,···,x_n) 0, which converts x ═ f (x) (x ∈ R)ⁿ) The state space of this system is divided into an upper and a lower part s>0 and s<0. As shown in fig. 1, there are 3 cases of movement points on the switching plane. The point A is a normal point, and when the switching surface s is close to 0, the moving point passes through the point A; the point B is a starting point, and when the switching surface s is close to 0, the moving point leaves the point B from two sides of the switching surface; the point C is an end point, and when the switching plane s is close to 0, the motion point approaches the point C from both sides of the switching plane.

In the sliding mode variant, the end point has a special meaning, while the start point has substantially no meaning from the normal point. When the moving point is the end point in a certain area on the switching surface, and moves in the area once moving toward the area. In this case, this region is referred to as a "sliding mode" region, i.e., a "sliding mode" region, and the movement of the system in this region is referred to as a "sliding mode movement".

With reference to fig. 2, the present invention discloses a speed sensorless control system based on an SMO (Sliding mode observer), which includes an inverter unit 1, a PMSM (Permanent Magnet Synchronous Motor) unit 2, a first Clark transformation unit 3, a Park transformation unit 4, a second Clark transformation unit 5, a Sliding mode observer unit 6, a first comparator unit 7, a first PI adjustment unit 8, a second comparator unit 9, a second PI adjustment unit 10, a third comparator unit 11, a third PI adjustment unit 12, a Park inverse transformation unit 13, and an SVPWM (Space Vector pulse width Modulation) unit 14, wherein:

the PMSM unit 2 is used for detecting and outputting three-phase current I_a、I_bAnd I_c；

The first Clark conversion unit 3 is used for converting the three-phase current I output by the PMSM unit 2_a、I_bAnd I_cOutputting two-phase stator current i under a two-phase static rectangular coordinate system α - β after Clark conversion_αAnd i_β；

The Park conversion unit 4 is used for converting the two-phase stator current i output by the first Clark conversion unit 3_αAnd i_βAfter being converted by Park, the two-phase current I under the two-phase synchronous rotating coordinate system d-q is output_dAnd I_q；

The second Clark conversion unit 5 is used for converting the three-phase voltage U output by the inverter unit 1_a、U_bAnd U_cAfter Clark conversion, two-phase stator voltage u under a two-phase static rectangular coordinate system α - β is output_αAnd u_β；

The sliding mode observer unit 6 is configured to output the two-phase stator current i output by the first Clark transformation unit 3_αAnd i_βAnd the two-phase stator voltage u output by the second Clark conversion unit 5_αAnd u_βPerforming estimation processing to estimate the estimated value of the rotor speedAnd an estimate of rotor positionAs shown in fig. 4;

the first comparator unit 7 is used for estimating the estimated value of the rotor rotating speed in the sliding mode observer unit 6Multiplying a constant to obtain an estimated rotor speed n, and performing difference operation on the estimated rotor speed n and the actual rotor speed n;

the first PI regulationA unit 8 for outputting a q-axis reference current after the difference compared by the first comparator unit 7 is adjusted by PI

The second comparator unit 9 is configured to output the q-axis reference current after being regulated by the first PI regulation unit 8And the two-phase current I output by the Park conversion unit 4_qPerforming difference operation;

the second PI adjustment unit 10 is configured to output a q-axis reference voltage after the difference value compared by the second comparator unit 9 is PI adjusted

The third comparator unit 11 is used for referencing a d-axis currentAnd the current I output by the Park conversion unit 4_dPerforming difference operation;

the third PI adjustment unit 12 is configured to output a d-axis reference voltage after the difference value compared by the third comparator unit 11 is subjected to PI adjustment

The Park inverse transformation unit 13 is configured to inverse-transform the q-axis reference voltage output by the second PI adjustment unit 10And a d-axis reference voltage output by the third PI regulation unit 12Outputting two-phase static right angle seat after Park inverse transformationTwo-phase control voltage of α - βAnd

the SVPWM unit 14 is used for controlling two-phase control voltageAndperforming space vector pulse width modulation, outputting a PWM waveform to the inverter unit 1, and inputting a three-phase voltage U to the PMSM unit 2 by the inverter unit 1_a、U_bAnd U_cThereby controlling the PMSM unit 2.

