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Flux-Based PM Controller

Controller for a flux-based permanent magnet synchronous motor

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  • Powertrain Blockset / Propulsion / Electric Motor Controllers

  • Flux-Based PM Controller block

Description

The Flux Based PM Controller block implements a flux-based, field-oriented controller for an interior permanent magnet synchronous motor (PMSM) with an optional outer-loop speed controller. The internal torque control implements strategies for achieving maximum torque per ampere (MTPA) and weakening the magnetic flux. You can specify either the speed or torque control type.

The Flux Based PM Controller implements equations for speed control, torque determination, regulators, transforms, and motors.

The figure illustrates the information flow in the block.

The block implements equations using these variables.

ω

Rotor speed

ω*

Rotor speed command

T*

Torque command

id

i*d

d-axis current

d-axis current command

iq

i*q

q-axis current

q-axis current command

vd,

v*d

d-axis voltage

d-axis voltage command

vq

v*q

q-axis voltage

q-axis voltage command

va, vb, vc

Stator phase a, b, c voltages

ia, ib, ic

Stator phase a, b, c currents

Speed Controller

To implement the speed controller, select the Control Type parameter Speed Control. If you select the Control Type parameter Torque Control, the block does not implement the speed controller.

The speed controller determines the torque command by implementing a state filter, and calculating the feedforward and feedback commands. If you do not implement the speed controller, input a torque command to the Flux Based PM Controller block.

State Filter

The state filter is a low-pass filter that generates the acceleration command based on the speed command. The discrete form of characteristic equation is given by:

z+KsfTsm1

The filter calculates the gain using this equation.

Ksf=1exp(Tsm2πEVsf)Tsm

The equations use these variables.

EVsf

Bandwidth of the speed command filter

Tsm

Motion controller sample time

Ksf

Speed regulator time constant

State Feedback

To generate the state feedback torque, the block uses the filtered speed error signal from the state filter. To filter the speed, the block uses a proportional integral (PI) controller.

Tcmd=Kpω(ωm*ωm)+KiωzTsmz1(ωm*ωm)

The equations use these variables.

ωm

Rotor speed

ω*m

Rotor speed command

Tcmd

Torque command

Kpω

Speed regulator proportional gain

Kiω

Speed regulator integral gain

Tsm

Speed regulator sample rate

Command Feedforward

To generate the state feedforward torque, the block uses the filtered speed and acceleration from the state filter. Also, the feedforward torque calculation uses the inertia, viscous damping, and static friction. To achieve zero tracking error, the torque command is the sum of the feedforward and feedback torque commands.

The feedforward torque command uses this equation.

Tcmd_ff= Jpω˙m+Fvωm+Fs ωm|ωm|

where:

Jp

Rotor inertia

Tcmd_ff

Torque command feedforward

Fs

Static friction torque constant

Fv

Viscous friction torque constant

Fs

Static friction torque constant

ωm

Rotor speed

Current Command

The block uses lookup tables to determine the d-axis and q-axis current commands. The lookup tables are functions of mechanical speed and torque. To determine the lookup tables, you can use an external finite element analysis (FEA) models or dynamometer test results.

idref=f(|ωm|,|Tref|)iqref=sign(Tref)f(|ωm|,|Tref|)

The equations use these variables.

ωm

Rotor speed

Tref

Torque command

idref, iqref

d- and q-axis reference current, respectively

Voltage Command

The block uses these equations to calculate the voltage in the motor reference frame.

vd=dψddt+Rsidωeψqvq=dψqdt+Rsiq+ωeψd

dψddt+Rsid=Kpd(id*id)+KidzTstz1(id*id)dψqdt+Rsiq=Kpq(iq*iq)+KiqzTstz1(iq*iq)vd=Kpi(id*id)+KidzTstz1(id*id)+ωeψqvq=Kpi(iq*iq)+KiqzTstz1(iq*iq)ωeψdψq=f(id,iq)ψd=f(id,iq)

The equations use these variables.

ωm

Rotor mechanical speed

ωe

Rotor electrical speed

Rs, Rr

Resistance of the stator and rotor windings, respectively

iq, id

q- and d-axis current, respectively

vq, vd

q- and d-axis voltage, respectively

Ψq, Ψd

q- and d-axis magnet flux, respectively

Tst

Current regulator sample rate

Kid , Kiq

d- and q- axis integral gain, respectively

Kpd , Kpq

d- and q- axis proportional gain, respectively

Transforms

To calculate the voltages and currents in balanced three-phase (a, b) quantities, quadrature two-phase (α, β) quantities, and rotating (d, q) reference frames, the block uses the Clarke and Park Transforms.

