mcb.calcFOCGains

Compute gains and transfer functions for PI controller in field-oriented control of PMSM

Since R2025a

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    Syntax

    [PI_Params,OLTF,CLTF] = mcb.calcFOCGains(motor,Ts,Ts_speed)
    [PI_Params,OLTF,CLTF] = mcb.calcFOCGains(motor,Ts,Ts_speed,Name=Value)

    Description

    [PI_Params,OLTF,CLTF] = mcb.calcFOCGains(motor,Ts,Ts_speed) computes the PI controller gains Kp and Ki, open-loop transfer function OLTF, and closed-loop transfer function CLTF for field-oriented control of a permanent magnet synchronous motor (PMSM) with parameters motor.

    [PI_Params,OLTF,CLTF] = mcb.calcFOCGains(motor,Ts,Ts_speed,Name=Value) specifies options using one or more name-value arguments in addition to the input arguments in the previous syntax. For example, to specify PU system base values, set Base to PU_System where PU_System is a struct of base values.

    The function computes the PI controller gains based on Optimum theory. For more information, see Obtain Controller Gains to Run Motor Using Field-Oriented Control.

    example

    Examples

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    Set the pulse-width modulation (PWM) switching frequency and sample times.

    PWM_frequency = 20e3;
T_pwm         = 1/PWM_frequency;
Ts            = T_pwm;
Ts_speed      = 10*Ts;

    Get parameters for your motor and inverter. This example uses a BLY171D PMSM and DRV8312-C2-KIT inverter.

    pmsm = mcb.getPMSMParameters("BLY171D");
inverter = mcb.getInverterParameters("DRV8312-C2-KIT");

    Get the per-unit base values for the PMSM and inverter.

    PU_System = mcb.getPUSystemParameters(pmsm,inverter);

    Get the PI controller parameters and transfer functions for the PMSM in per-unit system.

    [PI_params,OLTF,CLTF] = mcb.calcFOCGains(pmsm,Ts,Ts_speed,Base=PU_System)
    PI_params = 

  struct with fields:

        Ti_i: 0.0014
        Kp_i: 6.5531
        Ki_i: 4.6808e+03
       Ti_id: 0.0014
       Kp_id: 6.5531
       Ki_id: 4.6808e+03
    Ti_speed: 0.0023
    Kp_speed: 4.3403
    Ki_speed: 1.8871e+03


OLTF = 

  struct with fields:

    DCurrLoop: [1×1 struct]
    QCurrLoop: [1×1 struct]
      SpdLoop: [1×1 struct]


CLTF = 

  struct with fields:

    DCurrLoop: [1×1 struct]
    QCurrLoop: [1×1 struct]
      SpdLoop: [1×1 struct]

    Get the polynomial coefficients of a transfer function, for example, the d-axis current open-loop transfer function.

    OLTF.DCurrLoop
    ans = 

  struct with fields:

      Numerator: 2.1364
    Denominator: [7.0000e-08 0.0014 1]

    Set the PWM switching frequency and sample times.

    PWM_frequency = 20e3;
T_pwm         = 1/PWM_frequency;
Ts            = T_pwm;
Ts_speed      = 10*Ts;

    Get parameters for your motor and inverter. This example uses a BLY171D PMSM and DRV8312-C2-KIT inverter.

    pmsm = mcb.getPMSMParameters("BLY171D");
inverter = mcb.getInverterParameters("DRV8312-C2-KIT");

    Get the per-unit base values for the PMSM and inverter.

    PU_System = mcb.getPUSystemParameters(pmsm,inverter);

    Get the PI controller parameters and transfer functions for the PMSM in per-unit system. Specify the delay in the current loop forward path. For this example, specify two delay elements, one with a gain of 1 and time constant of 1e-4 seconds, and the other with a gain of 0.5 and time constant of 1e-5 seconds.

    delay.Gain = [1 0.5];
delay.TimeConstant = [1e-4 1e-5];
[PI_params,OLTF,CLTF] = mcb.calcFOCGains(pmsm,Ts,Ts_speed,...
  Base=PU_System,CLForwardPathDelay=delay)
    PI_params = 

  struct with fields:

        Ti_i: 0.0014
        Kp_i: 4.0957
        Ki_i: 2.9255e+03
       Ti_id: 0.0014
       Kp_id: 4.0957
       Ki_id: 2.9255e+03
    Ti_speed: 0.0032
    Kp_speed: 3.1392
    Ki_speed: 987.1666


OLTF = 

  struct with fields:

    DCurrLoop: [1×1 struct]
    QCurrLoop: [1×1 struct]
      SpdLoop: [1×1 struct]


CLTF = 

  struct with fields:

    DCurrLoop: [1×1 struct]
    QCurrLoop: [1×1 struct]
      SpdLoop: [1×1 struct]

    Get the polynomial coefficients of a transfer function, for example, the d-axis current open-loop transfer function.

    OLTF.DCurrLoop
    ans = 

  struct with fields:

      Numerator: 1.0682
    Denominator: [2.2400e-07 0.0016 1]

    Input Arguments

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    PMSM parameters, specified as a struct.

    Specify lumped linear parameters with the following required fields:

    • Ld — d-axis stator winding inductance (in henries), specified as a scalar

    • Lq — q-axis stator winding inductance (in henries), specified as a scalar

    • FluxPM — Permanent magnet flux linkage (in webers), specified as a scalar

    • p — Number of pole pairs, specified as a scalar

    • Rs — Stator resistance (in ohms), specified as a scalar

    • B — Viscous damping coefficient (in kg-m2/ sec), specified as a scalar

    • I_rated — Rated current (in amperes), specified as a scalar

    You can create a structure with lumped linear parameters using mcb.getPMSMParameters.

    Alternatively, specify non-linear lookup table data with the following required fields:

    • PMSMLUT.idvec — d-axis current breakpoints (in amperes) of lookup tables, specified as a vector

    • PMSMLUT.iqvec — q-axis current breakpoints (in amperes) of lookup tables, specified as a vector

    • PMSMLUT.LdTable — d-axis inductance (in henries) lookup table, specified as matrix

    • PMSMLUT.LqTable — q-axis inductance (in henries) lookup table, specified as a matrix

    • PMSMLUT.FluxPMTable — Permanent magnet flux linkage (in weber) lookup table, specified as a matrix

    or the following required fields:

    • PMSMLUT.idvec — d-axis current breakpoints (in amperes) of lookup tables, specified as a vector

    • PMSMLUT.iqvec — q-axis current breakpoints (in amperes) of lookup tables, specified as a vector

    • PMSMLUT.FluxDTable — d-axis flux linkage lookup table, specified as a matrix

    • PMSMLUT.FluxQTable — q-axis flux linkage lookup table, specified as a matrix

    The structure can also contain the following optional fields:

    • model — Manufacturer's model number, specified as a character vector

    • sn — Manufacturer's serial number, specified as a character vector

    • J — Motor inertia coefficient (in kg-m2), specified as a scalar

    • Ke — Back EMF constant (in volts/krpm), specified as a scalar

    • Kt — Torque constant (in Nm/amperes), specified as a scalar

    • N_max — Maximum rotor speed (in rpm), specified as a scalar

    • PositionOffset — Rotor position offset (in PU), specified as a scalar

    • QEPSlits — Number of quadrature encoder pulse (QEP) slits, specified as a scalar

    • T_rated — Rated torque (in Nm), specified as a scalar

    Data Types: struct

    Control system sample time (in seconds), specified as a scalar.

    Data Types: double

    Speed controller sample time (in seconds), specified as a scalar.

    Data Types: double

    Name-Value Arguments

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    Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

    Example: mcb.calcFOCGains(pmsm,Ts,Ts_speed,SpdLPFltCoeff=0,.5)

    Base values of PU system for voltage, current, and motor speed, specified as a struct with the following fields:

    • V_base — Base voltage (in volts)

    • I_base — Base current (in amperes)

    • N_base — Base speed (in rpm)

    Example: mcb.calcFOCGains(pmsm,Ts,Ts_speed,Base=PU_System) specifies PU system base values from the PU_System structure.