In the first Clark conversion unit 3, a three-phase current I is supplied_a、I_bAnd I_cThe two-phase stator current i under a two-phase static rectangular coordinate system α - β is output through Clark transformation_αAnd i_βThe conversion formula specifically involved is as follows:

$\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]$

in the Park conversion unit 4, a two-phase stator current i is applied_αAnd i_βAfter Park conversion, two-phase current I under a two-phase synchronous rotating coordinate system d-q is output_dAnd I_qThe conversion formula specifically involved is as follows:

$\left[\begin{array}{c}{I}_d\\ I_q\end{array}\right]=\left[\begin{array}{cc}\cos \widehat{\mathrm{\&theta;}}& \sin \widehat{\mathrm{\&theta;}}\\ -\sin \widehat{\mathrm{\&theta;}}& \cos \widehat{\mathrm{\&theta;}}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right]$

wherein,is the estimated rotor angle.

In the second Clark conversion unit 5, the three-phase voltage U output by the inverter unit 1 is converted into the three-phase voltage U_a、U_bAnd U_cThe two-phase stator voltage u under a two-phase static rectangular coordinate system α - β is output through Clark conversion_αAnd u_βThe conversion formula specifically involved is as follows:

$\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}}\\ u_{\mathrm{\&beta;}}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{U}_a\\ U_b\\ U_c\end{array}\right]$

further, with reference to fig. 3, the sliding-mode observer unit 6 specifically includes an SMO optimization algorithm subunit 61, a fourth comparator subunit 62, a switching function calculation subunit 63, a low-pass filter subunit 64, a rotation speed estimation subunit 65, a position compensation subunit 66, a position estimation subunit 67, and a summation unit 68, where:

the SMO optimization algorithm subunit 61 is configured to apply the two-phase stator voltage u output by the second Clark transformation unit 5_αAnd u_βAnd the back electromotive force e output after being processed by the switching function calculating subunit 63_αAnd e_βOutput current estimated value calculated by SMO optimization algorithmAnd

the fourth comparator subunit 62 is configured to estimate the current output by the SMO optimization algorithm subunit 61Andand the two-phase stator current i output by the first Clark conversion unit 3_αAnd i_βPerforming a difference operation to obtain αβ axis current error valueAnd

the switching function calculating subunit 63 is configured to calculate the current error value on the αβ axis output by the fourth comparator subunit 62Andobtaining back electromotive force e after the operation processing of the switching function_αAnd e_β；

The low-pass filter subunit 64 is configured to output the back electromotive force e processed by the switching function calculating subunit 63_αAnd e_βObtaining a back electromotive force estimated value estimated by the sliding mode observer after low-pass filteringAnd

the rotation speed estimation subunit 65 is configured to perform low-pass filtering on the low-pass filter subunit 64 to obtain a low-pass filtered back electromotive force estimation valueAndobtaining an estimate of rotor speed by speed estimation

The position estimating subunit 67 is configured to low-pass filter the low-pass filter subunit 64 to obtain a low-pass filtered back electromotive force estimation valueAndobtaining estimated value before rotor position uncompensation through position estimation

The position compensation subunit 66 is configured to obtain a phase compensation amount after kalman filtering by performing lag compensation on the phase

The summing unit 68 is configured to obtain an estimation value before the rotor position is not compensated, which is obtained by the position estimating subunit 67And the amount of phase compensation obtained by the position compensation subunit 66Summing to obtain the estimated value of the rotor position

