Single-phase induction machine direct torque control
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The Induction Machine Direct Torque Control (Single-Phase) block implements a single-phase induction machine direct torque control structure.
This diagram shows the direct torque control architecture for single-phase machines
The torque and flux estimation is based on machine voltage equations. The discrete-time voltage equations using the backward Euler discretization method, are:
Ras and Rbs are the main winding resistance and the auxiliary winding resistance, respectively.
ia and ib are the main winding current and the auxiliary winding current, respectively.
va and vb are the main and auxiliary winding voltage, respectively.
ψa and ψb are the main and auxiliary winding flux, respectively.
The torque and flux are obtained from:
p is the number of pole pairs.
a is the auxiliary to main windings turn
Employing simple hysteresis comparators detects the status of flux and torque errors. The following figures illustrate the hysteresis comparators and the switching sectors.
The table shows the optimum switching table (inverter high side).
|cψ, cT, S(θ)||S0||S1||S2||S3|
|1, 1||0, 1||0, 0||1, 0|
|1, 0||1, 1||0, 1||0, 0|
|0, 1||0, 0||1, 0||1, 1|
|0, 0||1, 0||1, 1||0, 1|
The torque reference can be provided as an input, or, in the case of speed control, be generated internally using a PI speed controller.
The flux reference is generated internally using:
ωr is the rotor angular mechanical speed in rad/s.
fn is the rated frequency.
ψn is the rated flux.
The power inverter dead-times are not considered in this block. For hardware implementation, add the dead-time externally.
Reference— Torque or angular velocity reference
Specify the angular velocity reference in rad/s or the torque reference in Nm.
iab— Stator currents
Stator currents for main and auxiliary windings.
vab— Stator voltages
Stator voltages for main and auxiliary windings.
wr— Rotor angular speed
Measure rotor angular speed in rad/s.
G— Inverter gate pulses
Inverter gate pulses, specified as a Boolean. The dead-time is not considered.
Visualization— Internal signals for visualization
Bus containing internal signals for visualization. The signals are:
Reference torque or speed
Rotor velocity, in rad/s
Torque Reference, in Nm
Flux Reference, in Wb
Torque, in Nm
Flux, in Wb
Control mode— Specify control mode
Speed control(default) |
Specify the control mode. The reference input is taken as angular speed, in rad/s, for
Speed control and torque, in Nm, for
Rated electrical frequency (Hz)— Specify rated electrical frequency
60(default) | positive scalar
Rated electrical frequency, in Hz.
Number of pole pairs— Specify pole pairs
2(default) | positive scalar
Number of pole pairs.
Main winding stator resistance, Ras (Ohm)— Specify main winding stator resistance
1.8180(default) | positive scalar
Resistance of the main winding stator, in Ohms.
Auxiliary winding stator resistance, Rbs (Ohm)— Specify auxiliary winding stator resistance
6.4260(default) | positive scalar
Resistance of the auxiliary winding stator, in Ohms.
Auxiliary/main windings turn ratio— Specify the auxiliary-to-main windings turn ratio
1.1(default) | positive scalar
Auxiliary-to-main windings turns ratio.
Sample time (-1 for inherited)— Block sample time
-1(default) | positive scalar
Time, in s, between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? (Simulink) and Specify Sample Time (Simulink).
If this block is inside a triggered subsystem, inherit the
sample time by setting this parameter to
-1. If this block is in a
continuous variable-step model, specify the sample time explicitly using a positive
This table shows how the visibility of some parameters in the Outer Loop tab depends on the option that you choose for the Control mode parameter in the General tab.
|Control mode||Available Parameters|
|Speed control||Speed controller proportional gain|
|Speed controller integral gain|
|Speed controller integral anti-windup gain|
|Maximum torque (Nm)|
|Minimum torque (Nm)|
|Rated flux (Wb)|
|Torque control||Rated flux (Wb)|
Speed controller proportional gain— Specify the speed controller proportional gain
1(default) | positive scalar
Proportional gain for the PI speed controller.
Speed controller integral gain— Specify the speed controller integral gain
10(default) | positive scalar
Integral gain for the PI speed controller.
Speed controller integral anti-windup gain— Specify the speed controller integral anti-windup gain
1000(default) | positive scalar
Integral anti-windup gain.
Maximum torque (Nm)— Specify the maximum torque
5(default) | positive scalar
Maximum torque used in speed controller saturation, in Nm.
Minimum torque (Nm)— Specify the minimum torque
-5(default) | scalar
Minimum torque used in speed controller saturation, in Nm.
Rated flux (Wb)— Specify the rated flux
0.5(default) | positive scalar
Rated flux, in Wb. The rated flux is used to compute the flux reference.
Flux hysteresis band (Wb)— Specify the flux hysteresis band
0.02(default) | positive scalar
Flux hysteresis band for the controller, in Wb.
Torque hysteresis band (Nm)— Specify the torque hysteresis band
0.1(default) | positive scalar
Torque hysteresis band for the controller, in Nm.
 Takahashi, I., and T. Noguchi. "A New Quick-Response and High-Efficiency Control Strategy of an Induction Motor." IEEE Transactions on Industry Applications. Vol. IA-22, Number 5, 1986, pp. 820 - 827.