In the transform equations.

ωe=Pωmdθedt= ωe

TransformDescriptionEquations

Clarke

Converts balanced three-phase quantities (a, b) into balanced two-phase quadrature quantities (α, β).

xα= 23xa 13xb 13xcxβ= 32xb 32xc

Park

Converts balanced two-phase orthogonal stationary quantities (α, β) into an orthogonal rotating reference frame (d, q).

xd= xαcosθe+ xβsinθexq= xαsinθe+ xβcosθe

Inverse Clarke

Converts balanced two-phase quadrature quantities (α, β) into balanced three-phase quantities (a, b).

xa= xaxb= 12xα+ 32xβxc= 12xα 32xβ

Inverse Park

Converts an orthogonal rotating reference frame (d, q) into balanced two-phase orthogonal stationary quantities (α, β).

xα= xdcosθe xqsinθexβ= xdsinθe+ xqcosθe

The transforms use these variables.

ωm

Rotor speed

P

Rotor pole pairs

ωe

Rotor electrical speed

Θe

Rotor electrical angle

x

Phase current or voltage

Motor

The block uses the phase currents and phase voltages to estimate the DC bus current. Positive current indicates battery discharge. Negative current indicates battery charge.

The block uses these equations.

Load power

LdPwr=va ia+ vb ib+ vc ic

Source power

SrcPwr= LdPwr+PwrLoss

DC bus current

ibus= SrcPwrvbus

Estimated rotor torque

Te=1.5P[ψdiqψqid]

Power loss for single efficiency source to load

PwrLoss=100EffEffLdPwr

Power loss for single efficiency load to source

PwrLoss=100Eff100|LdPwr|

Power loss for tabulated efficiency

PwrLoss= f(ωm,MtrTrqest)

The equations use these variables.

va, vb, vc

Stator phase a, b, c voltages

vbus

Estimated DC bus voltage

ia, ib, ic

Stator phase a, b, c currents

ibus

Estimated DC bus current

Eff

Overall inverter efficiency

ωm

Rotor mechanical speed

Lq, Ld

q- and d-axis winding inductance, respectively

Ψq, Ψd

q- and d-axis magnet flux, respectively

iq, id

q- and d-axis current, respectively

λ

Permanent magnet flux linkage

P

Rotor pole pairs

Electrical Losses

To specify the electrical losses, on the Electrical Losses tab, for Parameterize losses by, select one of these options.

SettingBlock Implementation
Single efficiency measurement

Electrical loss calculated using a constant value for inverter efficiency.

Tabulated loss data

Electrical loss calculated as a function of motor speeds and load torques.

Tabulated efficiency data

Electrical loss calculated using inverter efficiency that is a function of motor speeds and load torques.

  • Converts the efficiency values you provide into losses and uses the tabulated losses for simulation.

  • Ignores efficiency values you provide for zero speed or zero torque. Losses are assumed zero when either torque or speed is zero.

  • Uses linear interpolation to determine losses. Provide tabulated data for low speeds and low torques, as required, to get the desired level of accuracy for lower power conditions.

  • Does not extrapolate loss values for speed and torque magnitudes that exceed the range of the table.

For best practice, use Tabulated loss data instead of Tabulated efficiency data:

  • Efficiency becomes ill defined for zero speed or zero torque.

  • You can account for fixed losses that are still present for zero speed or torque.

Ports

Input

expand all

Rotor speed command, ω*m, in rad/s.

Dependencies

To create this port, select Speed Control for the Control Type parameter.

Torque command, T*, in N·m.

Dependencies

To create this port, select Torque Control for the Control Type parameter.

DC bus voltage, vbus, in V.

Stator current phase a, ia, in A.

Stator current phase b, ib, in A.

Rotor speed, ωm, in rad/s.

Rotor electrical angle, Θm, in rad.

Output

expand all

Bus signal containing these block calculations.

SignalDescriptionUnits

SrcPwr

Source power

W

LdPwr

Load power

W

PwrLoss

Power loss

W

MtrTrqEst

Estimated motor torque

N·m

Estimated DC bus current, ibus, in A.

Stator terminal voltages, Va, Vb, and Vc, in V.

Parameters

expand all

Block Options

If you select Torque Control, the block does not implement the speed controller.

This table summarizes the port configurations.

Port ConfigurationCreates Ports
Speed Control

SpdReq

Torque Control

TrqCmd

Motor Parameters

Motor pole pairs, P.

d-axis current, id_index, in A.

q-axis current, iq_index, in A.

d-axis flux, λd, in Wb.

q-axis flux, λq, in Wb.