As an embodiment, the SMO optimization algorithm in the SMO optimization algorithm subunit 61 specifically includes the following calculation steps:

firstly, establishing a mathematical model of the alternating current permanent magnet synchronous motor in a two-phase static rectangular coordinate system alpha-beta:

$\stackrel{\&CenterDot;}{i_{\mathrm{\&alpha;}}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&alpha;}}-\frac{1}{L_s}{e}_{\mathrm{\&alpha;}}+\frac{u_{\mathrm{\&alpha;}}}{L_s}---\left(1\right)$

$\stackrel{\&CenterDot;}{i_{\mathrm{\&beta;}}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&beta;}}-\frac{1}{L_s}{e}_{\mathrm{\&beta;}}+\frac{u_{\mathrm{\&beta;}}}{L_s}---\left(2\right)$

wherein,is the current value i of the current i on the α axis_αThe derivative of (a) of (b),is the current value i of the current i on the β axis_βDerivative of (A), R_SIs stator winding resistance, Ls is equivalent inductance, e_αBack EMF on α axis for sliding mode observer, e_βFor the back EMF of the sliding-mode observer on the β axis_αThe voltage value of voltage U on α axis，u_βIs the voltage value of the voltage U on the β axis;

next, the back emf equation is substituted:

e_α＝-ψ_fω_rsinθ (3)

e_β＝ψ_fω_rcosθ (4)

wherein psi_fFlux linkage, omega, produced for permanent magnets on the rotor_rFor synchronous speed, θ is the rotor angular position;

furthermore, an SMO optimization calculation equation of the alternating current permanent magnet synchronous motor in a two-phase static rectangular coordinate system alpha-beta is as follows:

$\stackrel{\&CenterDot;}{\widehat{i_{\mathrm{\&alpha;}}}}=-\frac{R_s}{L_s}\widehat{i_{\mathrm{\&alpha;}}}+\frac{u_{\mathrm{\&alpha;}}}{L_s}-\frac{k}{L_s}sign(\widehat{i_{\mathrm{\&alpha;}}}-i_{\mathrm{\&alpha;}})---\left(5\right)$

$\stackrel{\&CenterDot;}{\widehat{i_{\mathrm{\&beta;}}}}=-\frac{R_s}{L_s}\widehat{i_{\mathrm{\&beta;}}}+\frac{u_{\mathrm{\&beta;}}}{L_s}-\frac{k}{L_s}sign(\widehat{i_{\mathrm{\&beta;}}}-i_{\mathrm{\&beta;}})---\left(6\right)$

wherein,are respectively i_α、i_βK is the sliding mode switching gain;

finally, from the above available current estimation error equation:

$\stackrel{\&CenterDot;}{\widetilde{i_{\mathrm{\&alpha;}}}}=-\frac{R_s}{L_s}\widetilde{i_{\mathrm{\&alpha;}}}+\frac{e_{\mathrm{\&alpha;}}}{L_s}-\frac{k}{L_s}sign\left(\widetilde{i_{\mathrm{\&alpha;}}}\right)---\left(7\right)$

$\stackrel{\&CenterDot;}{\widetilde{i_{\mathrm{\&beta;}}}}=-\frac{R_s}{L_s}\widetilde{i_{\mathrm{\&beta;}}}+\frac{e_{\mathrm{\&beta;}}}{L_s}-\frac{k}{L_s}sign\left(\widetilde{i_{\mathrm{\&beta;}}}\right)---\left(8\right)$

wherein,is the current error value on the α axis,is the current error value on the β axis.

As an example, the current error value in the fourth comparator subunit 62Andthe calculation equation of (a) is:

$\widetilde{i_{\mathrm{\&alpha;}}}={\hat{i}}_{\mathrm{\&alpha;}}-i_{\mathrm{\&alpha;}}---\left(9\right)$

$\widetilde{i_{\mathrm{\&beta;}}}={\hat{i}}_{\mathrm{\&beta;}}-i_{\mathrm{\&beta;}}---\left(10\right)$

wherein,and i_αFor the current error value on axis α, the current estimate value and the current value,and i_βCurrent error value, current estimate value and current value on axis β.

