22. 22
各种参数和状态以及自动控制有关的信息输入、交换识别、存取运算、判断及决策 均属于
该技术领域。机电一体化系统的计算机与信息处理装置是系统的核心。它是控制和指 挥整
个系统运行,了解各个部件和环境状态的核心。
自动控制技术:控制技术是在无人直接参与的情况下,通过控制器实现被控对象或过程自
动按规律运行。主要技术包括:系统建 模,控制系统设计理论和方法,系统仿真。自动控制作
为机一体化系统中重要支撑技术,是 其核心组成部分。控制技术是机电一体化系统在无人直
接参与的环境下,通过控制器完成预 定控制目标的技术保证。
6.伺服传动技术:主要是指机电一体化系统在执行元件的驱动装置
设计技术,伺服装置包括电动,气动及液压等,是实现电信号到机械动作的转换装置。对系
统的动态性能、控制质量和功能有决定性的影响。作为机电一体化系统的主要执行部件,担
负着机电一体化系统的最终功能实现,是实现电信号到机械动作的转换和控制装置和部件。
伺服驱动系统包括:电气、气动、液压各种类型的传动装置。
12、试利用 MATLAB/SIMULINK 仿真平台对一种实际系统进行仿真。
“矩阵变频器馈送三相感应电机的直接转矩控制”
Direct Torque Control using Matrix Converters
The Direct Torque Control (DTC) is a high-dynamic and high performance control technique
for induction motor drives which has been developed in the last two decades as possible alternative
solution to DC servo drives.
In direct-torque-controlled adjustable speed drives the motor flux and the electromagnetic torque
are the reference quantities which are directly controlled by the applied inverter voltage vector. At
any cycle period, accordingly to the position of the motor flux space vector and the output signals of
a flux and a torque hysteresis comparators the most opportune inverter switching state is selected.
The main advantages of the basic DTC scheme are:
The simplicity, as no coordinate trasformation is required;
The high dynamic;
The robustness;
The sensorless operation;
23. 23
DTC has also some disadvantages, as the difficulty to control the torque and the flux at very
low speed, the higher current and torque ripple which imply higher machine losses and noise, the
inherent variable switching frequency, the lack of direct current control. A general block diagram of
DTC scheme is represented in Fig. 1.
Fig. 1.Basic DTC block diagram.
It is evident by the diode rectifier that the AC drive shown in Fig.1 does not have bidirectional
energy flow capability. This limit might be overcome by a traditional inverter backto-back
arrangement but it might be also solved in a more elegant and effective way by using a matrix
converter. The matrix converter would allow, in addition to a straight-forward bidirectional energy
flow, sinusoidal input currents and the control capability of the input power factor, as consequence
of its higher number of switching state configurations compared to traditional voltage source
inverter (VSI).
After a short introduction to the direct torque control scheme of induction machines, it is
presented a control method for matrix converters which allows, under the constraint of unity input
power factor, the generation of the voltage vectors required to implement DTC.
The performance of the proposed control method are analyzed and discussed on the basis of
realistic numerical simulations as well as experimental tests of the whole drive system . The control
method has been implemented on a matrix converter adjustable speed drive prototype with the
Institute of Energy Technology at the University of Aalborg, Denmark.
1. Direct Torque Control of induction machines
The induction motor stator winding the following equation in terms of space vectors can be
written with reference to a stator frame:
(1.1)
where s
v
and s
i
are the stator voltage and current space vectors respectively. If it is assumed,
for simplicity, to neglect the voltage drop on the stator resistance Rs and to consider a short finite
time t , representing the control cycle period, equation (1.1) reduces to the following equation
(1.2)
Some remarks can be made with regard to equation (1.2)
dt
d
i
R
v s
s
s
s
t
vs
s
.
24. 24
Fig.2. Schematic circuit of a voltage source inverter and relevant
switching configurations voltage vectors
First, it shows that the applied inverter voltage vector, s
k v
v
, directly impresses the
stator flux space vector. This means that the required stator flux vector locus will be obtained by
using the opportune inverter output voltage vectors and hence inverter configurations.
Second, equation (1.2) shows that the stator flux space vector moves by the discrete amount
s
in the direction of the voltage vector applied by the inverter. The amplitude of the variation
depends on the DC link voltage, by way of equation:
(1.3)
(1.3) gives the general expression for a VSI voltage vector, where UDC is the DC link voltage. For a
given DC link voltage level, setting the control cycle period t the minimum stator flux vector
variation
s
is defined.
