Interior PM Controller

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

Library:
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
i_d i_d*	d-axis current d-axis current command
i_q i_q*	q-axis current q-axis current command
v_d, v_d*	d-axis voltage d-axis voltage command
v_q v_q*	q-axis voltage q-axis voltage command
v_a, v_b, v_c	Stator phase a, b, c voltages
i_a, i_b, i_c	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 time constant, Ksf gain based on the state filter bandwidth, select Calculate Speed Regulator Gains.

The discrete form of characteristic equation is given by:

$z + K_{s f} T_{s m} - 1$

The filter calculates the gain using this equation.

$K_{s f} = \frac{1 - \exp (- T_{s m} 2 π E V_{s f})}{T_{s m}}$

The equations use these variables.

EV_sf	Bandwidth of the speed command filter
T_sm	Motion controller sample time
K_sf	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	$z^{3} + \frac{(- 3 J_{p} + T_{s} b_{a} + T_{s}^{2} K_{s a} + T_{s}^{3} K_{i s a})}{J_{p}} z^{2} + \frac{(3 J_{p} - 2 T_{s} b_{a} - T_{s}^{2} K_{s a})}{J_{p}} z + \frac{- J_{p} + T_{s} b_{a}}{J_{p}}$ $(z - p_{1}) (z - p_{2}) (z - p_{3}) = z^{3} + (p_{1} + p_{2} + p_{3}) z^{2} + (p_{1} p_{2} + p_{2} p_{3} + p_{1} 3) z^{2} - p_{1} p_{2} p_{3}$
Speed regulator proportional gain	$b_{a} = \frac{J_{p} - J_{p} p_{1} p_{2} p_{3}}{T_{s m}}$
Speed regulator integral gain	$K_{s a} = \frac{J_{p} (p_{1} p_{2} + p_{2} p_{3} + p_{3} p_{1}) - 3 J_{p} + 2 b_{a} T_{s m}}{T_{s m}^{2}}$
Speed regulator double integral gain	$K_{i s a} = \frac{- J_{p} (p_{1} + p_{2} + p_{3}) + 3 J_{p} - b_{a} T_{s m} - K_{s a} T_{s m}^{2}}{T_{s m}^{3}}$

The equations use these variables.

P	Motor pole pairs
b_a	Speed regulator proportional gain
K_sa	Speed regulator integral gain
K_isa	Speed regulator double integral gain
J_p	Motor inertia
T_sm	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.

$T_{c m d_f f} = J_{p} {\dot{ω}}_{m} + F_{v} ω_{m} + F_{s} \frac{ω_{m}}{| ω_{m} |}$

where:

J_p	Motor inertia
T_{cmd_ff}	Torque command feedforward
F_s	Static friction torque constant
F_v	Viscous friction torque constant
F_s	Static friction torque constant
ω_m	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	$ω_{b a s e} = \frac{v_{m a x}}{\sqrt{{(L_{q} i_{q})}^{2} + {(L_{d} i_{d} + λ_{p m})}^{2}}}$
d-axis voltage	$v_{d} = - ω_{e} L_{q} i_{q_{m a x}}$
q-axis voltage	$v_{q} = ω_{e} (L_{d} i_{d_m a x} + λ_{p m})$
Maximum phase current	$i_{m a x}^{2} = i_{d_\max}^{2} + i_{q_\max}^{2}$
Maximum line to neutral voltage	$v_{m a x} = \frac{v_{b u s}}{\sqrt{3}}$
d-axis phase current MTPA table	$\begin{array}{l} I_{m} = \frac{2 T_{m a x}}{3 P λ_{p m}} \\ i_{d_m t p a} = \frac{λ_{p m}}{4 (L_{q} - L_{d})} - \sqrt{\frac{λ_{p m}^{2}}{16 {(L_{q} - L_{d})}^{2}} + \frac{I_{m}^{2}}{2}} \end{array}$
q-axis phase current MTPA table	$i_{q_m t p a} = \sqrt{I_{m}^{2} - {(i_{m t p a})}^{2}}$
Torque MTPA breakpoints	$T_{m t p a} = \frac{3}{2} P (λ_{p m} i_{q} + (L_{d} - L_{q}) i_{d} i_{q})$
Field weakening, using the speed-based voltage limits	${(L_{q} i_{q})}^{2} + {(L_{d} i_{d} + λ_{p m})}^{2} \leq \frac{v_{m a x}^{2}}{ω_{e}^{2}}$ $i_{q} = \sqrt{i_{m a x}^{2} - i_{d}^{2}}$ $(L_{d}^{2} - L_{q}^{2}) i_{d}^{2} + 2 λ_{p m} L_{d} i_{d} + λ_{p m} + L_{q}^{2} i_{m a x}^{2} - \frac{v_{m a x}^{2}}{ω_{e}^{2}} = 0$ $i_{d}_{f w} = \frac{- λ_{p m} L_{d} + \sqrt{{(λ_{p m} L_{d})}^{2} - (L_{d}^{2} - L_{q}^{2}) (λ_{p m}^{2} + L_{q}^{2} i_{m a x}^{2} - \frac{v_{m a x}^{2}}{ω_{e}^{2}})}}{(L_{d}^{2} - L_{q}^{2})}$ $T_{f w} = \frac{3}{2} P (λ_{p m} i_{q f w} + (L_{d} - L_{q}) i_{d f w} i_{q f w})$
Current command	If $\| ω_{e} \| \leq ω_{b a s e}$ $\begin{array}{l} i_{d r e f} = i_{d_{m t p a}} (T_{r e f}) \\ i_{q r e f} = i_{q_{m t p a}} (T_{r e f}) \end{array}$ Else $\begin{array}{l} i_{d f w} = \max (i_{d f w}, - i_{m a x}) \\ i_{q f w} = \sqrt{i_{m a x}^{2} - i_{d}^{2}} \end{array}$ If $T_{f w} < T_{r e f}$ $\begin{array}{l} i_{d r e f} = i_{d_{f w}} \\ i_{q r e f} = i_{q_{f w}} \end{array}$ Else $\begin{array}{l} i_{d r e f} = i_{d_{f w}} \\ i_{q r e f} = \frac{T_{r e f}}{\frac{3}{2} P (λ_{p m} + (L_{d} - L_{q}) i_{d f w})} \end{array}$ End End