As an example, the back electromotive force e in the switching function calculation subunit 63_αAnd e_βRespectively comprises the following steps:

firstly, a sign switching function is selected to perform switching function operation, as shown in fig. 4, that is:

$sign=\left\{\begin{array}{cc}1& x>0\\ -1& x<0\end{array}\right.---\left(11\right)$

secondly, selecting a Lyapunov function:

$V=\frac{1}{2}{\widetilde{i_{\mathrm{\&alpha;}}}}^2+\frac{1}{2}{\widetilde{i_{\mathrm{\&beta;}}}}^2---\left(12\right)$

derivative of V when k>max(|e_α|,|e_βIf | thenV is more than 0, the current sliding mode observer is stable according to the Lyapunov stability theorem, the current error is selected as the sliding mode switching surface, and when the sliding mode enters, the current sliding mode observer hasAndwhen the temperature of the water is higher than the set temperature,

$e_{\mathrm{\&alpha;}}=ksign\left(\widetilde{i_{\mathrm{\&alpha;}}}\right)---\left(13\right)$

$e_{\mathrm{\&beta;}}=ksign\left(\widetilde{i_{\mathrm{\&beta;}}}\right)---\left(14\right)$

wherein e is_αAnd e_βIs the back electromotive force of the sliding-mode observer,is the current error value on the α axis,for the current error value on the β axis, k is the sliding mode switching gain.

As an embodiment, the low-pass filter subunit 64 obtains the back electromotive force estimated by the sliding-mode observer through a low-pass filterAndthe calculation process of (2) includes:

using a low-pass filter, the discontinuous switching signal is converted into an equivalent continuous signal, and the corresponding calculation formula is as follows:

${\hat{e}}_{\mathrm{\&alpha;}}=\frac{{\mathrm{\&omega;}}_c}{s+{\mathrm{\&omega;}}_c}{e}_{\mathrm{\&alpha;}}---\left(15\right)$

${\hat{e}}_{\mathrm{\&beta;}}=\frac{{\mathrm{\&omega;}}_c}{s+{\mathrm{\&omega;}}_c}{e}_{\mathrm{\&beta;}}---\left(16\right)$

wherein,andestimated back electromotive force, ω, for sliding mode observer estimation_cIs the cut-off frequency of the low-pass filter, s is the Laplace operator, e_αAnd e_βIs the back electromotive force of the sliding mode observer.

As an embodiment, the estimated value of the rotor speed after low-pass filtering in the speed estimation subunit 65 is obtained by the following formula:

$\widehat{\mathrm{\&omega;}}=\frac{\sqrt{{\widehat{e_{\mathrm{\&alpha;}}}}^2+{\widehat{e_{\mathrm{\&beta;}}}}^2}}{{\mathrm{\&psi;}}_f}---\left(17\right)$

wherein,in order to estimate the rotational speed of the rotor,andback electromotive force, psi, estimated for sliding mode observer_fThe flux linkage generated by the permanent magnets on the rotor.

As an example, the estimation value of the low-pass filtered rotor position in the position estimation subunit 67 is obtained by the following formula:

$\widehat{{\mathrm{\&theta;}}_c}=-\arctan \left(\frac{\widehat{e_{\mathrm{\&alpha;}}}}{\widehat{e_{\mathrm{\&beta;}}}}\right)---\left(18\right)$

wherein,for the estimation of the position of the rotor,andback emf estimated for a sliding mode observer.

In an embodiment, the phase of the position compensation subunit 66 has a certain hysteresis due to the use of a low-pass filter, and the phase compensation amount after kalman filtering is:

$\mathrm{\&Delta;}\widehat{\mathrm{\&theta;}}=-\arctan \left(\frac{\mathrm{\&omega;}}{{\mathrm{\&omega;}}_c}\right)---\left(19\right)$

wherein,is the phase compensation quantity, omega is the rotation speed at steady state, omega_cThe cut-off frequency of the low-pass filter.