Current Controller

Torque control sample time, Tst, in s.

d-axis proportional gain, Kpd, in V/A.

q-axis proportional gain, Kpq, in V/A.

d-axis integral gain, Kid, in V/A·s.

q- axis integral gain, Kiq, in V/A·s.

Speed breakpoints, ωbp, in rad/s.

Torque breakpoints, Tbp, in N·m.

d-axis reference current, idref, in A.

q-axis reference current, iqref, in A.

Speed Controller

Speed regulator time constant, Ksf, in 1/s.

Dependencies

To enable this parameter, for the Control Type parameter, select Speed Control.

Proportional gain, Kpω, in N·m/(rad/s).

Dependencies

To enable this parameter, for the Control Type parameter, select Speed Control.

Integral gain, Kiω N·m/rad.

Dependencies

To enable this parameter, for the Control Type parameter, select Speed Control.

Inertia compensation, in kg·m^2.

Dependencies

To enable this parameter, for the Control Type parameter, select Speed Control.

Static friction, in N·m.

Dependencies

To enable this parameter, for the Control Type parameter, select Speed Control.

Viscous damping compensation, in N·m/(rad/s).

Dependencies

To enable this parameter, for the Control Type parameter, select Speed Control.

Electrical Losses

SettingBlock Implementation
Single efficiency measurement

Electrical loss calculated using a constant value for inverter efficiency.

Tabulated loss data

Electrical loss calculated as a function of motor speeds and load torques.

Tabulated efficiency data

Electrical loss calculated using inverter efficiency that is a function of motor speeds and load torques.

  • Converts the efficiency values you provide into losses and uses the tabulated losses for simulation.

  • Ignores efficiency values you provide for zero speed or zero torque. Losses are assumed zero when either torque or speed is zero.

  • Uses linear interpolation to determine losses. Provide tabulated data for low speeds and low torques, as required, to get the desired level of accuracy for lower power conditions.

  • Does not extrapolate loss values for speed and torque magnitudes that exceed the range of the table.

For best practice, use Tabulated loss data instead of Tabulated efficiency data:

  • Efficiency becomes ill defined for zero speed or zero torque.

  • You can account for fixed losses that are still present for zero speed or torque.

Overall inverter efficiency, Eff, in %.

Dependencies

To enable this parameter, for Parameterize losses by, select Tabulated loss data.

Speed breakpoints for lookup table when calculating losses, in rad/s.

Dependencies

To enable this parameter, for Parameterize losses by, select Tabulated loss data.

Torque breakpoints for lookup table when calculating losses, in N·m.

Dependencies

To enable this parameter, for Parameterize losses by, select Tabulated loss data.

Array of values for electrical losses as a function of M speeds and N torques, in W. Each value specifies the losses for a specific combination of speed and torque. The matrix size must match the dimensions defined by the speed and torque vectors.

Dependencies

To enable this parameter, for Parameterize losses by, select Tabulated loss data.

Speed breakpoints for lookup table when calculating efficiency, in rad/s.

Dependencies

To enable this parameter, for Parameterize losses by, select Tabulated efficiency data.

Torque breakpoints for lookup table when calculating efficiency, in N·m.

Dependencies

To enable this parameter, for Parameterize losses by, select Tabulated efficiency data.

Array of efficiency as a function of M speeds and N torque, in %. Each value specifies the efficiency for a specific combination of speed and torque. The matrix size must match the dimensions defined by the speed and torque vectors.

The block ignores efficiency values for zero speed or zero torque. Losses are zero when either torque or speed is zero. The block uses linear interpolation.

To get the desired level of accuracy for lower power conditions, you can provide tabulated data for low speeds and low torques.

Dependencies

To enable this parameter, for Parameterize losses by, select Tabulated efficiency data.

References

[1] Hu, Dakai, Yazan Alsmadi, and Longya Xu. “High fidelity nonlinear IPM modeling based on measured stator winding flux linkage.” IEEE® Transactions on Industry Applications, Vol. 51, No. 4, July/August 2015.

[2] Chen, Xiao, Jiabin Wang, Bhaskar Sen, Panagiotis Lasari, Tianfu Sun. “A High-Fidelity and Computationally Efficient Model for Interior Permanent-Magnet Machines Considering the Magnetic Saturation, Spatial Harmonics, and Iron Loss Effect.” IEEE Transactions on Industrial Electronics, Vol. 62, No. 7, July 2015.

[3] Ottosson, J., M. Alakula. “A compact field weakening controller implementation.” International Symposium on Power Electronics, Electrical Drives, Automation and Motion, July, 2006.

Extended Capabilities

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Introduced in R2017b