Interior PM Controller

Torque-based, field-oriented controller for an internal permanent magnet synchronous motor

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Libraries:
Powertrain Blockset / Propulsion / Electric Motor Controllers

Description

The Interior PM Controller block implements a torque-based, field-oriented controller for an internal 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 Interior 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 that use 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 Interior PM Controller block.

State Filter

The state filter is a low-pass filter that generates the acceleration command based on the speed command. On the Speed Controller tab:

• To make the speed-command lag time negligible, specify a Bandwidth of the state filter parameter.

• To calculate a Speed regulation time constant, Ksf gain based on the state filter bandwidth, select Calculate Speed Regulator Gains.

The discrete form of characteristic equation is given by:

$z+K_{sf}{T}_{sm}-1$

The filter calculates the gain using this equation.

$K_{sf}=\frac{1-\exp \left(-T_{sm}2\pi E{V}_{sf}\right)}{T_{sm}}$

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. The feedback torque calculation also requires gains for speed regulator.

On the Speed Controller tab, select Calculate Speed Regulator Gains to calculate:

• Proportional gain, ba

• Angular gain, Ksa

• Rotational gain, Kisa

For the gain calculations, the block uses the inertia from the Physical inertia, viscous damping, static friction parameter value on the Motor Parameters tab.

The gains for the state feedback are calculated using these equations.

Calculation	Equations
Discrete forms of characteristic equation	$z^3+\frac{\left(-3J_p+T_s{b}_a+ T_s^2{K}_{sa}+T_s^3{K}_{isa}\right)}{J_p}{z}^2+\frac{\left(3J_p- 2T_s{b}_a- T_s^2{K}_{sa}\right)}{J_p}z+\frac{-J_p+T_s{b}_a}{J_p}$ $$(z-p_1)(z-p_2)(z-p_3)=z^3+(p_1+p_2+p_3)z^2+(p_1{p}_2+p_2{p}_3+p_{1}3)z^2-p_1{p}_2{p}_3$$
Speed regulator proportional gain	$b_a=\frac{J_p-J_p{p}_1{p}_2{p}_3}{T_{sm}}$
Speed regulator integral gain	$K_{sa}=\frac{J_p\left(p_1{p}_2+p_2{p}_3+p_3{p}_1\right)-3J_p+2b_a{T}_{sm}}{T_{sm}^2}$
Speed regulator double integral gain	$K_{isa}=\frac{-J_p\left(p_1+p_2+p_3\right)+3J_p-b_a{T}_{sm}-K_{sa}{T}_{sm}^2}{T_{sm}^3}$

The equations use these variables.

P	Motor pole pairs
ba	Speed regulator proportional gain
Ksa	Speed regulator integral gain
Kisa	Speed regulator double integral gain
Jp	Motor inertia
Tsm	Motion controller sample time

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.

Selecting Calculate Speed Regulator Gains on the Speed Controller tab updates the inertia, viscous damping, and static friction with the Physical inertia, viscous damping, static friction parameter values on the Motor Parameters tab.

The feedforward torque command uses this equation.

$$T_{cmd\_ff}= J_p{\dot{\omega }}_m+F_v{\omega }_m+F_{s }\frac{{\omega }_m}{\left|{\omega }_m\right|}$$

where:

Jp	Motor inertia
Tcmd_ff	Torque command feedforward
Fs	Static friction torque constant
Fv	Viscous friction torque constant
Fs	Static friction torque constant
ωm	Rotor speed

Torque Determination

The block uses a maximum torque per ampere (MTPA) trajectory to calculate the base speed and the current commands. The available bus voltage determines the base speed. The direct (d) and quadrature (q) permanent magnet (PM) determines the induced voltage.