The equations use these variables.

i_max	Maximum phase current
i_d	d-axis current
i_q	q-axis current
i_{d_max}	Maximum d-axis phase current
i_{q_max}	Maximum q-axis phase current
i_{d_mtpa}	d-axis phase current MTPA table
i_{q_mtpa}	q-axis phase current MTPA table
I_m	Estimated maximum current
i_dfw	d-axis field weakening current
i_qfw	q-axis field weakening current
ω_e	Rotor electrical speed
λ_pm	Permanent magnet flux linkage
v_d	d-axis voltage
v_q	q-axis voltage
v_max	Maximum line to neutral voltage
v_bus	DC bus voltage
L_d	d-axis winding inductance
L_q	q-axis winding inductance
P	Motor pole pairs
T_fw	Field weakening torque
T_mtpa	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	$\begin{array}{l} L_{d} \frac{d i_{d}}{d t} = v_{d} - R_{s} i_{d} + p ω_{m} L_{q} i_{q} \\ L_{d} \frac{d i_{q}}{d t} = v_{q} - R_{s} i_{q} - p ω_{m} L_{d} i_{d} - p ω_{m} λ_{p m} \end{array}$
Current regulator gains	$\begin{array}{l} ω_{b} = 2 π E V_{c u r r e n t} \\ K_{p_d} = L_{d} ω_{b} \\ K_{p_q} = L_{q} ω_{b} \\ K_{i} = R_{s} ω_{b} \end{array}$
Transfer functions	$\begin{array}{l} \frac{i_{d}}{i_{d r e f}} = \frac{ω_{b}}{s + ω_{b}} \\ \frac{i_{q}}{i_{q r e f}} = \frac{ω_{b}}{s + ω_{b}} \end{array}$

The equations use these variables.

EV_current	Current regulator bandwidth
i_d	d-axis current
i_q	q-axis current
K_{p_d}	Current regulator d-axis gain
K_{p_q}	Current regulator q-axis gain
L_d	d-axis winding inductance
L_q	q-axis winding inductance
R_s	Stator phase winding resistance
ω_m	Rotor speed
v_d	d-axis voltage
v_q	q-axis voltage
λ_pm	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.

