I-F Controller

Implement I-F control for a three-phase permanent magnet synchronous motor

Since R2024a

• 

Libraries:
Motor Control Blockset / Controls / Controllers

Description

The I-F Controller block implements I-F control based sensorless startup algorithm for a three-phase permanent magnet synchronous motor (PMSM).

Similar to the VbyF Controller block, the I-F Controller block enables sensorless motor startup, however, I-F Controller generates a higher startup torque in the motor.

The block computes the d- and q-axis reference currents along with reference electrical position for the PMSM. It accepts electrical position, q-axis current, as well as reference and actual mechanical speeds as inputs.

The block supports both the SI unit and per-unit (PU) systems. For more information about the per-unit system, see Per-Unit System.

For information about the block algorithm, see Algorithm.

Examples

Sensorless Field-Oriented Control of PMSM Using I-F Control-Based Startup

Implements field-oriented control (FOC) using sensorless position estimation and I-F control-based startup to control the speed of a three-phase permanent magnet synchronous motor (PMSM).

Open Model

Ports

Input

Enable — Option to enable block algorithm

scalar

Signal that enables block algorithm:

• 1 — Enables block algorithm.

• 0 — Reset block algorithm.

Data Types: single | double | fixed point

θ_e — Electrical position of motor

scalar

The electrical position of the rotor.

Data Types: single | double | fixed point

ω_m ^ref — Reference motor mechanical speed

scalar

Reference mechanical speed for running the motor using I-F control.

Data Types: single | double | fixed point

ω_m — Motor mechanical speed

scalar

Actual mechanical speed of the motor.

Data Types: single | double | fixed point

I_q — Q-axis stator current

scalar

Stator current along the q-axis of the rotating dq reference frame..

Data Types: single | double | fixed point

Output

I_d^ref — Reference d-axis current

scalar

Reference d-axis stator current leading to currents that drive the motor.

Data Types: single | double | fixed point

I_q^ref — Reference q-axis current

scalar

Reference q-axis stator current leading to currents that drive the motor.

Data Types: single | double | fixed point

θ_e^ref — Generated reference electrical position of motor

scalar

Reference electrical position of motor generated by the block that drives the motor.

Data Types: single | double | fixed point

Status — I-F control status

scalar

Status of the I-F control algorithm.

• 1 — Indicates that I-F control is inactive.

• 0 — Indicates that I-F control is active.

Data Types: single | double | fixed point

Parameters

Enable speed damping — Option to enable block to apply speed oscillation damping compensation

off (default) | on

Select this parameter to apply speed oscillation damping to the motor electrical speed (according to assumed motor position) with speed oscillations.

Number of pole pairs — Number of pole pairs available in motor

4 (default) | scalar

Number of pole pairs available in the motor.

Position unit — Unit of electrical position

Degrees (default) | Radians | Per-unit

Unit of θ_e input and θ_e^ref output used by the block.

Select Per-unit to use per-unit system for the reference electrical position input and output. For more information about the per-unit system, see Per-Unit System.

Speed unit — Unit of the speed inputs

Degrees/Sec (default) | Radians/Sec | RPM | Per-unit

Units of the ω_m^ref and ω_m inputs.

Select Per-unit to use per-unit system for the two speed inputs. For more information about the per-unit system, see Per-Unit System.

Per unit speed (RPM) — Speed corresponding to one per-unit

6000 (default) | scalar

Speed value corresponding to one per-unit. For details, see Per-Unit System.

Dependencies

To enable this parameter, set Speed unit to Per-unit.

Current unit — Unit of motor currents

SI unit (default) | Per-unit

Unit of I_q input as well as I_d^ref and I_q^ref outputs of the block.

Select Per-unit to use per-unit system for these motor currents. For more information about the per-unit system, see Per-Unit System.

Base current (A) — Nominal current corresponding to one per-unit

21.4286 (default) | scalar

Nominal current value corresponding to one per-unit. For details, see Per-Unit System.

Dependencies

To enable this parameter, set Current unit to Per-unit.

