IM Controller

Internal torque-based, field-oriented controller for an induction motor with an optional outer-loop speed controller

Library:
Powertrain Blockset / Propulsion / Electric Motor Controllers

Description

The IM Controller block implements an internal torque-based, field-oriented controller for an induction motor (IM) with an optional outer-loop speed controller. The torque control implements a strategy to control the motor flux. You can specify either speed or torque control.

The IM 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 IM 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 equation uses 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 compute:

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 Parameter 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 Parameter tab.

The feedforward torque command uses this equation.

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

The equation uses these variables.

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 mechanical speed

Torque Determination

The block uses a quadrature current to determine the base speed and the current commands. The motor ratings determine the rated electrical speed.

Calculation	Equations
Current commands	$i_{q r e f} = \frac{T_{c m d}}{i_{s q_0} \cdot P \cdot (\frac{L^{2}_{m}}{L_{r}})}$ If $\| ω_{e} \| \leq ω_{r a t e d}$ $i_{d r e f} = i_{s d_0}$ Else $i_{d r e f} = \frac{i_{s d_0}}{\| ω_{e} \|}$ End
Inductance	$\begin{array}{l} L_{r} = L_{l r} + L_{m} \\ L_{s} = L_{l s} + L_{m} \end{array}$

The equations use these variables.

i_dref	d-axis reference current
i_qref	q-axis reference current
i_{sd_0}	d-axis rated current
i_{sq_0}	q-axis rated current
ω_e	Rotor electrical speed
ω_rated	Rated electrical speed
L_lr	Rotor leaking inductance
L_r	Rotor winding inductance
L_ls	Stator leaking inductance
L_s	Stator winding inductance
L_m	Motor magnetizing inductance
P	Motor pole pairs
T_cmd	Commanded motor maximum torque

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 stator reference frame	$\begin{array}{l} σ = 1 - \frac{L^{2}_{m}}{L_{s} L_{r}} \\ v_{s d} = R_{s} i_{s d} + σ L_{s} \frac{d i_{s d}}{d t} + \frac{L_{m}}{L_{r}} \frac{d λ_{r d}}{d t} - P ω_{m} σ L_{s} i_{s q} \\ v_{s q} = R_{s} i_{s q} + σ L_{s} \frac{d i_{s q}}{d t} + ω_{d} \frac{L_{m}}{L_{r}} \frac{d λ_{r d}}{d t} + P ω_{m} σ L_{s} i_{s d} \end{array}$
Current regulator gains	$\begin{array}{l} ω_{b} = 2 π E V_{c u r r e n t} \\ K_{p} = σ L_{d} ω_{b} \\ K_{i} = R_{s} ω_{b} \end{array}$
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
i_sq	Stator q-axis current
i_sd	Stator d-axis current
v_sd	Stator d-axis voltage
v_sq	Stator q-axis voltage
K_p	Current regulator d-axis gain
K_i	Current regulator integrator gain
L_s	Stator winding inductance
L_m	Motor magnetizing inductance
L_r	Rotor winding inductance
R_s	Stator phase winding resistance
λ_rd	Rotor d-axis magnetic flux
σ	Leakage factor
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 mechanical 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	$M t r T r q_{e s t} = P λ_{r d} i_{s q} \frac{L_{m}}{L_{r}}$
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_r	Rotor winding inductance
L_m	Motor magnetizing inductance
λ_rd	Rotor d-axis magnetic flux
i_sq	q-axis current
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 mechanical speed command
`scalar`

Rotor mechanical 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 mechanical speed
`scalar`

Rotor mechanical speed, ω_m, in rad/s.

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

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

Stator phase winding resistance, R_s, in ohm.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Stator resistance, Rs	D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Id and Iq Calculation
D and Q axis integral gain, Ki	Current Controller

Parameter

Used to Derive

Parameter

Tab

Stator resistance, Rs

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Id and Iq Calculation

D and Q axis integral gain, Ki

Current Controller

`Stator leakage inductance, Lls` — Inductance
`0.0139` (default) | `scalar`

Stator leakage inductance, L_ls, in H.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Stator leakage inductance, Lls	D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Id and Iq Calculation
D and Q axis proportional gain, Kp D and Q axis integral gain, Ki	Current Controller

Parameter

Used to Derive

Parameter

Tab

Stator leakage inductance, Lls

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Id and Iq Calculation

D and Q axis proportional gain, Kp

D and Q axis integral gain, Ki

Current Controller

`Rotor resistance, Rr` — Resistance
`1.34` (default) | `scalar`

Rotor resistance, R_r, in ohm.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Rotor resistance, Rr	D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Id and Iq Calculation