$\begin{array}{l} ω_{e} = P ω_{m} \\ \frac{d θ_{e}}{d t} = ω_{e} \end{array}$

Transform	Description	Equations
Clarke	Converts balanced three-phase quantities (a, b) into balanced two-phase quadrature quantities (α, β).	$\begin{array}{l} x_{α} = \frac{2}{3} x_{a} - \frac{1}{3} x_{b} - \frac{1}{3} x_{c} \\ x_{β} = \frac{\sqrt{3}}{2} x_{b} - \frac{\sqrt{3}}{2} x_{c} \end{array}$
Park	Converts balanced two-phase orthogonal stationary quantities (α, β) into an orthogonal rotating reference frame (d, q).	$\begin{array}{l} x_{d} = x_{α} \cos θ_{e} + x_{β} \sin θ_{e} \\ x_{q} = - x_{α} \sin θ_{e} + x_{β} \cos θ_{e} \end{array}$
Inverse Clarke	Converts balanced two-phase quadrature quantities (α, β) into balanced three-phase quantities (a, b).	$\begin{array}{l} x_{a} = x_{a} \\ x_{b} = - \frac{1}{2} x_{α} + \frac{\sqrt{3}}{2} x_{β} \\ x_{c} = - \frac{1}{2} x_{α} - \frac{\sqrt{3}}{2} x_{β} \end{array}$
Inverse Park	Converts an orthogonal rotating reference frame (d, q) into balanced two-phase orthogonal stationary quantities (α, β).	$\begin{array}{l} x_{α} = x_{d} \cos θ_{e} - x_{q} \sin θ_{e} \\ x_{β} = x_{d} \sin θ_{e} + x_{q} \cos θ_{e} \end{array}$

The transforms use these variables.

ω_m	Rotor speed
P	Motor pole pairs
ω_e	Rotor electrical speed
Θ_e	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	$L d_{P w r} = v_{a} i_{a} + v_{b} i_{b} + v_{c} i_{c}$
Source power	$S r c_{P w r} = L d_{P w r} + P w r_{L o s s}$
DC bus current	$i_{b u s} = \frac{S r c_{P w r}}{v_{b u s}}$
Estimated rotor torque	$M t r T r q_{e s t} = 1.5 P [λ i_{q} + (L_{d} - L_{q}) i_{d} i_{q}]$
Power loss for single efficiency source to load	$P w r_{L o s s} = \frac{100 - E f f}{E f f} \cdot L d_{P w r}$
Power loss for single efficiency load to source	$P w r_{L o s s} = \frac{100 - E f f}{100} \cdot \| L d_{P w r} \|$
Power loss for tabulated efficiency	$P w r_{L o s s} = f (ω_{m}, M t r T r q_{e s t})$

The equations use these variables.

v_a, v_b, v_c	Stator phase a, b, c voltages
v_bus	Estimated DC bus voltage
i_a, i_b, i_c	Stator phase a, b, c currents
i_bus	Estimated DC bus current
Eff	Overall inverter efficiency
ω_m	Rotor mechanical speed
L_q	q-axis winding inductance
L_d	d-axis winding inductance
i_q	q-axis current
i_d	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

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.

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

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`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

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`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

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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	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
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

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
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

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
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

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
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

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
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

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

`Maximum torque, T_max` — Torque
`60` (default) | `scalar`

Maximum torque, in N·m.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
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

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
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

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
Derived Parameter on Id and Iq Calculation tab		Parameter	Tab
Torque Breakpoints, T_mtpa	$T_{m t p a} = \frac{3}{2} P (λ_{p m} i_{q} + (L_{d} - L_{q}) i_{d} i_{q})$	Maximum torque, T_max MTPA table breakpoints, pb	Id and Iq Calculation
D-axis table data, id_mtpa	$\begin{array}{l} I_{m} = \frac{2 T_{m a x}}{3 P λ_{p m}} \\ i_{d_m t p a} = \frac{λ_{p m}}{4 (L_{q} - L_{d})} - \sqrt{\frac{λ_{p m}^{2}}{16 {(L_{q} - L_{d})}^{2}} + \frac{I_{m}^{2}}{2}} \end{array}$	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	$i_{q_m t p a} = \sqrt{I_{m}^{2} - {(i_{m t p a})}^{2}}$
D, Q, and max current limits, idq_limits	$i_{q_m t p a} = \sqrt{I_{m}^{2} - {(i_{m t p a})}^{2}}$

The equations use these variables.

i_max	Maximum phase current
i_d	d-axis current
i_q	q-axis current
i_{d_max}	Maximum d-axis phase current
i_{q_max}	Maximum q-axis phase current
i_{d_mtpa}	d-axis phase current MTPA table
i_{q_mtpa}	q-axis phase current MTPA table
λ_pm	Permanent magnet flux linkage
L_d	d-axis winding inductance
L_q	q-axis winding inductance
P	Motor pole pairs
T_mtpa	Torque MTPA breakpoints
I_m	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
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

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
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

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
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

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
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

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
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

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	Parameter	Tab
Sample time for the torque control, Tst	Speed 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
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

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	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	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	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
Bandwidth of the motion controller, EV_motion	Proportional gain, ba Angular gain, Ksa Rotational gain, Kisa	Speed Controller