Discrete step size (s) — Interval between consecutive block executions

50e-6 (default) | scalar

The fixed time interval in seconds between two consecutive instances of block execution.

Controller Parameters

Speed to exit I-F controller (RPM), ω1 — Speed (after motor starts) at which I-F control stops

410.7 (default) | scalar

Speed (after motor starts) until which the I-F controller remains active (in RPM). When the motor speed exceeds this value, the I-F controller becomes inactive and the Status block output turns true.

Speed to re-enter I-F controller (RPM), ω2 — Speed required to re-enter I-F control

287.49 (default) | scalar

After exiting I-F control (and entering closed-loop control), speed required to reactivate the I-F controller (in RPM). When the motor speed falls below this value, the I-F controller becomes active again and the Status block output turns false.

Maximum current (A), Imax — Maximum motor current during I-F control

6.39 (default) | scalar

Maximum current (in amperes) that is supplied to the motor when I-F control is active.

Maximum rate of speed change (RPM/s) — Maximum rate of speed change during I-F control

960 (default) | scalar

Maximum rate at which motor speed can change (in RPM/s) when I-F control is active.

Maximum current decay rate (A/s) — Maximum rate of current decay during I-F control

111.8250 (default) | scalar

Maximum rate at which motor current can decay (in amperes/s) when I-F control is active.

Idle time (s) — Time of constant speed and current

1 (default) | scalar

Time (in seconds) during which both motor speed and current remains constant when I-F control is active.

Minimum allowed position error for transition (rad) — Threshold error for closed-loop transition

0.1745 (default) | scalar

Threshold electrical position error (between θ_e and θ_e^ref ) below which the block transitions from I-F control to closed-loop control.

Advanced Parameters

To enable this tab, select the Enable speed damping parameter.

Voltage unit — Unit of stator voltages

SI unit (default) | Per-unit

Unit of V_α and V_β stator voltages.

Select Per-unit to use per-unit system for these voltages. For more information about the per-unit system, see Per-Unit System.

Dependencies

To enable this parameter, select the Enable speed damping parameter.

Base voltage (V) — Nominal voltage corresponding to one per-unit

13.8564 (default) | scalar

Nominal voltage value corresponding to one per-unit. For details about the per-unit system, see Per-Unit System.

Dependencies

To enable this parameter:

• Select the Enable speed damping parameter.

• Set Voltage unit to Per-unit.

Damping coefficient — Speed oscillation damping coefficient value

2.6172 (default) | scalar

Value of the speed oscillation damping coefficient (K) that the block should use.

Dependencies

To enable this parameter, select the Enable speed damping parameter.

Algorithms

The following equations explain the I-F control algorithm used by the block for a PMSM.

The preceding figure explains the I-F control operation. It shows the γ-ẟ rotating orthogonal axes (aligned with assumed rotor position), the d-q axes in the rotating reference frame, and the stationary α-β reference frame.

The following equation describes the electrical torque of PMSM when I-F control is active:

$$\begin{array}{l}Te=1.5p\left[{\lambda }_{pm}{i}_q+\left(L_d-L_q\right)i_d{i}_q\right]\\ =\frac{3p}{2}{I}_m{\lambda }_{pm}\cos \left({\theta }_{err}\right)+\frac{3p}{4}{I}_m^2\left(L_d-L_q\right)\sin \left(2{\theta }_{err}\right)\\ \approx 1.5p{I}_m{\lambda }_{pm}\cos \left({\theta }_{err}\right)\end{array}$$

The mechanical equation of PMSM is

$$\frac{d{\omega }_e}{dt}=\frac{p}{J}{T}_e-\frac{p}{J}{T}_l-\frac{B}{J}{\omega }_e$$

During steady state operation:

$$T_e\approx T_l+pB{\omega }_e$$

The following equation describes the relationship between θ_err and I_m:

$$\cos \left({\theta }_{err}\right)\approx \frac{T_l+pB{\omega }_e}{1.5P{\lambda }_{pm}{I}_m}$$

where:

• T_e is the electromagnetic torque of the motor (in Nm).