Calculation	Equations
Electrical base speed transition into field weakening	${\omega }_{base}= \frac{v_{max}}{\sqrt{{\left(L_q{i}_q\right)}^2+{\left(L_d{i}_d+ {\lambda }_{pm}\right)}^2}}$
d-axis voltage	$$v_d=-{\omega }_e{L}_q{i}_{q_{max}}$$
q-axis voltage	$$v_q={\omega }_e(L_d{i}_{d\_max}+ {\lambda }_{pm})$$
Maximum phase current	$$i_{max}{}^2=i_{d\_\max }^2+i_{q\_\max }^2$$
Maximum line to neutral voltage	$$v_{max}= \frac{v_{bus} }{\sqrt{3}}$$
d-axis phase current MTPA table	$$\begin{array}{l}{I}_m=\frac{2T_{max}}{3P{\lambda }_{pm}}\\ i_{d\_mtpa}=\frac{{\lambda }_{pm}}{4\left(L_q-L_d\right)}-\sqrt{\frac{{\lambda }_{pm}^2}{16{\left(L_q-L_d\right)}^2}+\frac{I_m^2}{2}}\end{array}$$
q-axis phase current MTPA table	$i_{q\_mtpa}=\sqrt{I_m^2-{\left(i_{mtpa}\right)}^2}$
Torque MTPA breakpoints	$T_{mtpa}= \frac{3}{2}P\left({\lambda }_{pm}{i}_q+\left(L_d- L_q\right)i_d{i}_q\right)$
Field weakening, using the speed-based voltage limits	${\left(L_q{i}_q\right)}^2+{\left(L_d{i}_d+ {\lambda }_{pm}\right)}^2\le \frac{v_{max}^2}{{\omega }_e^2}$ $i_q= \sqrt{i_{max}^2- i_d^2}$ $\left(L_d^2- L_q^2\right)i_d^2+2{\lambda }_{pm}{L}_d{i}_d+ {\lambda }_{pm}+ L_q^2{i}_{max}^2-\frac{v_{max}^2}{{\omega }_e^2}=0$ $i_d{}_{fw}= \frac{-{\lambda }_{pm}{L}_d+ \sqrt{{\left({\lambda }_{pm}{L}_d\right)}^2- \left(L_d^2- L_q^2\right)\left({\lambda }_{pm}^2+ L_q^2{i}_{max}^2- \frac{v_{max}^2}{{\omega }_e^2} \right)}}{\left(L_d^2- L_q^2\right)}$ $T_{fw}= \frac{3}{2}P\left({\lambda }_{pm}{i}_{qfw}+\left(L_d- L_q\right)i_{dfw}{i}_{qfw}\right)$
Current command	If$\left|{\omega }_e\right|\le {\omega }_{base}$ $\begin{array}{l}{i}_{dref}= i_{d_{mtpa}}(T_{ref})\\ i_{qref}= i_{q_{mtpa}}(T_{ref})\end{array}$ Else $$\begin{array}{l} i_{dfw}= \max \left(i_{dfw},-i_{max}\right)\\ i_{qfw}= \sqrt{i_{max}^2- i_d^2}\end{array}$$ If $$T_{fw}<T_{ref}$$ $\begin{array}{l}{i}_{dref}= i_{d_{fw}}\\ i_{qref}= i_{q_{fw}}\end{array}$ Else $\begin{array}{l}{i}_{dref}= i_{d_{fw}}\\ i_{qref}= \frac{T_{ref}}{\frac{3}{2}P\left({\lambda }_{pm}+\left(L_d- L_q\right)i_{dfw}\right)}\end{array}$ End End

The equations use these variables.

imax	Maximum phase current
id	d-axis current
iq	q-axis current
id_max	Maximum d-axis phase current
iq_max	Maximum q-axis phase current
id_mtpa	d-axis phase current MTPA table
iq_mtpa	q-axis phase current MTPA table
Im	Estimated maximum current
idfw	d-axis field weakening current
iqfw	q-axis field weakening current
ωe	Rotor electrical speed
λpm	Permanent magnet flux linkage
vd	d-axis voltage
vq	q-axis voltage
vmax	Maximum line to neutral voltage
vbus	DC bus voltage
Ld	d-axis winding inductance
Lq	q-axis winding inductance
P	Motor pole pairs
Tfw	Field weakening torque
Tmtpa	Torque MTPA breakpoints

Current Regulators

The block regulates the current with an anti-windup feature. Classic proportional-integrator (PI) current regulators do not consider the d-axis and q-axis coupling or the back-electromagnetic force (EMF) coupling. As a result, transient performance deteriorates. To account for the coupling, the block implements the complex vector current regulator (CVCR) in the scalar format of the rotor reference frame. The CVCR decouples:

• d-axis and q-axis current cross-coupling

• Back-EMF cross-coupling

The current frequency response is a first-order system, with a bandwidth of EV_current.

The block implements these equations.

