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.

In addition, you can use the advanced options to enable the ParameterBus input port, which you can use with the Compute Parameter block to update the block parameters optimally at run-time. You can use this functionality when motor parameters can change over time, for example, while building applications that may require swapping of motors at run-time.

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

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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

V_q — Q-axis stator voltage
scalar

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

Data Types: single | double | fixed point

ParameterBus — Computed parameters for I-F controller
bus

Computed parameters for the I-F Controller block. The input port accepts the following parameters:

Number of pole pairs
Speed to exit I-F controller (RPM), ω1
Speed to re-enter I-F controller (RPM), ω2
Maximum current (A), Imax
Maximum rate of speed change (RPM/s)
Maximum current decay rate (A/s)
Idle time (s)
Damping coefficient, ζ

Use this port along with the Compute Parameter block to update the preceding block parameters optimally at run-time.

Dependencies

To enable this port, select the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

Data Types: single | double

Output

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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

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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.

Use input port for computed parameters (run-time motor swap) — Option to enable input port to accept computed parameters
`off` (default) | on

Select this parameter to enable the ParameterBus input port and disable the following parameters:

Number of pole pairs
Current unit
Base current (A)
Speed to exit I-F controller (RPM), ω1
Speed to re-enter I-F controller (RPM), ω2
Maximum current (A), Imax
Maximum rate of speed change (RPM/s)
Maximum current decay rate (A/s)
Idle time (s)
Voltage unit
Base voltage (V)
Damping coefficient, ζ

This parameter enables you to use the input port along with the Compute Parameter block to update block parameters optimally at run-time.

Number of pole pairs — Number of pole pairs available in motor
`4` (default) | scalar

Number of pole pairs available in the motor.

Dependencies

To enable this parameter, clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

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.

Dependencies

To enable this parameter, clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

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:

Clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.
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.

Dependencies

To enable this parameter, clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

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.

Dependencies

To enable this parameter, clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

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.

Dependencies

To enable this parameter, clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

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.

Dependencies

To enable this parameter, clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

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.

Dependencies

To enable this parameter, clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

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.

Dependencies

To enable this parameter, clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

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.
Clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

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.
Clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.
Set Voltage unit to Per-unit.

Damping coefficient, ζ — 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.
Clear the Use input port for computed parameters (run-time motor swap) parameter available in the Advanced Options section.

Algorithms

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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:

$\begin{array}{l} T e = 1.5 p [λ_{p m} i_{q} + (L_{d} - L_{q}) i_{d} i_{q}] \\ = \frac{3 p}{2} I_{m} λ_{p m} \cos (θ_{e r r}) + \frac{3 p}{4} I_{m}^{2} (L_{d} - L_{q}) \sin (2 θ_{e r r}) \\ \approx 1.5 p I_{m} λ_{p m} \cos (θ_{e r r}) \end{array}$

The mechanical equation of PMSM is

$\frac{d ω_{e}}{d t} = \frac{p}{J} T_{e} - \frac{p}{J} T_{l} - \frac{B}{J} ω_{e}$

During steady state operation:

$T_{e} \approx T_{l} + p B ω_{e}$

The following equation describes the relationship between θ_err and I_m:

$\cos (θ_{e r r}) \approx \frac{T_{l} + p B ω_{e}}{1.5 P λ_{p m} I_{m}}$

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).

$ω_{i} = ω_{i}^{*} - K Δ P$

$P \approx \frac{3}{2} (V_{q} I_{q})$

$θ_{i} = \int ω_{i} d t$

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_q is the stator voltage along the q-axis of the rotating dq reference frame.
I_q is the stator current along the q-axis of the rotating dq 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

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced in R2024a

I-F Controller

Description

Examples

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

Ports

Input

Enable — Option to enable block algorithm scalar

θe — Electrical position of motor scalar

ωm ref — Reference motor mechanical speed scalar

ωm — Motor mechanical speed scalar

Iq — Q-axis stator current scalar

Vq — Q-axis stator voltage scalar

ParameterBus — Computed parameters for I-F controller bus

Dependencies

Output

Idref — Reference d-axis current scalar

Iqref — Reference q-axis current scalar

θeref — Generated reference electrical position of motor scalar

Status — I-F control status scalar

Parameters

Enable speed damping — Option to enable block to apply speed oscillation damping compensation off (default) | on