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	Parameter	Tab
Bandwidth of the state filter, EV_sf	Speed 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
Derived Parameter on Speed Controller tab		Parameter	Tab
Proportional gain, ba	$b_{a} = \frac{J_{p} - J_{p} p_{1} p_{2} p_{3}}{T_{s m}}$	Bandwidth of the motion controller, EV_motion Bandwidth of the state filter, EV_sf	Speed Controller
Angular gain, Ksa	$K_{s a} = \frac{J_{p} (p_{1} p_{2} + p_{2} p_{3} + p_{3} p_{1}) - 3 J_{p} + 2 b_{a} T_{s m}}{T_{s m}^{2}}$	Sample time for the torque control, Tst	Current Controller
Rotational gain, Kisa	$K_{i s a} = \frac{- J_{p} (p_{1} + p_{2} + p_{3}) + 3 J_{p} - b_{a} T_{s m} - K_{s a} T_{s m}^{2}}{T_{s m}^{3}}$	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
Speed time constant, Ksf	$K_{s f} = \frac{1 - \exp (- T_{s m} 2 π E V_{s f})}{T_{s m}}$		Motor Parameters
Inertia compensation, Jcomp	J_comp = J_p	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
Viscous damping compensation, Fv	F_v
Static friction, Fs	F_s

The equations use these variables.

P	Motor pole pairs
b_a	Speed regulator proportional gain
K_sa	Speed regulator integral gain
K_isa	Speed regulator double integral gain
K_sf	Speed regulator time constant
J_p	Motor inertia
EV_sf	State filter bandwidth
EV_motion	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	Parameter	Tab
Proportional gain, ba	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
Proportional gain, ba	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	Parameter	Tab
Angular gain, Ksa	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
Angular gain, Ksa	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	Parameter	Tab
Rotational gain, Kisa	Physical inertia, viscous damping, static friction, Mechanical	Motor Parameters
Rotational gain, Kisa	Bandwidth of the motion controller, EV_motion	Speed Controller

`Speed time constant, Ksf` — Derived
`1217.9727` (default) | `scalar`

Derived speed time constant, in 1/s.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Dependency
Parameter	Parameter	Tab
Speed time constant, Ksf	Sample time for the torque control, Tst	Current Controller
Speed time constant, Ksf	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	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	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	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

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.

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.

Documentation

Interior PM Controller

Description

Speed Controller

State Filter

State Feedback

Command Feedforward

Torque Determination

Current Regulators

Transforms

Motor

Electrical Losses

Ports

Input

SpdReq — Rotor speed command scalar

Dependencies

TrqCmd — Torque command scalar

Dependencies

BusVolt — DC bus voltage scalar

PhaseCurrA — Current scalar

PhaseCurrB — Current scalar

SpdFdbk — Rotor speed scalar

PosFdbk — Rotor electrical angle scalar

Output

Info — Bus signal bus

BusCurr — Bus current scalar

PhaseVolt — Stator terminal voltages array

Parameters

Block Options

Control Type — Select control Speed Control (default) | Torque Control

Motor Parameters

Stator resistance, Rs — Resistance 0.02 (default) | scalar

Dependencies

D-axis inductance, Ld — Inductance 1.7e-3 (default) | scalar

Dependencies

Q-axis inductance, Lq — Inductance 3.2e-3 (default) | scalar

Dependencies

Permanent magnet flux, lambda_pm — Flux 0.2205 (default) | scalar

Dependencies

Number of pole pairs, PolePairs — Poles 4 (default) | scalar

Dependencies

Physical inertia, viscous damping, static friction, Mechanical — Inertia, damping, friction [0.0027, 4.924e-4, 0] (default) | vector

Dependencies

Id and Iq Calculation

Maximum torque, T_max — Torque 60 (default) | scalar

Dependencies

MTPA table breakpoints, bp — Number of breakpoints 10 (default) | scalar

Dependencies

Calculate MTPA Table Data — Derive parameters button

Dependencies

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

Dependencies

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

Dependencies

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

Dependencies

D, Q, and max current limits, idq_limits — Derived [-11.2210468862948 42.1352838229553 43.6038305205566] (default) | array

Dependencies

Current Controller

Bandwidth of the current regulator, EV_current — Bandwidth 200 (default) | scalar