The control quantities through which the DTC tracks the reference flux and torque are the
radial
sr
and the tangential
st
components of the stator flux variation
s
impressed by the inverter voltage vector applied to the motor. The expression of the stator flux
vector variation
s
in terms of its radial and tangential components is given by:
(1.4)
t
r st
sr
st
sr
s .
.
25. 25
Substituting equation (1.2) in equation (1.4) the following is obtained:
(1.5)
Equation (1.5) explicitly states that the decoupled control of the stator flux and the
electromagnetic torque can be carried out by way of the selection of the opportune inverter voltage
vector, and hence switching configuration. It is worth noting that due to the fixed direction of the
inverter voltage vectors and to the rotating motion of the stator flux vector
s
in the d-q stator
frame, for each inverter voltage vector the amplitude of its radial and tangential components will be
variable within a sector.
At each cycle period, hereinafter indicated by tC, the selection of the proper inverter voltage
vector is made in order to maintain the estimated torque and stator flux within the limits of two
hysteresis bands. More precisely, the vector choice is made on the basis of the position of the stator
flux vector and the instantaneous errors in torque and stator flux magnitude.
As an example, considering the stator flux vector laying in sector , as shown in Fig.2, the
voltage vectors
2
V and
6
V can be selected in order to increase the flux while
3
V and
5
V can
be applied to decrease the flux. Among these,
2
V and
3
V determine a torque increase, while
5
V and
6
V a torque decrease. The zero voltage vectors are selected when the output of the torque
comparator is zero, irrespective to the stator flux condition. Using the basic switching table given in
Table I it is possible to implement DTC scheme having good performance.
Table I
Basic DTC inverter configuration selection table.
It should be noted that Table I is not the only possible DTC switching table. In general,
modified switching table have been proposed in literature with the intention to improve the
performance of the DTC scheme at very low and very high rotor speed.
2. Matrix Converter space vector representation
The proposed control method relies on a space vector representation of the matrix converter
switching configurations. This control method make use of the active and zero configurations only,
t
t
v
r
v
t
v
t
r st
sr
s
st
sr
).
.
.
(
.
.
.
26. 26
which are quoted in Table II. In Table II the output line-to-neutral voltage space vector
0
e is
considered.
For the output line-to-neutral voltage vector
0
e and the matrix converter input current vector
i
i the following expressions hold.
(1.6)
(1.7)
Table II
Switching configurations of the matrix converter used in the proposed DTC control scheme.
In Fig.3 and Fig.4 the output line-to-neutral voltage and the input current vectors for the active
configurations are respectively shown.
)
(
0
3
4
3
2
0
)
(
.
.
3
2 t
j
oC
i
oB
i
oA
o e
t
e
e
e
e
e
e
e
)
(
3
4
3
2
)
(
.
.
3
2 t
j
i
ic
i
ib
i
ia
i
i
e
t
i
i
e
i
e
i
i
27. 27
Fig.3.Output voltage vectors for active Fig.4.Input current vectors for active
configurations and reference output configurations and reference input
voltage vector. current vector.
3. The use of matrix converter in DTC
In the same way as for matrix converter space vector modulated control method, the reference
control quantities are the output voltage vector and the input current vector phase displacement with
respect to the input line-to-neutral voltage vector. But the choice of the switching configuration to
apply is made on a totally different basis.
The control of the output voltage is based on the classical DTC scheme described in Fig 1. As a
consequence, at each cycle period the optimum vector, among the eight generated by a VSI, is
selected in switching Table I accordingly to the position of the stator flux vector and the output
signals C and CT of the stator flux and torque hysteresis comparators. In Fig.5 and Fig.6 the
two-level stator flux and the three-level electromagnetic torque hysteresis comparators are
respectively shown. Once the classical DTC control scheme has selected the optimum vector to be
applied to the machine, it is a matter of determining the correspondent matrix converter switching
configuration. If it is assume, for example, that the VSI output vector
1
V has been chosen,
looking at Table II and Figs.2 and Figs.3, it can be seen that matrix converter can generate the same
vector by means of the switching configurations 1, 2, 3. But not all of them can be usefully
employed to provide vector
1
V .
Fig.5.Two-level stator flux hysteresis Fig.6.Three-level torque hysteresis
comparator. comparator.
28. 28
In fact, at any instant, the magnitude and the direction of their corresponding output voltage
vectors depend on the position of the input line-to-neutral voltage vector
i
e . Among the 6 vectors,
those having the same direction of
1
V and the maximum magnitude are considered.