Calculation	Equations
Motor voltage, in the rotor reference frame	$$\begin{array}{l}{L}_d\frac{d{i}_d}{dt}= v_d-R_s{i}_d+p{\omega }_m{L}_q{i}_q\\ L_q\frac{d{i}_q}{dt}= v_q-R_s{i}_q-p{\omega }_m{L}_d{i}_d-p{\omega }_m{\lambda }_{pm}\end{array}$$
Current regulator gains	$\begin{array}{l}{\omega }_b=2\pi E{V}_{current}\\ K_{p\_d}=L_d{\omega }_b\\ K_{p\_q}=L_q{\omega }_b\\ K_i=R_s{\omega }_b\end{array}$
Transfer functions	$\begin{array}{l}\frac{i_d}{i_{dref}}= \frac{{\omega }_b}{s+{\omega }_b}\\ \frac{i_q}{i_{qref}}= \frac{{\omega }_b}{s+{\omega }_b}\end{array}$

The equations use these variables.

EVcurrent	Current regulator bandwidth
id	d-axis current
iq	q-axis current
Kp_d	Current regulator d-axis gain
Kp_q	Current regulator q-axis gain
Ld	d-axis winding inductance
Lq	q-axis winding inductance
Rs	Stator phase winding resistance
ωm	Rotor speed
vd	d-axis voltage
vq	q-axis voltage
λpm	Permanent magnet flux linkage
P	Motor pole pairs

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.

$\begin{array}{l}{\omega }_e=P{\omega }_m\\ \frac{d{\theta }_e}{dt}= {\omega }_e\end{array}$

Transform	Description	Equations
Clarke	Converts balanced three-phase quantities (a, b) into balanced two-phase quadrature quantities (α, β).	$\begin{array}{l}{x}_{\alpha }= \frac{2}{3}{x}_a- \frac{1}{3}{x}_b -\frac{1}{3}{x}_c\\ x_{\beta }= \frac{\sqrt{3}}{2}{x}_b- \frac{\sqrt{3}}{2}{x}_c\end{array}$
Park	Converts balanced two-phase orthogonal stationary quantities (α, β) into an orthogonal rotating reference frame (d, q).	$\begin{array}{l}{x}_d= x_{\alpha }\cos {\theta }_e+ x_{\beta }\sin {\theta }_e\\ x_q= -x_{\alpha }\sin {\theta }_e+ x_{\beta }\cos {\theta }_e\end{array}$
Inverse Clarke	Converts balanced two-phase quadrature quantities (α, β) into balanced three-phase quantities (a, b).	$\begin{array}{l}{x}_a= x_a\\ x_b= -\frac{1}{2}{x}_{\alpha }+ \frac{\sqrt{3}}{2}{x}_{\beta }\\ x_c= -\frac{1}{2}{x}_{\alpha }- \frac{\sqrt{3}}{2}{x}_{\beta }\end{array}$
Inverse Park	Converts an orthogonal rotating reference frame (d, q) into balanced two-phase orthogonal stationary quantities (α, β).	$\begin{array}{l}{x}_{\alpha }= x_d\cos {\theta }_e- x_q\sin {\theta }_e\\ x_{\beta }= x_d\sin {\theta }_e+ x_q\cos {\theta }_e\end{array}$

The transforms use these variables.

ωm	Rotor speed
P	Motor 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	$L{d}_{Pwr}=v_a i_a+ v_b i_b+ v_c i_c$
Source power	$Sr{c}_{Pwr}= L{d}_{Pwr}+Pw{r}_{Loss}$
DC bus current	$i_{bus}= \frac{Sr{c}_{Pwr}}{v_{bus}}$
Estimated rotor torque	$MtrTr{q}_{est}=1.5P[\lambda i_q+(L_d-L_q)i_d{i}_q]$
Power loss for single efficiency source to load	$$Pw{r}_{Loss}=\frac{100-Eff}{Eff}\cdot L{d}_{Pwr}$$
Power loss for single efficiency load to source	$$Pw{r}_{Loss}=\frac{100-Eff}{100}\cdot \left|L{d}_{Pwr}\right|$$
Power loss for tabulated efficiency	$Pw{r}_{Loss}= f({\omega }_m,MtrTr{q}_{est})$

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	q-axis winding inductance
Ld	d-axis winding inductance
iq	q-axis current
id	d-axis current
λ	Permanent magnet flux linkage
P	Motor pole pairs

Electrical Losses

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

Setting	Block 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

SpdReq — Rotor speed command

scalar

Rotor speed command, ω*_m, in rad/s.

