Resolver

A rotating transformer that measures the angle of rotation.

blockType: AcausalElectricPowerSystems.Sensors.Resolver

Path in the library:

/Physical Modeling/Electrical/Sensors & Transducers/Resolver

Description

Block Resolver It simulates a universal resolver that measures the electrical phase angle of a signal using electromagnetic coupling. The resolver consists of a rotating transformer that transmits an alternating voltage applied to the primary winding to two secondary windings. These secondary windings are located at an angle of 90 degrees to each other. When the rotation angle of the rotor changes, the relative coupling between the primary and the two secondary windings changes. In the block model Resolver The first secondary winding is oriented in such a way that its maximum coupling occurs at the moment when the rotor is at an angle of 0 degrees. In this case, the second secondary winding has minimal coupling.

resolver 1

Without loss of generality, it is assumed that the coefficient of transformation between the primary winding and the rotor winding is equal to 1. This leads to the fact that the current and voltage of the rotor are equal to the current and voltage of the primary winding.

The block equations can be defined in two ways:

Eliminate the dynamics by neglecting the inductance of the transformer. This model is valid only if the sensor is driven by a sine wave, since any constant component on the primary side will transfer to the secondary.
Take into account the inductive components, thereby capturing voltage amplitude losses and phase differences. This model is valid for any input waveform. In this option, you can either specify the inductors and the maximum coupling coefficient directly, or specify the transformation coefficient and the measured impedance, and then the unit uses these values to determine the inductive components.

Equations in a dynamic-free mode

The equations are based on a superposition of two ideal transformers, both of which have coupling coefficients that depend on the angle of rotation of the rotor. Two ideal transformers have a common primary winding. Additional information about modeling ideal transformers is provided on the block page. Ideal Transformer.

The equations look like this:

where

and — the voltage and current of the rotor (primary winding), respectively;
and — voltage and current of the first secondary winding, respectively;
and — voltage and current of the second secondary winding, respectively;
— coupling coefficient for the first secondary winding;
— coupling coefficient for the second secondary winding;
— the transformation coefficient;
— the number of pairs of poles;
— the angle of rotation of the rotor.

Equations in dynamic mode

The equations are based on a superposition of two mutual inductance coils, both of which have coupling coefficients that depend on the angle of rotation of the rotor. The two mutual inductance coils have a common primary winding. Additional information about mutual inductance modeling is provided on the block page. Mutual Inductor.

The equations look like this:

where

and — the voltage and current of the rotor (primary winding), respectively;
and — voltage and current of the first secondary winding, respectively;
and — voltage and current of the second secondary winding, respectively;
— resistance of the rotor (or primary winding);
— inductance of the rotor (or primary winding);
— resistance of the stator (or secondary winding);
— inductance of the stator (or secondary winding);
— the number of pairs of poles;
— communication coefficient;
— the angle of rotation of the rotor.

It is assumed that there is no magnetic coupling between the two secondary windings.

Specifications usually do not specify coupling and inductance coefficients, but instead specify the transformation coefficient. and measured total resistances. If the parameter Parameterization it matters Specify transformation ratio and measured impedances, then the set values are used to determine the values of the coefficients of the equation, as indicated above.

Assumptions and limitations

The resolver does not create any torque between the mechanical rotary ports R and C.
The transformer between the primary winding and the rotor winding is ideal with the ratio 1:1.
There is no connection between the two secondary windings.

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# p1 — the positive terminal of the primary winding
electricity

Details

A non-directional port connected to the positive terminal of the primary winding.

Program usage name

p

# p2 — the negative terminal of the primary winding
electricity

Details

A non-directional port connected to the negative terminal of the primary winding.

Program usage name

n

# R — the resolver rotor
rotational mechanics

Details

A mechanical rotary port corresponding to the rotor.

Program usage name

rod_flange

# C — the body of the resolver
rotational mechanics

Details

A mechanical rotary port corresponding to the housing.

Program usage name

case_flange

# x1 — the positive terminal of the secondary winding
electricity

Details

An electrical non-directional port connected to the positive terminal of the secondary winding .

Program usage name

p_x

# x2 — the negative terminal of the secondary winding
electricity

Details

An electrical non-directional port connected to the negative terminal of the secondary winding .

Program usage name

n_x

# y1 — the positive terminal of the secondary winding
electricity

Details

An electrical non-directional port connected to the positive terminal of the secondary winding .

Program usage name

p_y

# y2 — the negative terminal of the secondary winding
electricity

Details

An electrical non-directional port connected to the negative terminal of the secondary winding .