Use input port for computed parameters (run-time motor swap) — Option to enable input port to accept computed parameters off (default) | on

Number of pole pairs — Number of pole pairs available in motor 4 (default) | scalar

Dependencies

Position unit — Unit of electrical position Degrees (default) | Radians | Per-unit

Speed unit — Unit of the speed inputs Degrees/Sec (default) | Radians/Sec | RPM | Per-unit

Per unit speed (RPM) — Speed corresponding to one per-unit 6000 (default) | scalar

Dependencies

Current unit — Unit of motor currents SI unit (default) | Per-unit

Dependencies

Base current (A) — Nominal current corresponding to one per-unit 21.4286 (default) | scalar

Dependencies

Discrete step size (s) — Interval between consecutive block executions 50e-6 (default) | scalar

Controller Parameters

Speed to exit I-F controller (RPM), ω1 — Speed (after motor starts) at which I-F control stops 410.7 (default) | scalar

Dependencies

Speed to re-enter I-F controller (RPM), ω2 — Speed required to re-enter I-F control 287.49 (default) | scalar

Dependencies

Maximum current (A), Imax — Maximum motor current during I-F control 6.39 (default) | scalar

Dependencies

Maximum rate of speed change (RPM/s) — Maximum rate of speed change during I-F control 960 (default) | scalar

Dependencies

Maximum current decay rate (A/s) — Maximum rate of current decay during I-F control 111.8250 (default) | scalar

Dependencies

Idle time (s) — Time of constant speed and current 1 (default) | scalar

Dependencies

Minimum allowed position error for transition (rad) — Threshold error for closed-loop transition 0.1745 (default) | scalar

Advanced Parameters

Voltage unit — Unit of stator voltages SI unit (default) | Per-unit

Dependencies

Base voltage (V) — Nominal voltage corresponding to one per-unit 13.8564 (default) | scalar

Dependencies

Damping coefficient, ζ — Speed oscillation damping coefficient value 2.6172 (default) | scalar

Dependencies

Algorithms

Speed Oscillation Damping

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

See Also

Topics

Enable — Option to enable block algorithm
scalar

θ_e — Electrical position of motor
scalar

ω_m ^ref — Reference motor mechanical speed
scalar

ω_m — Motor mechanical speed
scalar

I_q — Q-axis stator current
scalar

V_q — Q-axis stator voltage
scalar

ParameterBus — Computed parameters for I-F controller
bus

I_d^ref — Reference d-axis current
scalar

I_q^ref — Reference q-axis current
scalar

θ_e^ref — Generated reference electrical position of motor
scalar

Status — I-F control status
scalar

Enable speed damping — Option to enable block to apply speed oscillation damping compensation
`off` (default) | on

Use input port for computed parameters (run-time motor swap) — Option to enable input port to accept computed parameters
`off` (default) | on

Number of pole pairs — Number of pole pairs available in motor
`4` (default) | scalar

Position unit — Unit of electrical position
`Degrees` (default) | `Radians` | `Per-unit`

Speed unit — Unit of the speed inputs
`Degrees/Sec` (default) | `Radians/Sec` | `RPM` | `Per-unit`

Per unit speed (RPM) — Speed corresponding to one per-unit
`6000` (default) | scalar

Current unit — Unit of motor currents
`SI unit` (default) | `Per-unit`

Base current (A) — Nominal current corresponding to one per-unit
`21.4286` (default) | scalar

Discrete step size (s) — Interval between consecutive block executions
`50e-6` (default) | scalar

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

Speed to re-enter I-F controller (RPM), ω2 — Speed required to re-enter I-F control
`287.49` (default) | scalar

Maximum current (A), Imax — Maximum motor current during I-F control
`6.39` (default) | scalar

Maximum rate of speed change (RPM/s) — Maximum rate of speed change during I-F control
`960` (default) | scalar

Maximum current decay rate (A/s) — Maximum rate of current decay during I-F control
`111.8250` (default) | scalar

Idle time (s) — Time of constant speed and current
`1` (default) | scalar

Minimum allowed position error for transition (rad) — Threshold error for closed-loop transition
`0.1745` (default) | scalar

Voltage unit — Unit of stator voltages
`SI unit` (default) | `Per-unit`

Base voltage (V) — Nominal voltage corresponding to one per-unit
`13.8564` (default) | scalar

Damping coefficient, ζ — Speed oscillation damping coefficient value
`2.6172` (default) | scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.