Parameter

Used to Derive

Parameter

Tab

Rotor resistance, Rr

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Id and Iq Calculation

`Rotor leakage inductance, Llr` — Inductance
`0.0121` (default) | `scalar`

Rotor leakage inductance, L_lr, in H.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Rotor leakage inductance, Llr	D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Id and Iq Calculation
D and Q axis proportional gain, Kp	Current Controller

Parameter

Used to Derive

Parameter

Tab

Rotor leakage inductance, Llr

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Id and Iq Calculation

D and Q axis proportional gain, Kp

Current Controller

`Rotor magnetizing inductance, Lm` — Inductance
`0.3687` (default) | `scalar`

Rotor magnetizing inductance, L_m, in H.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Rotor leakage inductance, Llr	D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Id and Iq Calculation
D and Q axis proportional gain, Kp	Current Controller

Parameter

Used to Derive

Parameter

Tab

Rotor leakage inductance, Llr

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Id and Iq Calculation

D and Q axis proportional gain, Kp

Current Controller

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

Motor pole pairs, P.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Parameter	Parameter	Tab
Rotor leakage inductance, Llr	Torque at rated current, Tem	Id and Iq Calculation

`Physical inertia, viscous damping, static friction, Mechanical` — Mechanical properties of motor
`[0.025, 0, 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.

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

`Rated synchronous speed, Frate` — Motor frequency
`60` (default) | `scalar`

Motor-rated electrical frequency, F_rate, in Hz.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Rated synchronous speed, Frate	D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Id and Iq Calculation

Parameter

Used to Derive

Parameter

Tab

Rated synchronous speed, Frate

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Id and Iq Calculation

`Rated line to line voltage RMS, Vrate` — Motor voltage
`460` (default) | `scalar`

Motor-rated line-to-line voltage, V_rate, in V.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Rated synchronous speed, Frate	D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Id and Iq Calculation

Parameter

Used to Derive

Parameter

Tab

Rated synchronous speed, Frate

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Id and Iq Calculation

`Rated slip, Srate` — Motor slip speed
`0.0172` (default) | `scalar`

Motor-rated slip speed, S_rate, dimensionless.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Rated slip, Srate	D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Id and Iq Calculation

Parameter

Used to Derive

Parameter

Tab

Rated slip, Srate

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Id and Iq Calculation

`Calculate Rated Stator Flux Current` — Derive parameters
button

Click to derive parameters.

Dependencies

On the Id and Iq Calculation tab, when you select Calculate Rated Stator Flux Current, the block calculates derived parameters. The table summarizes the derived parameters that depend on other block parameters.

Derived Parameter on Id and Iq Calculation tab	Dependency
D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Rated synchronous speed, Frate Rated line to line voltage RMS, Vrate Rated slip, Srate	Id and Iq Calculation
Stator resistance, Rs Stator leakage inductance, Lls Rotor resistance, Rr Rotor leakage inductance, Llr Rotor magnetizing inductance, Lm	Motor Parameters

Derived Parameter on Id and Iq Calculation tab

Dependency

Parameter

Tab

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Rated synchronous speed, Frate

Rated line to line voltage RMS, Vrate

Rated slip, Srate

Id and Iq Calculation

Stator resistance, Rs

Stator leakage inductance, Lls

Rotor resistance, Rr

Rotor leakage inductance, Llr

Rotor magnetizing inductance, Lm

Motor Parameters

`D-axis rated current, Isd_0` — Derived
`3.1004` (default) | `scalar`

Derived d-axis rated current, in A.

Dependencies

Derived Parameter on Id and Iq Calculation tab	Dependency
D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Rated synchronous speed, Frate Rated line to line voltage RMS, Vrate Rated slip, Srate	Id and Iq Calculation
Stator resistance, Rs Stator leakage inductance, Lls Rotor resistance, Rr Rotor leakage inductance, Llr Rotor magnetizing inductance, Lm	Motor Parameters

Derived Parameter on Id and Iq Calculation tab

Dependency

Parameter

Tab

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Rated synchronous speed, Frate

Rated line to line voltage RMS, Vrate

Rated slip, Srate

Id and Iq Calculation

Stator resistance, Rs

Stator leakage inductance, Lls

Rotor resistance, Rr

Rotor leakage inductance, Llr

Rotor magnetizing inductance, Lm

Motor Parameters

`Q-axis rated current, Isq_0` — Derived
`5.7131` (default) | `scalar`

Derived q-axis rated current, in A.