Program usage name

n_y

Parameters

# Parameterization — parameterization of the resolver
Specify transformation ratio and omit dynamics | Specify transformation ratio and measured impedances | Specify equation parameters directly

Details

Select one of the following block parameterization methods:

Specify transformation ratio and omit dynamics — specify only the values of the transformation coefficient, the number of pole pairs, and the initial angle of the rotor. This model neglects the inductive components of the transformer and is valid only if the sensor is driven by a sine wave. The equations are given in Equations in a dynamic-free mode.
Specify transformation ratio and measured impedances — specify additional values to determine the inductive terms of the transformer in order to simulate voltage amplitude loss and phase difference. This model is valid for any input waveform. The equations are given in Equations in dynamic mode.
Specify equation parameters directly — the model takes into account the dynamics, but it is necessary to set the values of the rotor and stator inductors and the maximum coupling coefficient instead of the transformation coefficient and the measured total resistances. This model is valid for any input waveform. The equations are given in Equations in dynamic mode.

Values	`Specify transformation ratio and omit dynamics` \| `Specify transformation ratio and measured impedances` \| `Specify equation parameters directly`
Default value	`Specify transformation ratio and omit dynamics`
Program usage name	`parameterization`
Evaluatable	No

# Transformation ratio — the ratio of peak output voltage to input voltage

Details

The transformation coefficient, defined as the ratio between the peak output voltage and the peak input voltage with a negligible drop in secondary voltage due to resistance and inductance.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Specify transformation ratio and omit dynamics or Specify transformation ratio and measured impedances. If the value is selected Specify transformation ratio and measured impedances, then the transformation coefficient will take into account the voltage drop due to the resistance of the primary winding.

Default value	`0.5`
Program usage name	`transformation_ratio`
Evaluatable	Yes

# Rotor resistance — resistance of the primary winding
Ohm | mOhm | kOhm | MOhm | GOhm

Details

Active resistance of the rotor. This resistance is also called the resistance of the primary winding.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Specify transformation ratio and measured impedances or Specify equation parameters directly.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`70.0 Ohm`
Program usage name	`R_r`
Evaluatable	Yes

# Stator resistance — resistance of the secondary winding
Ohm | mOhm | kOhm | MOhm | GOhm

Details

Active resistance of the stator. This resistance is also called the resistance of the secondary winding. It is assumed that both secondary windings have the same resistance.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Specify transformation ratio and measured impedances or Specify equation parameters directly.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`180.0 Ohm`
Program usage name	`R_s`
Evaluatable	Yes

# Rotor reactance — reactance of the primary winding
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reactance of the rotor when the secondary winding is open. This reactance is also called the reactance of the primary winding.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Specify transformation ratio and measured impedances.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`100.0 Ohm`
Program usage name	`X_r`
Evaluatable	Yes

# Stator reactance — reactance of the secondary winding
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reactance of the stator when the primary winding is open. This reactance is also called the reactance of the secondary winding.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Specify transformation ratio and measured impedances.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`300.0 Ohm`
Program usage name	`X_s`
Evaluatable	Yes

# Frequency at which reactances and transformation ratio are specified — frequency of the sinusoidal source
Hz | kHz | MHz | GHz

Details

The frequency of the sinusoidal source used for measuring reactants.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Specify transformation ratio and measured impedances.

Units	`Hz` \| `kHz` \| `MHz` \| `GHz`
Default value	`10.0 kHz`
Program usage name	`f`
Evaluatable	Yes

# Rotor inductance — primary winding inductance
H | nH | uH | mH

Details

Inductance of the rotor or primary winding .

Dependencies

To use this parameter, set for the parameter Parameterization meaning Specify equation parameters directly.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`0.0016 H`
Program usage name	`L_r`
Evaluatable	Yes

# Stator inductance — the inductance of the secondary winding
H | nH | uH | mH

Details

Inductance of the stator or secondary winding .

Dependencies

To use this parameter, set for the parameter Parameterization meaning Specify equation parameters directly.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`0.0048 H`
Program usage name	`L_s`
Evaluatable	Yes

# Peak coefficient of coupling — maximum coupling coefficient

Details

The maximum coupling coefficient between the primary and secondary windings.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Specify equation parameters directly.

Default value	`0.35`
Program usage name	`k`
Evaluatable	Yes

# Number of pole pairs — number of pairs of rotor poles

Details

The number of pairs of rotor poles.

Default value	`1`
Program usage name	`N_pole_pairs`
Evaluatable	Yes