Dependencies

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

TrqCmd — Torque command

scalar

Torque command, T*, in N·m.

Dependencies

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

BusVolt — DC bus voltage

scalar

DC bus voltage, v_bus, in V.

PhaseCurrA — Current

scalar

Stator current phase a, i_a, in A.

PhaseCurrB — Current

scalar

Stator current phase b, i_b, in A.

SpdFdbk — Rotor speed

scalar

Rotor speed, ω_m, in rad/s.

PosFdbk — Rotor electrical angle

scalar

Rotor electrical angle, Θ_m, in rad.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal	Description	Units
SrcPwr	Source power	W
LdPwr	Load power	W
PwrLoss	Power loss	W
MtrTrqEst	Estimated motor torque	N·m

BusCurr — Bus current

scalar

Estimated DC bus current, i_bus, in A.

PhaseVolt — Stator terminal voltages

array

Stator terminal voltages, V_a, V_b, and V_c, in V.

Parameters

Block Options

Control Type — Select control

Speed Control (default) | Torque Control

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

This table summarizes the port configurations.

Port Configuration	Creates Ports
Speed Control	SpdReq
Torque Control	TrqCmd

Motor Parameters

Stator resistance, Rs — Resistance

0.02 (default) | scalar

Stator phase winding resistance, R_s, in ohm.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
Stator resistance, Rs	D and Q axis integral gain, Ki	Current Controller

D-axis inductance, Ld — Inductance

1.7e-3 (default) | scalar

D-axis winding inductance, L_d, in H.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
D-axis inductance, Ld	Torque Breakpoints, T_mtpa D-axis table data, id_mtpa Q-axis table data, iq_mtpa D, q, and max current limits, idq_limits	Id and Iq Calculation

Q-axis inductance, Lq — Inductance

3.2e-3 (default) | scalar

Q-axis winding inductance, L_q, in H.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
Q-axis inductance, Lq	Torque Breakpoints, T_mtpa D-axis table data, id_mtpa Q-axis table data, iq_mtpa D, Q, and max current limits, idq_limits	Id and Iq Calculation

Permanent magnet flux, lambda_pm — Flux

0.2205 (default) | scalar

Permanent magnet flux, λ_pm, in Wb.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
Permanent magnet flux, lambda_pm	Torque Breakpoints, T_mtpa D-axis table data, id_mtpa Q-axis table data, iq_mtpa D, Q, and max current limits, idq_limits	Id and Iq Calculation

Number of pole pairs, PolePairs — Poles

4 (default) | scalar

Motor pole pairs, P.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
Number of pole pairs, PolePairs	Torque Breakpoints, T_mtpa D-axis table data, id_mtpa Q-axis table data, iq_mtpa D, Q, and max current limits, idq_limits	Id and Iq Calculation

Physical inertia, viscous damping, static friction, Mechanical — Inertia, damping, friction

[0.0027, 4.924e-4, 0] (default) | vector

Mechanical properties of the motor:

• Motor inertia, F_v, in kgm^2

• Viscous friction torque constant, F_v, in N·m/(rad/s)

• Static friction torque constant, F_s, in N·m

Dependencies

To enable this parameter, set the Control Type parameter to Speed Control.

For the gain calculations, the block uses the inertia from the Physical inertia, viscous damping, static friction parameter value that is on the Motor Parameters tab.

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
Physical inertia, viscous damping, static friction, Mechanical	Proportional gain, ba Angular gain, Ksa Rotational gain, Kisa Inertia compensation, Jcomp Viscous damping compensation, Fv Static friction, Fs	Speed Controller

Id and Iq Calculation

Motor constraint — Motor constraint

Maximum Torque (default) | Maximum Current

Motor constraint for MTPA control.

Maximum current, I_max — Current

44 (default) | scalar

Maximum current, in A.

Dependencies

To enable this parameter, set Motor constraint to Maximum Current.

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
Maximum torque, T_max	Torque Breakpoints, T_mtpa D-axis table data, id_mtpa Q-axis table data, iq_mtpa D, Q, and max current limits, idq_limits	Id and Iq Calculation

Maximum torque, T_max — Torque

60 (default) | scalar

Maximum torque, in N·m.

Dependencies

To enable this parameter, set Motor constraint to Maximum Torque.