Dependencies

Derived Parameter on Id and Iq Calculation tab	Dependency
D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Rated synchronous speed, Frate Rated line to line voltage RMS, Vrate Rated slip, Srate	Id and Iq Calculation
Stator resistance, Rs Stator leakage inductance, Lls Rotor resistance, Rr Rotor leakage inductance, Llr Rotor magnetizing inductance, Lm	Motor Parameters

Derived Parameter on Id and Iq Calculation tab

Dependency

Parameter

Tab

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Rated synchronous speed, Frate

Rated line to line voltage RMS, Vrate

Rated slip, Srate

Id and Iq Calculation

Stator resistance, Rs

Stator leakage inductance, Lls

Rotor resistance, Rr

Rotor leakage inductance, Llr

Rotor magnetizing inductance, Lm

Motor Parameters

`Torque at rated current, Tem` — Derived
`12.6467` (default) | `scalar`

Torque at rated current, in N·m.

Dependencies

Derived Parameter on Id and Iq Calculation tab	Dependency
D-axis rated current, Isd_0 Q-axis rated current, Isq_0 Torque at rated current, Tem	Rated synchronous speed, Frate Rated line to line voltage RMS, Vrate Rated slip, Srate	Id and Iq Calculation
Stator resistance, Rs Stator leakage inductance, Lls Rotor resistance, Rr Rotor leakage inductance, Llr Rotor magnetizing inductance, Lm	Motor Parameters

Derived Parameter on Id and Iq Calculation tab

Dependency

Parameter

Tab

D-axis rated current, Isd_0

Q-axis rated current, Isq_0

Torque at rated current, Tem

Rated synchronous speed, Frate

Rated line to line voltage RMS, Vrate

Rated slip, Srate

Id and Iq Calculation

Stator resistance, Rs

Stator leakage inductance, Lls

Rotor resistance, Rr

Rotor leakage inductance, Llr

Rotor magnetizing inductance, Lm

Motor Parameters

Current Controller

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

Current regulator bandwidth, in Hz.

Dependencies

This table summarizes the parameter dependencies.

Parameter	Used to Derive
Bandwidth of the current regulator, EV_current	D and Q axis integral gain, Ki D and Q axis proportional gain, Kp	Current Controller

Parameter

Used to Derive

Parameter

Tab

Bandwidth of the current regulator, EV_current

D and Q axis integral gain, Ki

D and Q axis proportional gain, Kp

Current Controller

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

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 parameters that depend on other block parameters.

Derived Parameter on Current Controller tab	Dependency
D and Q axis proportional gain, Kp D and Q axis integral gain, Ki	Bandwidth of the current regulator, EV_current	Current Controller
Stator resistance, Rs Stator leakage inductance, Lls Rotor resistance, Rr Rotor leakage inductance, Llr Rotor magnetizing inductance, Lm	Motor Parameters

Derived Parameter on Current Controller tab

Dependency

Parameter

Tab

D and Q axis proportional gain, Kp

D and Q axis integral gain, Ki

Bandwidth of the current regulator, EV_current

Current Controller

Stator resistance, Rs

Stator leakage inductance, Lls

Rotor resistance, Rr

Rotor leakage inductance, Llr

Rotor magnetizing inductance, Lm

Motor Parameters

`D and Q axis proportional gain, Kp` — Derived
`32.1894` (default) | `scalar`

Derived proportional gain, in V/A.

Dependencies

Derived Parameter on Current Controller tab	Dependency
D and Q axis proportional gain, Kp D and Q axis integral gain, Ki	Bandwidth of the current regulator, EV_current	Current Controller
Stator resistance, Rs Stator leakage inductance, Lls Rotor resistance, Rr Rotor leakage inductance, Llr Rotor magnetizing inductance, Lm	Motor Parameters

Derived Parameter on Current Controller tab

Dependency

Parameter

Tab

D and Q axis proportional gain, Kp

D and Q axis integral gain, Ki

Bandwidth of the current regulator, EV_current

Current Controller

Stator resistance, Rs

Stator leakage inductance, Lls

Rotor resistance, Rr

Rotor leakage inductance, Llr

Rotor magnetizing inductance, Lm

Motor Parameters

`D and Q axis integral gain, Ki` — Derived
`2224.2476` (default) | `scalar`

Derived integral gain, in V/A*s.