Dependencies

Sample time for the torque control, Tst — Time 5e-5 (default) | scalar

Dependencies

Calculate Current Regulator Gains — Derive parameters button

Dependencies

D-axis proportional gain, Kp_d — Derived 2.1363 (default) | scalar

Dependencies

Q-axis proportional gain, Kp_q — Derived 4.0212 (default) | scalar

Dependencies

D and Q axis integral gain, Ki — Derived 25.1327 (default) | scalar

Dependencies

Speed Controller

Bandwidth of the motion controller, EV_motion — Bandwidth [20, 4, 0.8] (default) | vector

Dependencies

Bandwidth of the state filter, EV_sf — Bandwidth 200 (default) | scalar

Dependencies

Calculate Speed Regulator Gains — Derive parameters button

Dependencies

Proportional gain, ba — Derived 3.7477 (default) | scalar

Dependencies

`SpdReq` — Rotor speed command
`scalar`

`TrqCmd` — Torque command
`scalar`

`BusVolt` — DC bus voltage
`scalar`

`PhaseCurrA` — Current
`scalar`

`PhaseCurrB` — Current
`scalar`

`SpdFdbk` — Rotor speed
`scalar`

`PosFdbk` — Rotor electrical angle
`scalar`

`Info` — Bus signal
bus

`BusCurr` — Bus current
`scalar`

`PhaseVolt` — Stator terminal voltages
`array`

`Control Type` — Select control
`Speed Control` (default) | `Torque Control`

`Stator resistance, Rs` — Resistance
`0.02` (default) | `scalar`

`D-axis inductance, Ld` — Inductance
`1.7e-3` (default) | `scalar`

`Q-axis inductance, Lq` — Inductance
`3.2e-3` (default) | `scalar`

`Permanent magnet flux, lambda_pm` — Flux
`0.2205` (default) | `scalar`

`Number of pole pairs, PolePairs` — Poles
`4` (default) | `scalar`

`Physical inertia, viscous damping, static friction, Mechanical` — Inertia, damping, friction
`[0.0027, 4.924e-4, 0]` (default) | `vector`

`Maximum torque, T_max` — Torque
`60` (default) | `scalar`

`MTPA table breakpoints, bp` — Number of breakpoints
`10` (default) | `scalar`

`Calculate MTPA Table Data` — Derive parameters
button

`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`

`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`

`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`

`D, Q, and max current limits, idq_limits` — Derived
`[-11.2210468862948 42.1352838229553 43.6038305205566]` (default) | `array`

`Bandwidth of the current regulator, EV_current` — Bandwidth
`200` (default) | `scalar`

`Sample time for the torque control, Tst` — Time
`5e-5` (default) | `scalar`

`Calculate Current Regulator Gains` — Derive parameters
button

`D-axis proportional gain, Kp_d` — Derived
`2.1363` (default) | `scalar`

`Q-axis proportional gain, Kp_q` — Derived
`4.0212` (default) | `scalar`

`D and Q axis integral gain, Ki` — Derived
`25.1327` (default) | `scalar`

`Bandwidth of the motion controller, EV_motion` — Bandwidth
`[20, 4, 0.8]` (default) | `vector`

`Bandwidth of the state filter, EV_sf` — Bandwidth
`200` (default) | `scalar`

`Calculate Speed Regulator Gains` — Derive parameters
button

`Proportional gain, ba` — Derived
`3.7477` (default) | `scalar`

`Angular gain, Ksa` — Derived
`94.0877` (default) | `scalar`

`Rotational gain, Kisa` — Derived
`381.7822` (default) | `scalar`

`Speed time constant, Ksf` — Derived
`1217.9727` (default) | `scalar`

`Inertia compensation, Jcomp` — Derived
`0.025` (default) | `scalar`

`Viscous damping compensation, Fv` — Derived
`0` (default) | `scalar`

`Static friction, Fs` — Derived
`0` (default) | `scalar`

`Parameterize losses by` — Select type
`Single efficiency measurement` (default) | `Tabulated loss data` | `Tabulated efficiency data`

`Overall inverter efficiency, eff` — Constant
`98` (default) | `scalar`

`Vector of speeds (w) for tabulated loss, w_loss_bp` — Breakpoints
`[0 200 400 600 800 1000]` (default) | `1`-by-`M` vector

`Vector of torques (T) for tabulated loss, T_loss_bp` — Breakpoints
`[0 25 50 75 100]` (default) | `1`-by-`N` vector

`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

`Vector of speeds (w) for tabulated efficiency, w_eff_bp` — Breakpoints
`[200 400 600 800 1000]` (default) | `1`-by-`M` vector

`Vector of torques (T) for tabulated efficiency, T_eff_bp` — Breakpoints
`[25 50 75 100]` (default) | `1`-by-`N` vector

`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

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