Direct Torque Control (DTC)

Direct torque control (DTC) is a vector motor control technique that implements motor speed control by directly controlling the flux and torque of the motor. Unlike field-oriented control (FOC) that controls d- and q-axis motor currents, the DTC algorithm estimates the torque and flux values from the motor position and currents. Then it uses PI controllers to control the motor torque and flux to eventually generate the optimum voltages that run the motor.

Motor Control Blockset™ uses the DTC space vector pulse-width modulation (DTC-SVPWM) variant to control a permanent magnet synchronous motor (PMSM). The technique uses space vector modulation (SVM) to produce the pulse-width modulation (PWM) duty cycles that are used by the inverter to generate the three-phase voltages that run the PMSM.

The DTC-SVPWM algorithm estimates the motor torque and flux feedback values using the current feedback (in the α-β reference frame) from the motor. The algorithm uses the motor speed feedback to compute the flux reference value. The speed PI controller (part of the outer control loop) uses the speed error input to compute the torque reference value. The flux and torque PI controllers (part of the inner control loop) use these flux and torque references and flux and torque feedback values to compute the d-axis and q-axis reference voltages. The algorithm uses the PWM Reference Generator block to generate PWM duty-cycles (using SVM) from these reference voltages.

You can determine current rotor position using both sensor-based or sensorless approaches.

Flux and Torque Estimation

The DTC-SVPWM algorithm used by Motor Control Blockset uses these transient machine model equations to estimate flux and torque of a PMSM.

These equations describe flux estimation from the currents in the α-β reference frame and rotor position:

$${\psi }_{\alpha }=L_s\cdot i_{\alpha }+{\psi }_{PM}\cdot \cos \theta$$

$${\psi }_{\beta }=L_s\cdot i_{\beta }+{\psi }_{PM}\cdot \sin \theta$$

$$\psi =\sqrt{{\psi }_{\alpha }^2+{\psi }_{\beta }^2}$$

These equations describe the per-unit (PU) computation of flux:

$${\psi }_{\alpha }^{pu}=\left({\omega }_{base}\cdot L_s^{pu}\cdot i_{\alpha }^{pu}\right)+\left({\psi }_{PM}^{pu}\cdot \cos \theta \right)$$

$${\psi }_{\beta }^{pu}=\left({\omega }_{base}\cdot L_s^{pu}\cdot i_{\beta }^{pu}\right)+\left({\psi }_{PM}^{pu}\cdot \sin \theta \right)$$

$${\psi }^{pu}=\sqrt{{\left({\psi }_{\alpha }^{pu}\right)}^2+{\left({\psi }_{\beta }^{pu}\right)}^2}$$

$${\omega }_{base}=2\cdot \pi \cdot f_{base}$$

These equations describe torque estimation from the currents in the α-β reference frame:

$$T=\frac{3}{2}\cdot p\cdot \left({\psi }_{\alpha }{i}_{\beta }-{\psi }_{\beta }{i}_{\alpha }\right)$$

These equations describe the per-unit (PU) computation of torque:

$$T^{pu}=\frac{1}{{\psi }_{PM}^{pu}}\cdot \left({\psi }_{\alpha }^{pu}{i}_{\beta }^{pu}-{\psi }_{\beta }^{pu}{i}_{\alpha }^{pu}\right)$$

where:

• ψ is the rotor flux of PMSM (Weber).

• ψ^pu is the per-unit version of ψ (Weber).

• ψ_α is the rotor flux along the α-axis of the α-β reference frame (Weber).

• ψ_α^pu is the per-unit version of ψ_α (Weber).

• ψ_β is the rotor flux along the β-axis of the α-β reference frame (Weber).

• ψ_β^pu is the per-unit version of ψ_β (Weber).

• ψ_PM is the permanent magnet flux linkage of the PMSM (Weber).

• ψ_PM^pu is the per-unit version of ψ_PM (Weber).

• L_s is the stator inductance of the PMSM (Henry).

• L_s^pu is the per-unit version of L_s (Henry).

• i_α is the motor current along the α-axis of the α-β reference frame (Amperes).

• i_α^pu is the per-unit version of i_α (Amperes).

• i_β is the motor current along the β-axis of the α-β reference frame (Amperes).

• i_β^pu is the per-unit version of i_β (Amperes).

• θ is the rotor position (captured by a sensor or determined by sensorless position estimation) (Radians).

• ω_base is the mechanical base speed of the motor (Radians/ sec).

• f_base is the mechanical frequency of the motor (Hertz).

• T is the rotor torque (Nm).

• T^pu is the per-unit version of T (Nm).

• p is the number of pole pairs of the motor.