If it is assume, for example, that vector
i
e is in sector , the switching configurations to be
used are +1 and –3. In fact, looking at Fig.7 and Table II it can be seen that within sector these
two switching configurations are those which complies with the above mentioned selection
criteria.
It has been verified that, whatever is the sector which the vector
i
e is in, the matrix converter
makes always available two switching configurations for each VSI output vector chosen by the
classical DTC scheme.
Fig.7.Representation of the input line-to-line voltages in the time
domain for sector of the input line-to-neutral voltage vector.
Such redundancy gives the opportunity to control a further variable in addition to the stator flux
and the electromagnetic torque. In the proposed control method the average value of the sine of the
displacement angle i between the input current vector and the corresponding input line-to-neutral
voltage vector has been chosen as third variable. This variable will be indicated by sin i.
If the constraint to comply with is an unity input power factor, such aim can be achieved
keeping the value of sin ito zero. The variable sin iis directly controlled by the hysteresis
comparator shown in Fig.8. The average value of sin i is obtained applying a low pass filter to its
instantaneous estimated value.
Fig.8. Hysteresis comparator of the sin ivalue.
29. 29
The control of the input power factor is possible because the input current vector for switching
configurations +1 and –3 have different directions, as it can be seen from Table II and shown in
Fig.9.
Fig.9. Representation of an unity control of the input power factor.
Keep going with the previous example, it is assumed by Fig.9. that the reference input
displacement angle is set to zero. As a consequence the reference value of sin iis also set to zero,
sin i* 0 .
Now, if the estimated value of sin iis positive, C= +1, which means that the input current
vector
i
i is lagging the voltage vector
i
e , then the configuration –3 has to be applied.
On the contrary, if the estimated value of sin iis negative, C= -1, which means that the
input current vector
i
i is leading the voltage vector
i
e , the configuration +1 has to be applied.
The switching table based on these principles is shown in Table III.
Table III
Matrix Converter Switching Table for DTC control.
The first column on the left hand side contains the voltage vectors selected by the basic DTC
scheme in order to keep the stator flux and torque within the limits of the corresponding hysteresis
bands.
The other six bold columns, are related to the sector of the matrix converter input current vector
i
i . Depending on the output value of the C hysteresis comparator, the left or the right column has
30. 30
to be used in selecting the switching configuration of the matrix converter. When a zero voltage
vector is required from Table I, the zero configuration of the matrix converter which minimizes the
number of commutations is selected.
The output of the hysteresis regulator C, together with the sector number of the input
current vector and the voltage vector required by the DTC, are the input to the matrix converter
switching configuration selection algorithm represented by Table III. It is worth noting that in [19]
the sectors were related the input line-to-neutral voltage vector
i
e . The matrix converter
switching configurations selected on the basis of the ei or
i
i vectors sector are identical only in
the case of unity input power factor. In the case of an input power factor different from unity, for a
proper control of the matrix converter input current, the switching configuration selection has to be
referred to the sector of the
i
i vector.
But likewise to the space vector modulated matrix converter, if the input power factor is
controlled to be less than unity, a reduction in the voltage transfer ratio is the result, which in the
DTC application turns into a reduction of the dynamic performance of the drive. In Fig.5.11 it is
shown the block diagram of the proposed DTC control scheme for the matrix converter.
Fig.10.Block diagram of the proposed DTC scheme for matrix converter.
With reference to Fig.10, in the lower part of the diagram the estimators of the electromagnetic
torque, the stator flux and the average value of sin i are represented. It is evident that these
estimators require the knowledge of input and output voltages and currents. However, only the input
voltages and the output currents are measured in each cycle period, because the other quantities can
be calculated on the basis of the actual switching configuration of the matrix converter which is
known.
31. 31
4. Numerical simulations and experimental tests of a Matrix-DTC drive system
The test machine was a standard: Nominal power = 2238(VA), voltage (line-line) = 220 (V),
and frequency - 60 (Hz), Stator resistance and inductance: Rs = 0.435 (ohm) Lls = 2e-3 (H), Rotor
resistance and inductance: Rr'= 0.816 (ohm ) Llr' = 2e-3 (H), Mutual inductance: Lm = 69.31e-3
(H), Inertia: J = 0.089 (kg.m^2) , friction factor: F = 0.005 (N.m.s), pole pairs: p = 2
Fig.11.Block simulation of DTC method for matrix inverter, speed control loop using PI set.
.
4.1 Asynchronous motor
Use asynchronous motor model available in Simulink. This is the standard form of motor and is
almost the most realistic.