    Filter coefficient of IIR filter in speed loop, specified as a value greater than 0 and less than or equal to 1.

    Example: mcb.calcFOCGains(pmsm,Ts,Ts_speed,SpdLPFltCoeff=0.5) specifies a speed loop filter coefficient of 0.5.

    Data Types: double

    Delay in forward path of current loop, specified as a struct with fields Gain and Time (in sec). Specify these fields as arrays of scalars, one for each delay element.

    Example: mcb.calcFOCGains(pmsm,Ts,Ts_speed,CLForwardPathDelay=delay) specifies the delay in the current loop forward path from the delay struct.

    Data Types: double

    Delay in the feedback path of the current loop, specified as a struct with fields Gain and Time (in sec). Specify these fields as arrays of scalars, one for each delay element.

    Example: mcb.calcFOCGains(pmsm,Ts,Ts_speed,CLFeedbackPathDelay=delay) specifies the delay in the current loop feedback path from the delay struct.

    Data Types: double

    Delay in the forward path of the speed loop, specified as a struct with fields Gain and Time (in sec). Specify these fields as arrays of scalars, one for each delay element.

    Example: mcb.calcFOCGains(pmsm,Ts,Ts_speed,SLForwardPathDelay=delay) specifies the delay in the speed loop forward path from the delay struct.

    Data Types: double

    Delay in the feedback path of the speed loop, specified as a struct with fields Gain and Time (in sec). Specify these fields as arrays of scalars, one for each delay element.

    Example: mcb.calcFOCGains(pmsm,Ts,Ts_speed,SLFeedbackPathDelay=delay) specifies the delay in the speed loop feedback path from the delay struct.

    Data Types: double

    Factor multiplying proportional and integral gains of d-axis current controller, specified as a value greater than 0.

    Example: mcb.calcFOCGains(pmsm,Ts,Ts_speed,DCurrLoopFactor=2) specifies a d-axis current controller gain multiplier of 2.

    Data Types: double

    Factor multiplying proportional and integral gains of q-axis current controller, specified as a value greater than 0.

    Example: mcb.calcFOCGains(pmsm,Ts,Ts_speed,QCurrLoopFactor=2) specifies a q-axis current controller gain multiplier of 2.

    Data Types: double

    Factor multiplying proportional and integral gains of speed controller, specified as a value greater than 0.

    Example: mcb.calcFOCGains(motor,Ts,Ts_speed,SpdLoopFactor=2) specifies a speed controller gain multiplier of 2.

    Data Types: double

    Output Arguments

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    PI controller gains, returned as a struct with the following fields:

    • Ti_i — q-axis current controller integral time constant, returned as a scalar

    • Kp_i — q-axis current controller proportional gain, returned as a scalar

    • Ki_i — q-axis current controller integral gain, returned as a scalar

    • Ti_id — d-axis current controller integral time constant, returned as a scalar

    • Kp_id — d-axis current controller proportional gain, returned as a scalar

    • Ki_id — d-axis current controller integral gain, returned as a scalar

    • Ti_speed — Speed controller integral time constant, returned as a scalar

    • Kp_speed — Speed controller proportional gain, returned as a scalar

    • Ki_speed — Speed controller integral gain, returned as a scalar

    Open-loop transfer function, returned as a struct with the following fields:

    • DCurrLoop — d-axis current open-loop transfer function, returned as a struct

    • QCurrLoop — q-axis current open-loop transfer function, returned as a struct

    • SpdLoop — Speed loop transfer function, returned as a struct

    Each transfer function structure contains two fields Numerator and Denominator that list polynomial coefficients for the numerator and denominator of the transfer function, respectively.

    Closed-loop transfer function, returned as a struct with the following fields:

    • DCurrLoop — d-axis current closed-loop transfer function, returned as a struct

    • QCurrLoop — q-axis current closed-loop transfer function, returned as a struct

    • SpdLoop — Speed loop transfer function, returned as a struct

    Each transfer function structure contains two fields Numerator and Denominator that list polynomial coefficients for the numerator and denominator of the transfer function, respectively.

    Version History

    Introduced in R2025a

    See Also

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