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
Maximum torque, T_max	Torque Breakpoints, T_mtpa D-axis table data, id_mtpa Q-axis table data, iq_mtpa D, Q, and max current limits, idq_limits	Id and Iq Calculation

MTPA table breakpoints, bp — Number of breakpoints

10 (default) | scalar

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
MTPA table breakpoints, pb	Torque Breakpoints, T_mtpa D-axis table data, id_mtpa Q-axis table data, iq_mtpa D, Q, and max current limits, idq_limits	Id and Iq Calculation

Calculate MTPA Table Data — Derive parameters

button

Click to derive parameters.

Dependencies

On the Id and Iq Calculation tab, when you select Calculate MPTA Table data, the block calculates derived parameters. The table summarizes the derived parameter dependencies on other block parameters.

Derived Parameter on Id and Iq Calculation tab		Depends On
		Parameter	Tab
Torque Breakpoints, T_mtpa	$T_{mtpa}= \frac{3}{2}P\left({\lambda }_{pm}{i}_q+\left(L_d- L_q\right)i_d{i}_q\right)$	Maximum torque, T_max MTPA table breakpoints, pb	Id and Iq Calculation
D-axis table data, id_mtpa	$$\begin{array}{l}{I}_m=\frac{2T_{max}}{3P{\lambda }_{pm}}\\ i_{d\_mtpa}=\frac{{\lambda }_{pm}}{4\left(L_q-L_d\right)}-\sqrt{\frac{{\lambda }_{pm}^2}{16{\left(L_q-L_d\right)}^2}+\frac{I_m^2}{2}}\end{array}$$	Permanent magnet flux, lambda_pm D-axis inductance, Ld Q-axis inductance, Lq Number of pole pairs, PolePairs	Motor Parameters
Q-axis table data, iq_mtpa	$i_{q\_mtpa}=\sqrt{I_m^2-{\left(i_{mtpa}\right)}^2}$
D, Q, and max current limits, idq_limits

The equations use these variables.

imax	Maximum phase current
id	d-axis current
iq	q-axis current
id_max	Maximum d-axis phase current
iq_max	Maximum q-axis phase current
id_mtpa	d-axis phase current MTPA table
iq_mtpa	q-axis phase current MTPA table
λpm	Permanent magnet flux linkage
Ld	d-axis winding inductance
Lq	q-axis winding inductance
P	Motor pole pairs
Tmtpa	Torque MTPA breakpoints
Im	Estimated maximum current

Torque Breakpoints, T_mtpa — Derived

[0 6.41323967543524 12.8472271930531 19.3221671098192 25.8572437875407 32.4702594835269 39.177408529382 45.9931820911486 52.930379967864 60.0001984561834] (default) | vector

Derived torque breakpoints, in N·m.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
Torque Breakpoints, T_mtpa	Maximum torque, T_max MTPA table breakpoints, pb	Id and Iq Calculation
	Permanent magnet flux, lambda_pm D-axis inductance, Ld Q-axis inductance, Lq Number of pole pairs, PolePairs	Motor Parameters

D-axis table data, id_mtpa — Derived

[0 -0.159333276810563 -0.633258709677809 -1.41005695027301 -2.47173666500257 -3.79592548539108 -5.35786489234899 -7.13217478652462 -9.09420364751938 -11.2209236729158] (default) | vector

Derived d-axis table data, in A.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
D-axis table data, id_mtpa	Maximum torque, T_max MTPA table breakpoints, pb	Id and Iq Calculation
	Permanent magnet flux, lambda_pm D-axis inductance, Ld Q-axis inductance, Lq Number of pole pairs, PolePairs	Motor Parameters

Q-axis table data, iq_mtpa — Derived

[0 4.84224935172196 9.66902512748937 14.4660510262181 19.2212063070062 23.9250934510846 28.5711892538614 33.1556572971289 37.6769488702032 42.1353166357157] (default) | vector

Derived q-axis table data, in A.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
D-axis table data, id_mtpa	Maximum torque, T_max MTPA table breakpoints, pb	Id and Iq Calculation
	Permanent magnet flux, lambda_pm D-axis inductance, Ld Q-axis inductance, Lq Number of pole pairs, PolePairs	Motor Parameters

D, Q, and max current limits, idq_limits — Derived

[-11.2210468862948 42.1352838229553 43.6038305205566] (default) | array

Derived d, q, and maximum current limits, in A.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
D, Q, and max current limits, idq_limits	Maximum torque, T_max MTPA table breakpoints, pb	Id and Iq Calculation
	Permanent magnet flux, lambda_pm D-axis inductance, Ld Q-axis inductance, Lq Number of pole pairs, PolePairs	Motor Parameters