• T_l is the load torque of the motor (in Nm).

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

• λ_pm is the permanent magnet flux linkage (in Weber).

• i_d is the motor current along the d-axis of the d-q rotating reference frame (in amperes).

• i_q is the motor current along the q-axis of the d-q rotating reference frame (in amperes).

• L_d is the d-axis inductance of the motor (in henries).

• L_q is the q-axis inductance of the motor (in henries).

• I_m is the current injected by the I-F control algorithm (in amperes).

• θ_e is the actual rotor position (in radians).

• θ_i is the assumed (reference) rotor position (in radians).

• θ_err is the difference between the actual and assumed rotor position (in radians).

• ω_e is the electrical speed of the motor (in rad/s).

• J is the motor inertia (in kgm^2)

• B is the friction constant (in Nms).

When using this algorithm, the magnitude of the starting current determines the maximum electrical torque that the I-F control algorithm can generate.

The preceding equations also show that a very high acceleration value can affect the stability of I-F control. The error between actual and assumed motor position depends on the magnitude of the supplied current.

The following image shows the operation of the I-F control, which begins with motor-start followed by transition from I-F to closed-loop control and from closed-loop to I-F control.

The I-F control algorithm provides good control over torque during motor startup. The control algorithm starts the motor without any current overshoots as well as provides a smooth I-F control to closed-loop control transition.

Speed Oscillation Damping

The mechanical damping offered by the motor is not sufficient to reduce the oscillations in the motor speed. Compensating for these oscillations requires addition of negative feedback in the speed generation algorithm, which increases the damping coefficient (K).

This equation describes the compensated motor speed that the block generates (where KΔP is the applied compensation for speed oscillation damping).

$${\omega }_i={\omega }_i^{*}-K\Delta P$$

$$P=\frac{3}{2}\left(V_{\alpha }{I}_{\alpha }+V_{\beta }{I}_{\beta }\right)$$

$${\theta }_i={\displaystyle \int {\omega }_{i}dt}$$

where:

• ω_i is the reference motor electrical speed after compensation (in rad/s).

• ω_i^* is the reference motor electrical speed with speed oscillations (in rad/s).

• θ_i is the reference rotor position (in radians).

• K is the damping coefficient.

• P is the active power drawn by the motor (in watts).

• V_α is the stator voltage along the α-axis of the stationary αβ reference frame.

• V_β is the stator voltage along the β-axis of the stationary αβ reference frame.

• I_α is the stator current along the α-axis of the stationary αβ reference frame.

• I_β is the stator current along the β-axis of the stationary αβ reference frame.

References

[1] Z. Wang, K. Lu and F. Blaabjerg, "A Simple Startup Strategy Based on Current Regulation for Back-EMF-Based Sensorless Control of PMSM," in IEEE Transactions on Power Electronics, vol. 27, no. 8, pp. 3817-3825, Aug. 2012, doi: 10.1109/TPEL.2012.2186464.

[2] A. Borisavljevic, H. Polinder and J. A. Ferreira, "Realization of the I/f control method for a high-speed permanent magnet motor," The XIX International Conference on Electrical Machines - ICEM 2010, Rome, Italy, 2010, pp. 1-6, doi: 10.1109/ICELMACH.2010.5607892.

[3] S. V. Nair, K. Hatua, N. V. P. R. D. Prasad and D. K. Reddy, "A Quick I--f Starting of PMSM Drive With Pole Slipping Prevention and Reduced Speed Oscillations," in IEEE Transactions on Industrial Electronics, vol. 68, no. 8, pp. 6650-6661, Aug. 2021, doi: 10.1109/TIE.2020.3005070.

[4] Z. Song, W. Yao, K. Lee and W. Li, "An Efficient and Robust I-f Control of Sensorless IPMSM With Large Startup Torque Based on Current Vector Angle Controller," in IEEE Transactions on Power Electronics, vol. 37, no. 12, pp. 15308-15321, Dec. 2022, doi: 10.1109/TPEL.2022.3193565.

Extended Capabilities

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Version History

Introduced in R2024a