FOC Default Controller Gains

Compute controller gains for the FOC based algorithms at run time based on empirical method or optimum theory

Since R2023b

• 

Libraries:
Motor Control Blockset / Controls / Controllers

Description

The FOC Default Controller Gains block computes controller gains for PI controllers used in the field-oriented control (FOC) based algorithms based on empirical method or optimum theory.

If you select Empirical method option:

• The block calculates controller gains using approximation of control loops to a lower-order linear time-invariant system and by applying optimal theories considering the fixed delays in the system.

• The block computes the PI controller gains used in the current controller, speed controller, and field-weakening controller using the d-q frame of reference-based motor model. The block uses the function mcb.getPIControllerParameters internally to compute the control gains. For more details about this function, see Obtain Controller Gains Using Empirical Method.

• The block accepts motor parameters along with the current and speed controller sample times to generate a bus containing proportional and integral control gains, which you can use for PI controllers in an FOC-based algorithm.

• The block uses the value that you specify at the SlowdownFactor input port to modify the PI gains output to make them less aggressive and slow down the system response.

Note

• The block uses empirical calculation to compute the control gains. The gains computed by the block might not be optimal and might require additional tuning to improve dynamic performance.

• It is recommended that you use the block inside a triggered subsystem or a slow-running control loop.

• The block inputs accept values greater than zero.

If you select Based on optimum theory option:

• The block calculates controller gains using approximation of control loops to lower-order linear time-invariant system, and by applying optimal theories with capability to consider any number of delays present in the system (for example, delays due to hardware filters and observers (in case of sensorless FOC)).

• The block uses:.

  • Modulus optimum theory for calculation of current controller gains

  • Symmetric optimum theory for calculation of speed controller gains

• The block computes the PI controller gains used in the current controller and speed controller using the d-q frame of reference-based motor model. The block uses the function mcb.CalcFOCGains internally to compute the control gains. For more details about the usage of this function and the block, see Obtain Controller Gains to Run Motor Using Field-Oriented Control.

• The block accepts motor parameters along with the current and speed controller sample times to generate a bus containing proportional and integral control gains, which can be used with PI controllers to implement control algorithms for motor drive systems.

• If you select Per-unit for Output unit parameter, provide V_base (in Volts), I_base (in Amperes) and N_base (in RPM) as inputs via the corresponding ports.

• Provide overall time constant value for the delays present in feedback path of current loop and speed loop using the input ports CurrLoopDelay and SpeedLoopDelay respectively.

Examples

Obtain Controller Gains to Run Motor Using Field-Oriented Control

Obtain PI controller gains using Optimum theory for the current control loop and speed control loop in Field Oriented Control (FOC) of a Permanent Magnet Synchronous Motor (PMSM). This example provides multiple options that you can use to obtain PI controller gains:

• Open Live Script

Swap Motors with Single Model Deployment of Sensor-Based FOC Algorithm

Run a permanent magnet synchronous motor (PMSM) in an industrial drive application setup using position-sensor-based field-oriented control (FOC). Industrial drives enable you to swap motors in real-time without repeated deployment of code. An industrial drive setup needs a fixed inverter and software that has the ability to adapt the control algorithm according to the new motor using only the updated nameplate parameters.

• Open Example

Swap Motors with Single Deployment of Sensorless FOC Algorithm

Run a permanent magnet synchronous motor (PMSM) in an industrial drive application setup using a sensorless field-oriented control (FOC) algorithm. The example uses a sensorless Flux Observer to estimate the motor position. Industrial drives enable you to replace a motor with a new one without repeated deployment of code. An industrial drive setup needs only nameplate parameters to adapt the software to the new motor.

• Open Example

Generate Motor Control Models for Selected Algorithm and Hardware

Use Motor Control Blockset™ to generate a Simulink® model that is configured for a specific hardware and motor control technique.

• Open Live Script

Ports

Input

The display of input ports depends on the selection – Empirical method or Based on Optimum theory – in the block. For information on input ports, refer to the below sections: Empirical method or Optimum Theory.

Empirical method

R_s — Stator resistance

scalar

Stator resistance of the motor (in ohms).

Dependencies

To enable this port, select one or both of these parameters in the Block Output section of the Parameters tab:

• Current controller (d,q-axes)

• Field-weakening controller

Data Types: single | double

L_d — d-axis inductance

scalar

The d-axis inductance of a permanent magnet synchronous motor (PMSM) (in henries).

Dependencies

To enable this port:

• Set the Motor selection parameter to PMSM.

• Select the Current controller (d,q-axes) parameter available in the Block Output section of the Parameters tab.

Data Types: single | double

L_q — q-axis inductance

scalar

The q-axis inductance of a permanent magnet synchronous motor (PMSM) (in henries).

Dependencies

To enable this port:

• Set the Motor selection parameter to PMSM.