Current Controller

Bandwidth of the current regulator, EV_current — Bandwidth

200 (default) | scalar

Derived current regulator bandwidth, in Hz.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
Bandwidth of the current regulator, EV_current	D-axis proportional gain, Kp_d Q-axis proportional gain, Kp_q D and Q axis proportional gain, Ki	Current Controller

Sample time for the torque control, Tst — Time

5e-5 (default) | scalar

Derived torque control sample time, in s.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
	Parameter	Tab
Sample time for the torque control, Tst	Speed regulation time constant, Ksf	Speed Controller

Calculate Current Regulator Gains — Derive parameters

button

Click to derive parameters.

Dependencies

On the Current Controller tab, when you select Calculate Current Regulator Gains, the block calculates derived parameters. The table summarizes the derived parameter dependencies on other block parameters.

Derived Parameter on Current Controller tab	Dependency
	Parameter	Tab
D-axis proportional gain, Kp_d Q-axis proportional gain, Kp_q D and Q axis integral gain, Ki	Bandwidth of the current regulator, EV_current	Current Controller
	Stator resistance, Rs	Motor Parameters

D-axis proportional gain, Kp_d — Derived

2.1363 (default) | scalar

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

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
D-axis proportional gain, Kp_d	Bandwidth of the current regulator, EV_current	Current Controller

Q-axis proportional gain, Kp_q — Derived

4.0212 (default) | scalar

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

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
Q-axis proportional gain, Kp_q	Bandwidth of the current regulator, EV_current	Current Controller

D and Q axis integral gain, Ki — Derived

25.1327 (default) | scalar

Derived d- and q- axis integral gains, in V/A·s.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
D and Q axis integral gain, Ki	Stator resistance, Rs	Motor Parameters

Speed Controller

Bandwidth of the motion controller, EV_motion — Bandwidth

[20, 4, 0.8] (default) | vector

Motion controller bandwidth, in Hz. Set the first element of the vector to the desired cutoff frequency. Set the second and third elements of the vector to the higher-order cut off frequencies. You can set the value of the next element to 1/5 the value of the previous element. For example, if the desired cutoff frequency is 20 Hz, specify [20 4 0.8].

Dependencies

The parameter is enabled when the Control Type parameter is set to Speed Control.

Parameter	Used to Derive
	Parameter	Tab
Bandwidth of the motion controller, EV_motion	Proportional gain, ba Angular gain, Ksa Rotational gain, Kisa	Speed Controller

Bandwidth of the state filter, EV_sf — Bandwidth

200 (default) | scalar

State filter bandwidth, in Hz.

Dependencies

The parameter is enabled when the Control Type parameter is set to Speed Control.

Parameter	Used to Derive
	Parameter	Tab
Bandwidth of the state filter, EV_sf	Speed regulation time constant, Ksf	Speed Controller

Calculate Speed Regulator Gains — Derive parameters

button

Click to derive parameters.

Dependencies

On the Speed Controller tab, when you select Calculate Speed Regulator Gains, the block calculates derived parameters. The table summarizes the derived parameters that depend on other block parameters.

Derived Parameter on Speed Controller tab		Depends On
		Parameter	Tab
Proportional gain, ba	$b_a=\frac{J_p-J_p{p}_1{p}_2{p}_3}{T_{sm}}$	Bandwidth of the motion controller, EV_motion Bandwidth of the state filter, EV_sf	Speed Controller
Angular gain, Ksa	$K_{sa}=\frac{J_p\left(p_1{p}_2+p_2{p}_3+p_3{p}_1\right)-3J_p+2b_a{T}_{sm}}{T_{sm}^2}$	Sample time for the torque control, Tst	Current Controller
Rotational gain, Kisa	$K_{isa}=\frac{-J_p\left(p_1+p_2+p_3\right)+3J_p-b_a{T}_{sm}-K_{sa}{T}_{sm}^2}{T_{sm}^3}$	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
Speed regulation time constant, Ksf	$K_{sf}=\frac{1-\exp \left(-T_{sm}2\pi E{V}_{sf}\right)}{T_{sm}}$
Inertia compensation, Jcomp	Jcomp = Jp	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
Viscous damping compensation, Fv	Fv
Static friction, Fs	Fs

The equations use these variables.