In a first comparator unit 7, the sliding-mode observer unit 6 estimates an estimate of the rotor speedThe relationship with the estimated rotor speed n is:

$n=\frac{60\widehat{\mathrm{\&omega;}}}{2\mathrm{\&pi;}}=9.55\widehat{\mathrm{\&omega;}}$

i.e. the constant is 9.55.

In the Park inverse transformation unit 13, the q-axis reference voltage outputted from the second PI regulation unit 10 is adjustedAnd a d-axis reference voltage output in the third PI regulation unit 12After Park inverse transformation, two-phase control voltage under a two-phase static rectangular coordinate system α - β is outputAndin particular to the following conversion formula:

$\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}}^{*}\\ u_{\mathrm{\&beta;}}^{*}\end{array}\right]=\left[\begin{array}{cc}\cos \widehat{\mathrm{\&theta;}}& -\sin \widehat{\mathrm{\&theta;}}\\ \sin \widehat{\mathrm{\&theta;}}& \cos \widehat{\mathrm{\&theta;}}\end{array}\right]\left[\begin{array}{c}{u}_d^{*}\\ u_q^{*}\end{array}\right]$

wherein,is the estimated rotor angle.

To verify the effectiveness of the present invention, a system simulation graph was constructed, as shown in fig. 5, the motor parameters used herein are shown in table 1, and experimental results were achieved by simulation.

Meaning of parameters	Value taking
		Number of pole pairs p	4
Stator resistance Rs/omega	2.8750
		Inductances Ld and Lq/mH	8.5
Moment of inertia J/(kg.m2)	0.005
		DC bus voltage VDC/V	500
Magnetic linkage/Wb	0.175

TABLE 1 PMSM drive system Primary parameters

Fig. 6, fig. 7, fig. 8, and fig. 9 show that the sliding mode observer designed by the present invention can track the rotation speed and rotation angle change of the motor timely and accurately under the condition of sudden change of the rotation speed and sudden change of the load, and has the characteristics of high control accuracy, good dynamic performance, and strong robustness.

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (9)

1. The SMO-based speed sensorless control system is characterized by comprising an inverter unit, a PMSM unit, a first Clark conversion unit, a Park conversion unit, a second Clark conversion unit, a sliding mode observer unit, a first comparator unit, a first PI adjusting unit, a second comparator unit, a second PI adjusting unit, a third comparator unit, a third PI adjusting unit, a Park inverse conversion unit and an SVPWM unit, wherein:

the PMSM unit is used for detecting and outputting three-phase current I_a、I_bAnd I_c；

The first Clark conversion unit is used for converting the three-phase current I output by the PMSM unit_a、I_bAnd I_cOutputting two-phase stator current i under a two-phase static rectangular coordinate system α - β after Clark conversion_αAnd i_β；

The Park conversion unit is used for converting the two-phase stator current i output by the first Clark conversion unit_αAnd i_βAfter being converted by Park, the two-phase current I under the two-phase synchronous rotating coordinate system d-q is output_dAnd I_q；

The second Clark conversion unit is used for converting the three-phase voltage U output by the inverter unit_a、U_bAnd U_cAfter Clark conversion, two-phase stator voltage u under a two-phase static rectangular coordinate system α - β is output_αAnd u_β；

The sliding mode observer unit is used for converting the two-phase stator current i output by the first Clark conversion unit_αAnd i_βAnd the two-phase stator voltage u output by the second Clark conversion unit_αAnd u_βPerforming estimation processing to estimate the estimated value of the rotor speedAnd an estimate of rotor position