• Select one or both of the these parameters in the Block Output section of the Parameters tab:

  • Current controller (d,q-axes)

  • Field-weakening controller

Data Types: single | double

L_m — Magnetizing inductance

scalar

The magnetizing inductance of an AC induction motor (ACIM) (in henries).

Dependencies

To enable this port:

• Set the Motor selection parameter to ACIM.

• Select one or both of the these parameters in the Block Output section of the Parameters tab:

  • Current controller (d,q-axes)

  • Field-weakening controller

Data Types: single | double

L_ls — Stator leakage inductance

scalar

The stator leakage inductance of an AC induction motor (ACIM) (in henries).

Dependencies

To enable this port:

• Set the Motor selection parameter to ACIM.

• Select one or both of the these parameters in the Block Output section of the Parameters tab:

  • Current controller (d,q-axes)

  • Field-weakening controller

Data Types: single | double

L_lr — Rotor leakage inductance

scalar

The rotor leakage inductance of an AC induction motor (ACIM) (in henries).

Dependencies

To enable this port:

• Set the Motor selection parameter to ACIM.

• Select one or both of the these parameters in the Block Output section of the Parameters tab:

  • Current controller (d,q-axes)

  • Field-weakening controller

Data Types: single | double

J — Motor inertia

scalar

Inertia of the motor (in kg.m²).

Dependencies

To enable this port, select the Speed controller parameter in the Block Output section of the Parameters tab.

Data Types: single | double

T_s — Current controller sample time

scalar

Sample time (in seconds) of the current PI controller used in the FOC based motor control algorithm.

Data Types: single | double

T_sc — Speed controller sample time

scalar

Sample time (in seconds) of the speed PI controller used in the FOC based motor control algorithm.

Dependencies

To enable this port, select the Speed controller parameter in the Block Output section of the Parameters tab.

Data Types: single | double

SlowdownFactor — Factor to slow down system response

scalar in the range of [1, 20]

A factor, in the range of [1, 20], that you can provide to modify the output PI gains. A higher value makes the controller parameters less aggressive and slows down the system response.

Dependencies

To enable this port, clear the Specify filter and sensor delays parameter available in the Delays tab.

Data Types: single | double

I_Max — Maximum measurable peak-neutral current

scalar

Maximum AC current magnitude (peak value) in an inverter-based motor drive system (in amperes).

Dependencies

To enable this port, either:

• Select the Speed controller parameter in Block output section of Parameters tab.

or

• Select the Current controller (d,q-axes) parameter in Block output section of Parameters tab.

• Set the Output unit parameter to Per-Unit.

Data Types: single | double

V_dc — DC link voltage

scalar

DC link voltage of the inverter (in volts). The block uses $$\frac{V_{dc}}{\sqrt{3}}$$ as a base value for per-unit calculations when you set the Output unit parameter to Per-Unit.

Dependencies

To enable this port:

• Select the Current controller (d,q-axes) parameter in Block output section of Parameters tab.

• Set the Output unit parameter to Per-Unit.

Data Types: single | double

N_base — Motor rated speed

scalar

Base value of the speed of the motor (in rpm) for per-unit computation.

• Select the Speed controller parameter in Block output section of Parameters tab.

• Set the Output unit parameter to Per-Unit.

Data Types: single | double

Optimum Theory

R_s — Stator resistance

scalar

Stator resistance of the motor (in ohms).

Data Types: single | double

L_d — d-axis inductance

scalar

The d-axis inductance of a permanent magnet synchronous motor (PMSM) (in henries).

Data Types: single | double

L_q — q-axis inductance

scalar

The q-axis inductance of a permanent magnet synchronous motor (PMSM) (in henries).

Data Types: single | double

J — Motor inertia

scalar

Inertia of the motor (in kg.m²).

Data Types: single | double

p — Number of pole pairs available in the motor

scalar

Number of pole pairs available in the motor.

Data Types: single | double

Flux_PM — Peak permanent magnet flux linkage

scalar

Peak permanent magnet flux linkage, in weber.

Data Types: single | double

T_s — Current controller sample time

scalar

Sample time (in seconds) of the current PI controller used in the FOC based motor control algorithm.

Data Types: single | double

T_sc — Speed controller sample time

scalar

Sample time (in seconds) of the speed PI controller used in the FOC based motor control algorithm.

Data Types: single | double

CurrLoopDelay — Overall time constant value for the current delay present in feedback path

scalar

Overall time constant value (in seconds) for the current delay present in feedback path.

Data Types: single | double

SpeedLoopDelay — Overall time constant value for the speed delay present in feedback path

scalar

Overall time constant value (in seconds) for the speed delay present in feedback path.

Data Types: single | double

V_base — Base voltage

scalar

Base value of the voltage applied to the motor (in volts) for per-unit computation.