Dependencies

Derived Parameter on Current Controller tab	Dependency
D and Q axis proportional gain, Kp D and Q axis integral gain, Ki	Bandwidth of the current regulator, EV_current	Current Controller
Stator resistance, Rs Stator leakage inductance, Lls Rotor resistance, Rr Rotor leakage inductance, Llr Rotor magnetizing inductance, Lm	Motor Parameters

Derived Parameter on Current Controller tab

Dependency

Parameter

Tab

D and Q axis proportional gain, Kp

D and Q axis integral gain, Ki

Bandwidth of the current regulator, EV_current

Current Controller

Stator resistance, Rs

Stator leakage inductance, Lls

Rotor resistance, Rr

Rotor leakage inductance, Llr

Rotor magnetizing inductance, Lm

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] Shigeo Morimoto, Masayuka Sanada, 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] Muyang Li. “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

IM Controller

Description

Speed Controller

State Filter

State Feedback

Command Feedforward

Torque Determination

Current Regulators

Transforms

Motor

Electrical Losses

Ports

Input

SpdReq — Rotor mechanical speed command scalar

Dependencies

TrqCmd — Torque command scalar

Dependencies

BusVolt — DC bus voltage scalar

PhaseCurrA — Current scalar

PhaseCurrB — Current scalar

SpdFdbk — Rotor mechanical speed 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

Stator resistance, Rs — Resistance 1.77 (default) | scalar

Dependencies

Stator leakage inductance, Lls — Inductance 0.0139 (default) | scalar

Dependencies

Rotor resistance, Rr — Resistance 1.34 (default) | scalar

Dependencies

Rotor leakage inductance, Llr — Inductance 0.0121 (default) | scalar

Dependencies

Rotor magnetizing inductance, Lm — Inductance 0.3687 (default) | scalar

Dependencies

Number of pole pairs, PolePairs — Poles 2 (default) | scalar

Dependencies

Physical inertia, viscous damping, static friction, Mechanical — Mechanical properties of motor [0.025, 0, 0] (default) | vector

Dependencies

Id and Iq Calculation

Rated synchronous speed, Frate — Motor frequency 60 (default) | scalar

Dependencies

Rated line to line voltage RMS, Vrate — Motor voltage 460 (default) | scalar

Dependencies

Rated slip, Srate — Motor slip speed 0.0172 (default) | scalar

Dependencies

Calculate Rated Stator Flux Current — Derive parameters button

Dependencies

D-axis rated current, Isd_0 — Derived 3.1004 (default) | scalar

Dependencies

Q-axis rated current, Isq_0 — Derived 5.7131 (default) | scalar

Dependencies

Torque at rated current, Tem — Derived 12.6467 (default) | scalar

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 and Q axis proportional gain, Kp — Derived 32.1894 (default) | scalar

Dependencies

D and Q axis integral gain, Ki — Derived 2224.2476 (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

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

`SpdReq` — Rotor mechanical speed command
`scalar`

`TrqCmd` — Torque command
`scalar`

`BusVolt` — DC bus voltage
`scalar`

`PhaseCurrA` — Current
`scalar`

`PhaseCurrB` — Current
`scalar`

`SpdFdbk` — Rotor mechanical speed
`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
`1.77` (default) | `scalar`

`Stator leakage inductance, Lls` — Inductance
`0.0139` (default) | `scalar`

`Rotor resistance, Rr` — Resistance
`1.34` (default) | `scalar`

`Rotor leakage inductance, Llr` — Inductance
`0.0121` (default) | `scalar`

`Rotor magnetizing inductance, Lm` — Inductance
`0.3687` (default) | `scalar`

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

`Physical inertia, viscous damping, static friction, Mechanical` — Mechanical properties of motor
`[0.025, 0, 0]` (default) | `vector`

`Rated synchronous speed, Frate` — Motor frequency
`60` (default) | `scalar`

`Rated line to line voltage RMS, Vrate` — Motor voltage
`460` (default) | `scalar`

`Rated slip, Srate` — Motor slip speed
`0.0172` (default) | `scalar`

`Calculate Rated Stator Flux Current` — Derive parameters
button

`D-axis rated current, Isd_0` — Derived
`3.1004` (default) | `scalar`

`Q-axis rated current, Isq_0` — Derived
`5.7131` (default) | `scalar`

`Torque at rated current, Tem` — Derived
`12.6467` (default) | `scalar`

`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 and Q axis proportional gain, Kp` — Derived
`32.1894` (default) | `scalar`

`D and Q axis integral gain, Ki` — Derived
`2224.2476` (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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