The first comparator unit is used for estimating the estimated value of the rotor rotating speed in the sliding mode observer unitMultiplying a constant to obtain an estimated rotor speed n, and performing difference operation on the estimated rotor speed n and the actual rotor speed n;

the first PI adjusting unit is used for outputting q-axis reference current after the difference value compared by the first comparator unit is subjected to PI adjustment

The second comparator unit is used for outputting the q-axis reference current after being regulated by the first PI regulation unitAnd the two-phase current I output by the Park conversion unit_qPerforming difference operation;

the second PI regulating unit is used for regulating the difference value compared by the second comparator unit through PI and outputting a q-axis reference voltage

The third comparator unit for referencing a d-axis currentAnd the current I output by the Park conversion unit_dPerforming difference operation;

the third PI regulating unit is used for regulating the difference value compared by the third comparator unit through PI and outputting d-axis reference voltage

The Park inverse transformation unit is used for converting the q-axis reference voltage output by the second PI regulating unitAnd a d-axis reference voltage output by the third PI regulation unitOutputting two-phase control voltage under a two-phase static rectangular coordinate system α - β after Park inverse transformationAnd

the SVPWM unit is used for controlling two phases of voltageAndperforming space vector pulse width modulation, outputting PWM waveform to the inverter unit, and inputting three-phase voltage U to the PMSM unit by the inverter unit_a、U_bAnd U_cThereby controlling the PMSM unit.

2. An SMO-based sensorless control system according to claim 1, wherein the sliding-mode observer unit specifically comprises an SMO optimization algorithm subunit, a fourth comparator subunit, a switching function calculation subunit, a low-pass filter subunit, a rotational speed estimation subunit, a position compensation subunit, a position estimation subunit, and a summation unit, wherein: :

the SMO optimization algorithm subunit is used for converting the two-phase stator voltage u output by the second Clark conversion unit_αAnd u_βAnd the back electromotive force e output after being processed by the switching function calculation subunit_αAnd e_βOutput current estimated value calculated by SMO optimization algorithmAnd

the fourth comparator subunit is used for estimating the current output by the SMO optimization algorithm subunitAndand the two-phase stator current i output by the first Clark conversion unit_αAnd i_βPerforming a difference operation to obtain αβ axis current error valueAnd

the switching function calculating subunit is used for calculating the current error value on the αβ axis output by the fourth comparator subunitAndobtaining back electromotive force e after the operation processing of the switching function_αAnd e_β；

The low-pass filter subunit is used for processing the back electromotive force e output by the switching function calculation subunit_αAnd e_βObtaining a back electromotive force estimated value estimated by the sliding mode observer after low-pass filteringAnd

the rotating speed estimation subunit is configured to perform low-pass filtering on the low-pass filter subunit to obtain a low-pass filtered back electromotive force estimation valueAndobtained by estimation of the speed of rotationEstimation of rotor speed

The position estimation subunit is configured to perform low-pass filtering on the low-pass filter subunit to obtain a low-pass filtered back electromotive force estimation valueAndobtaining estimated value before rotor position uncompensation through position estimation

The position compensation subunit is used for obtaining a phase compensation quantity after Kalman filtering by performing lag compensation on the phase

The summation unit is used for estimating the estimated value of the rotor position obtained by the position estimation subunit before uncompensationAnd the phase compensation quantity obtained by the position compensation subunitSumming to obtain the estimated value of the rotor position

3. An SMO-based speed sensorless control system according to claim 2 wherein the SMO optimization algorithm in the SMO optimization algorithm subunit specifically comprises the following calculation steps:

firstly, establishing a mathematical model of the alternating current permanent magnet synchronous motor in a two-phase static rectangular coordinate system alpha-beta:

$\stackrel{\&CenterDot;}{i_{\mathrm{\&alpha;}}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&alpha;}}-\frac{1}{L_s}{e}_{\mathrm{\&alpha;}}+\frac{u_{\mathrm{\&alpha;}}}{L_s}---\left(1\right)$