Dependencies

To enable this port:

• Set the Output unit parameter to Per-Unit.

Data Types: single | double

I_base — Base current

scalar

Base value of the current applied to the motor (in volts) for per-unit computation.

Dependencies

To enable this port:

• Set the Output unit parameter to Per-Unit.

Data Types: single | double

N_base — Motor rated speed

scalar

Base value of the speed of the motor (in rpm) for per-unit computation.

Dependencies

To enable this port:

• Set the Output unit parameter to Per-Unit.

Data Types: single | double

Output

PI Gains — PI controller gains

bus

Control gains of one or more of these PI controllers used in an FOC motor control algorithm, for either Empirical method or Optimum theory.

If you select Empirical method, the value is also based on based on the Block output parameter selection:

• d- and q-axis current controller

• Speed controller

• Field-weakening controller

The following table summarizes the components of the PI Gains output bus for Empirical method:

Type of PI Controller selected for Empirical Method	Bus component			Description
d-axis current PI controller	Daxis_Kp			Control gain Kp of the d-axis current PI controller
	Daxis_Ki			Control gain Ki of the d-axis current PI controller
	Daxis_Ki*Ts			Control gain Ki of the d-axis current PI controller multiplied with the current controller sample time (TS)
q-axis current PI controller	Qaxis_Kp			Control gain Kp of the q-axis current PI controller
	Qaxis_Ki			Control gain Ki of the q-axis current PI controller
	Qaxis_Ki*Ts			Control gain Ki of the q-axis current PI controller multiplied with the current controller sample time (TS)
Speed PI controller	Speed_Kp			Control gain Kp of the speed PI controller
	Speed_Ki			Control gain Ki of the speed PI controller
	Speed_Ki*Tsc			Control gain Ki of the speed PI controller multiplied with the speed controller sample time (TSC)
Field-weakening PI controller	FWC_Kp			Control gain Kp of the field-weakening PI controller
	FWC_Ki			Control gain Ki of the field-weakening PI controller
	FWC_Ki*Ts			Control gain Ki of the field-weakening PI controller multiplied with the current controller sample time (TS)

Data Types: single | double

Status — PI gains computation status

true | false

Computation status of the PI gains, returned as one of these values:

• True indicates that the block has successfully computed the PI controller gains available at the PI Gains output port.

• False indicates that the block could not compute the PI controller gains as the value of one or more inputs was incorrect.

Data Types: Boolean

Parameters

Motor selection — Type of motor

PMSM (default) | ACIM

The type of motor for which you are implementing the control algorithm:

• ACIM — AC induction motor

• PMSM — Permanent magnet synchronous motor

Dependencies

This parameter is enabled for editing only if you select Empirical method option to compute controller gain.

Output unit — Unit of the block output

SI Unit (default) | Per-Unit

Unit of the elements in the bus that the block outputs at the PI Gains output port.

Block Output — Output of the block

Current controller (d,q-axes) | Field-weakening controller | Speed controller

Enable the block to compute and output one or more of the following elements through the PI Gains port:

• Current controller (d,q-axes) — Control gains (K_p and K_i) of the PI controllers for d- and q-axis current control.

• Field-weakening controller — Control gains (K_p and K_i) of the PI controller operating in the field-weakening region.

• Speed controller — Control gains (K_p and K_i) of the speed PI controller.

Dependencies

This parameter is enabled for editing only if you select Empirical method option to compute controller gain.

Delays

Specify filter and sensor delays — Enable addition of filter and sensor delays

off (default) | on

Select this option to specify speed filter delay and current and speed sensor delays. When you select this parameter, the block enables the Current sensor delay (s), Speed sensor delay (s), and Speed filter delay (s) parameters.

Dependencies

This parameter selection appears only if you select Empirical method option to compute controller gain.

Current sensor delay (s) — Delay due to current sensor

50e-6 (default) | scalar

Time delay (in seconds) due to the current sensor.

Dependencies

To enable this parameter, select the Specify filter and sensor delays parameter.

The Specify filter and sensor delays parameter appears only if you select Empirical method option to compute controller gain.

Speed sensor delay (s) — Delay due to speed sensor

50e-6 (default) | scalar

Time delay (in seconds) due to the speed sensor.

Dependencies

To enable this parameter, select the Specify filter and sensor delays parameter.

The Specify filter and sensor delays parameter appears only if you select Empirical method option to compute controller gain.

Speed filter delay (s) — Delay due to speed filtering

0.02 (default) | scalar

Time delay (in seconds) introduced by speed filtering.

Dependencies

To enable this parameter, select the Specify filter and sensor delays parameter.

The Specify filter and sensor delays parameter appears only if you select Empirical method option to compute controller gain.

Extended Capabilities

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

Version History

Introduced in R2023b