P	Motor pole pairs
ba	Speed regulator proportional gain
Ksa	Speed regulator integral gain
Kisa	Speed regulator double integral gain
Ksf	Speed regulator time constant
Jp	Motor inertia
EVsf	State filter bandwidth
EVmotion	Motion controller bandwidth

Proportional gain, ba — Derived

3.7477 (default) | scalar

Derived proportional gain, in N·m/(rad/s).

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
Proportional gain, ba	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
	Bandwidth of the motion controller, EV_motion	Speed Controller

Angular gain, Ksa — Derived

94.0877 (default) | scalar

Derived angular gain, in N·m/rad.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
Angular gain, Ksa	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
	Bandwidth of the motion controller, EV_motion	Speed Controller

Rotational gain, Kisa — Derived

381.7822 (default) | scalar

Derived rotational gain, in N·m/(rad*s).

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
Rotational gain, Kisa	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
	Bandwidth of the motion controller, EV_motion	Speed Controller

Speed regulation time constant, Ksf — Derived

1217.9727 (default) | scalar

Derived speed regulation time constant, in 1/s.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
Speed regulation time constant, Ksf	Sample time for the torque control, Tst	Current Controller
	Bandwidth of the state filter, EV_sf	Speed Controller

Inertia compensation, Jcomp — Derived

0.025 (default) | scalar

Derived inertia compensation, in kg·m^2.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
Inertia compensation, Jcomp	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters

Viscous damping compensation, Fv — Derived

0 (default) | scalar

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
Viscous damping compensation, Fv	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters

Static friction, Fs — Derived

0 (default) | scalar

Derived static friction, in N·m/(rad/s).

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
	Parameter	Tab
Static friction, Fs	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters

Electrical Losses

Parameterize losses by — Select type

Single efficiency measurement (default) | Tabulated loss data | Tabulated efficiency data

Setting	Block 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 — Constant

98 (default) | scalar

Overall inverter efficiency, Eff, in %.

Dependencies

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

Vector of speeds (w) for tabulated loss, w_loss_bp — Breakpoints

[0 200 400 600 800 1000] (default) | 1-by-M vector

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

Dependencies

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

Vector of torques (T) for tabulated loss, T_loss_bp — Breakpoints

[0 25 50 75 100] (default) | 1-by-N vector

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

Dependencies

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

Corresponding losses, losses_table — Table

[100 100 100 100 100;100 150 200 250 300;100 200 300 400 500;100 250 400 550 700;100 300 500 700 900;100 350 600 850 1100] (default) | M-by-N array

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.

Vector of speeds (w) for tabulated efficiency, w_eff_bp — Breakpoints

[200 400 600 800 1000] (default) | 1-by-M vector

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

Dependencies

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

Vector of torques (T) for tabulated efficiency, T_eff_bp — Breakpoints

[25 50 75 100] (default) | 1-by-N vector

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

Dependencies

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

Corresponding efficiency, efficiency_table — Table

[96.2 98.1 98.7 99;98.1 99 99.4 99.5;98.7 99.4 99.6 99.7;99 99.5 99.7 99.8;99.2 99.6 99.7 99.8] (default) | M-by-N array

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] Lorenz, Robert D., Thomas Lipo, and Donald W. Novotny. “Motion control with induction motors.” Proceedings of the IEEE^®, Vol. 82, Issue 8, August 1994, pp. 1215–1240.

[2] Morimoto, Shigeo, Masayuka Sanada, and Yoji Takeda. “Wide-speed operation of interior permanent magnet synchronous motors with high-performance current regulator.” IEEE Transactions on Industry Applications, Vol. 30, Issue 4, July/August 1994, pp. 920–926.

[3] Li, Muyang. “Flux-Weakening Control for Permanent-Magnet Synchronous Motors Based on Z-Source Inverters.” Master’s Thesis, Marquette University, e-Publications@Marquette, Fall 2014.

[4] Briz, Fernando, Michael W. Degner, and Robert D. Lorenz. "Analysis and design of current regulators using complex vectors." IEEE Transactions on Industry Applications, Vol. 36, Issue 3, May/June 2000, pp. 817–825.

[5] Briz, Fernando, et al. "Current and flux regulation in field-weakening operation [of induction motors]."IEEE Transactions on Industry Applications, Vol. 37, Issue 1, Jan/Feb 2001, pp. 42–50.

Extended Capabilities

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

Version History

Introduced in R2017a