$\stackrel{\&CenterDot;}{i_{\mathrm{\&beta;}}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&beta;}}-\frac{1}{L_s}{e}_{\mathrm{\&beta;}}+\frac{u_{\mathrm{\&beta;}}}{L_s}---\left(2\right)$

wherein,is the current value i of the current i on the α axis_αThe derivative of (a) of (b),is the current value i of the current i on the β axis_βDerivative of (A), R_SIs stator winding resistance, Ls is equivalent inductance, e_αBack EMF on α axis for sliding mode observer, e_βFor the back EMF of the sliding-mode observer on the β axis_αIs the voltage value of voltage U on α axis_βIs the voltage value of the voltage U on the β axis;

next, the back emf equation is substituted:

e_α＝-ψ_fω_rsinθ (3)

e_β＝ψ_fω_rcosθ (4)

wherein psi_fFlux linkage, omega, produced for permanent magnets on the rotor_rFor synchronous speed, θ is the rotor angular position;

furthermore, an SMO optimization calculation equation of the alternating current permanent magnet synchronous motor in a two-phase static rectangular coordinate system alpha-beta is as follows:

$\stackrel{\&CenterDot;}{\widehat{i_{\mathrm{\&alpha;}}}}=-\frac{R_s}{L_s}\widehat{i_{\mathrm{\&alpha;}}}+\frac{u_{\mathrm{\&alpha;}}}{L_s}-\frac{k}{L_s}sign(\widehat{i_{\mathrm{\&alpha;}}}-i_{\mathrm{\&alpha;}})---\left(5\right)$

$\stackrel{\&CenterDot;}{\widehat{i_{\mathrm{\&beta;}}}}=-\frac{R_s}{L_s}\widehat{i_{\mathrm{\&beta;}}}+\frac{u_{\mathrm{\&beta;}}}{L_s}-\frac{k}{L_s}sign(\widehat{i_{\mathrm{\&beta;}}}-i_{\mathrm{\&beta;}})---\left(6\right)$

wherein,are respectively i_α、i_βK is the sliding mode switching gain;

finally, from the above available current estimation error equation:

$\stackrel{\&CenterDot;}{\widetilde{i_{\mathrm{\&alpha;}}}}=-\frac{R_s}{L_s}\widetilde{i_{\mathrm{\&alpha;}}}+\frac{e_{\mathrm{\&alpha;}}}{L_s}-\frac{k}{L_s}sign\left(\widetilde{i_{\mathrm{\&alpha;}}}\right)---\left(7\right)$

$\stackrel{\&CenterDot;}{\widetilde{i_{\mathrm{\&beta;}}}}=-\frac{R_s}{L_s}\widetilde{i_{\mathrm{\&beta;}}}+\frac{e_{\mathrm{\&beta;}}}{L_s}-\frac{k}{L_s}sign\left(\widetilde{i_{\mathrm{\&beta;}}}\right)---\left(8\right)$

wherein,is the current error value on the α axis,is the current error value on the β axis.

4. An SMO-based speed sensorless control system as claimed in claim 2 wherein the current error value in the fourth comparator subunitAndthe calculation equation of (a) is:

$\widetilde{i_{\mathrm{\&alpha;}}}={\hat{i}}_{\mathrm{\&alpha;}}-i_{\mathrm{\&alpha;}}---\left(9\right)$

$\widetilde{i_{\mathrm{\&beta;}}}={\hat{i}}_{\mathrm{\&beta;}}-i_{\mathrm{\&beta;}}---\left(10\right)$

wherein,and i_αFor the current error value on axis α, the current estimate value and the current value,and i_βCurrent error value, current estimate value and current value on axis β.