Figure 12. Three-phase asynchronous motor model
4.2 CLARKE conversion block (abc => αβ)
- CLARKE conversion allows conversion of signals from 3 phases to 2 phases
- The basic formula for this conversion is: c
b
a
3
1
3
2
(1.8)
c
b
3
1
(1.9)
32. 32
Figure 13. CLARKE conversion block
- If the three-phase signal is perfectly symmetrical: 0
c
b
a . Therefore CLARKE
converters have a different formula based only on 2 elements of the input signal:
a
(1.10)
Figure 14. Clarke conversion description
(1.11)
4.3. Magnetic flux control ring and torque
- Parameter table provided for controlling magnetic flux and torque:
Figure 15. Parameter picker for DTC block
)
2
(
3
1
b
a
33. 33
4.4. Estimate flux and moment
During programming, the estimated flux value is calculated using the first-order inertia step
(essentially a low-pass filter). In the simulation, the magnetic flux is calculated based on the
Discrete-TimeIntegrator.
Figure 16. The block estimates the flux and torque
4.5. Comparison blocks have created late
Figure 17. Block for comparing flux and torque
4.6. The block determines the sector of the space vector
Figure 18. The block determines the sector of the space vector
In DTC method for matrix inverter, we need to determine the sector of input voltage vector
and stator magnetic flux vector. To determine the sector by this method, we need to calculate the
three-phase components a, b, c of vector.
34. 34
The grayed out sectors are those that represent the positive values of the components a, b, and c,
respectively. The sector definition table is summarized as follows. Logical level 1 corresponds to
positive values and logic 0 corresponds to negative values.
Figure 19. Simple sector identification method
4.7. The block defines the key configuration for the DTC matrix
Figure 20. The block defines the key configuration for the DTC matrix
4.8. The block defines the switching configuration for the basic DTC
Figure 21. Blocks define vector VSI
4.9. Speed control ring with fixed PI set
Figure 22. PI speed control unit
4.10. Simulation results for Matrix inverter application in DTC method with speed
feedback loop using normal PI set
With the simulation diagram designed as above, the 3-phase voltage source 220V / 50Hz,
the output frequency requires 25Hz we have some simulation results:
36. 36
Current stator:
Moment motor:
Comment: We see the moment when the pulse phenomenon. However, the engine is
essentially a low pass filter with a large L, so the motor operates with a pulsating moment without
causing damage.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-1
-0.5
0
0.5
1
1.5
2
Figure 25. Response motor stator
: Current stator
Time (Sec)
Figure 26: Response motor moment
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
: Moment hoi tiep
: Moment dat
Time (Sec)
Moment
(Nm)
37. 37
Speed response:
Describe the activities of the model (Figure 27)
+ At time t = 0, the engine set speed is 1000 rpm. According to the figures, the speed of response
is gradually increasing according to the set speed ramp function.
+ At time t = 0.5s (after the speed has reached the set state), the rated load torque of 0.13 Nm is
applied to the motor. Meanwhile, the engine speed has decreased slightly.
+ At the time t = 1s, the set speed is 500 rpm. The engine speed therefore decreases with a slope
of about 500 rpm.
+ At time t = 1.5s, the rated load torque of 0.22 Nm is applied to the engine. Meanwhile, the
engine speed has decreased slightly.
Zooming in to meet the speed of the motor at two times of loading can clearly see the effect
of the PI.
4.11 Conclusion
The main advantages of the DTC method are:
o Simple, no need for coordinated conversion blocks.
o High flexibility.
o Durable and accurate control.
o No need to use direct flux measurement sensor.
Combined with the advantages of matrix inverter. In this chapter, the author has built a model
of speed control asynchronous motor of three-phase rotor squirrel cage application matrix inverter
in DTC method with speed feedback loop using ordinary PI set. The results show that the feedback
speed is relatively tight compared to the set speed of the engine. Moment of motor moment of pulse
phenomenon. However, the engine is essentially a low pass filter with a large L, so the motor
operates with a pulsating moment without causing damage.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-200
0
200
400
600
800
1000
1200
Hình 27. Response motor speed
: Feedback speed
Speed
(RPM)
Time (Sec)
While there
moment of
loading
: Set speed
38. 38
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[3] Ahmed Abbou, Yassine Sayouti, Hassane Mahmoudi, “Recent patents on induction motor and
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[4] Jun Hu, Bin Wu, “New Integration Algorithms for Estimating Motor Flux over a Wide Speed
Range”, IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 5, SEPTEMBER
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