5. An SMO-based speed sensorless control system according to claim 2 wherein the back electromotive force e in the switching function calculation subunit_αAnd e_βRespectively comprises the following steps:

firstly, a sign switching function is selected to perform switching function operation, namely:

$sign=\left\{\begin{array}{cc}1& x>0\\ -1& x<0\end{array}\right.---\left(11\right)$

secondly, selecting a Lyapunov function:

$V=\frac{1}{2}{\widetilde{i_{\mathrm{\&alpha;}}}}^2+\frac{1}{2}{\widetilde{i_{\mathrm{\&beta;}}}}^2---\left(12\right)$

derivative of V when k>max(|e_α|,|e_βIf | thenV is more than 0, the current sliding mode observer is stable according to the Lyapunov stability theorem, the current error is selected as the sliding mode switching surface, and when the sliding mode enters, the current sliding mode observer hasAndwhen the temperature of the water is higher than the set temperature,

$e_{\mathrm{\&alpha;}}=ksign\left(\widetilde{i_{\mathrm{\&alpha;}}}\right)---\left(13\right)$

$e_{\mathrm{\&beta;}}=ksign\left(\widetilde{i_{\mathrm{\&beta;}}}\right)---\left(14\right)$

wherein e is_αAnd e_βIs the back electromotive force of the sliding-mode observer,is the current error value on the α axis,for the current error value on the β axis, k is the sliding mode switching gain.

6. An SMO-based sensorless control system according to claim 2 wherein the low pass filter subunit obtains the back electromotive force estimate estimated by the sliding mode observer via a low pass filterAndthe calculation process of (2) includes:

using a low-pass filter, the discontinuous switching signal is converted into an equivalent continuous signal, and the corresponding calculation formula is as follows:

${\hat{e}}_{\mathrm{\&alpha;}}=\frac{{\mathrm{\&omega;}}_c}{s+{\mathrm{\&omega;}}_c}{e}_{\mathrm{\&alpha;}}---\left(15\right)$

${\hat{e}}_{\mathrm{\&beta;}}=\frac{{\mathrm{\&omega;}}_c}{s+{\mathrm{\&omega;}}_c}{e}_{\mathrm{\&beta;}}---\left(16\right)$

wherein,andestimated back electromotive force, ω, for sliding mode observer estimation_cIs the cut-off frequency of the low-pass filter, s is the Laplace operator, e_αAnd e_βIs the back electromotive force of the sliding mode observer.

7. An SMO based speed sensorless control system according to claim 2 wherein the estimate of the low pass filtered rotor speed in the speed estimation subunit is derived by the following equation:

$\widehat{\mathrm{\&omega;}}=\frac{\sqrt{{\widehat{e_{\mathrm{\&alpha;}}}}^2+{\widehat{e_{\mathrm{\&beta;}}}}^2}}{{\mathrm{\&psi;}}_f}---\left(17\right)$

wherein,in order to estimate the rotational speed of the rotor,andback EMF estimation for sliding mode observer，ψ_fThe flux linkage generated by the permanent magnets on the rotor.

8. An SMO based speed sensorless control system according to claim 2 wherein the estimate of the low pass filtered rotor position in the position estimation subunit is derived by the following equation:

$\widehat{{\mathrm{\&theta;}}_c}=-arctan\left(\frac{\widehat{e_{\mathrm{\&alpha;}}}}{\widehat{e_{\mathrm{\&beta;}}}}\right)---\left(18\right)$

wherein,for the estimation of the position of the rotor,andback emf estimated for a sliding mode observer.

9. The SMO-based speed sensorless control system according to claim 2, wherein the phase compensation subunit is configured to perform a phase lag compensation, due to the use of a low-pass filter, the phase lag compensation is performed, and the Kalman-filtered phase compensation amount is:

$\mathrm{\&Delta;}\widehat{\mathrm{\&theta;}}=-\arctan \left(\frac{\mathrm{\&omega;}}{{\mathrm{\&omega;}}_c}\right)---\left(19\right)$

wherein,is the phase compensation quantity, omega is the rotation speed at steady state, omega_cThe cut-off frequency of the low-pass filter.