Engee documentation

Resolver

A rotating transformer that measures the angle of rotation.

resolver

Description

The Resolver unit models a universal resolver that measures the electrical phase angle of a signal using electromagnetic coupling. The resolver consists of a rotating transformer that transfers the AC voltage applied to the primary winding to two secondary windings. These secondary windings are arranged at an angle of 90 degrees to each other. As the angle of rotation of the rotor changes, the relative relationship between the primary and the two secondary windings changes. In the Resolver unit model, the first secondary winding is orientated so that its maximum coupling occurs when the rotor is at 0 degrees. At the same time, the second secondary winding has a minimum coupling.

resolver 1

Without loss of generality, it is assumed that the trasnformation coefficient between the primary winding and the rotor winding is equal to 1. This results in the rotor current and voltage being equal to the primary winding current and voltage.

The block equations can be defined in two ways:

  • Eliminate the dynamics by neglecting the transformer inductance. This model is only valid if the sensor is driven by a sine wave, since any DC component on the primary side will be passed to the secondary side.

  • Account for inductive components, thereby capturing voltage amplitude loss and phase difference. This model is valid for any input waveform. In this option you can either specify the inductances and maximum coupling coefficient directly, or you can specify the transformer ratio and measured total resistances, and then the unit uses these values to determine the inductive components.

Equations in non-dynamic mode

The equations are based on the superposition of two ideal transformers, both of which have coupling coefficients that depend on the rotor angle. The two ideal transformers share a common primary winding. For more information on modelling ideal transformers, see the block page at Ideal Transformer.

The equations are as follows:

,

,

,

,

,

where

  • and - 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;

  • - transformation coefficient;

  • - number of pole pairs;

  • - rotor rotation angle.

Equations in the mode with dynamics

The equations are based on the superposition of two mutual inductance coils, both of which have coupling coefficients that depend on the rotor angle. The two mutual inductance coils share a common primary winding. More information on mutual inductance modelling can be found on the block page at Mutual Inductor.

The equations are as follows:

where

  • and - rotor (primary winding) voltage and current, respectively;

  • and - voltage and current of the first secondary winding respectively;

  • and - voltage and current of the second secondary winding, respectively;

  • - rotor (or primary winding) resistance;

  • - rotor (or primary winding) inductance

  • - stator (or secondary winding) resistance;

  • - stator (or secondary winding) inductance;

  • - number of pole pairs;

  • - coupling coefficient;

  • - rotor rotation angle.

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

Specifications do not normally specify coupling ratios and inductances, but instead specify the transformation ratio and measured impedances. If the Parameterization parameter is set to Specify transformation ratio and measured impedances, the specified values are used to determine the values of the equation coefficients as above.

Assumptions and limitations

  • The resolver does not create torque between the mechanical rotary ports R and C.

  • The transformer between the primary winding and the rotor winding is ideal with a 1:1 ratio.

  • There is no coupling between the two secondary windings.

Ports

Non-directional

p1 - positive terminal of the primary winding
electricity

Non-directional port associated with the positive terminal of the primary winding.

p2 is the negative terminal of the primary winding
electricity

Non-directional port associated with the negative terminal of the primary winding.

R is the resolver rotor
`rotational mechanics

Mechanical rotational port corresponding to the rotor.

C - resolver housing
`rotational mechanics

Mechanical rotational port corresponding to the enclosure.

x1 - positive terminal of secondary winding x
electricity

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

x2 is the negative terminal of the secondary winding x
electricity

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

y1 is the positive terminal of the secondary winding y
electricity

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

y2 is the negative terminal of the secondary winding y
electricity

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

Parameters

parameterization - resolver parameterization
Specify transformation ratio and omit dynamics (by default) | Specify transformation ratio and measured impedances | Specify equation parameters directly

Select one of the following block parameterization methods:

  • `Specify transformation ratio and omit dynamics' - specify only the values for transformation ratio, number of pole pairs and initial rotor angle. This model neglects the inductive components of the transformer and is only valid if the encoder is driven by a sine wave. The equations are given in [Уравнения в режиме без динамики].

  • Specify transformer transform ratio and measured impedances - specify additional values to determine the transformer inductive terms to model the voltage amplitude loss and phase difference. This model is valid for any input waveform. The equations are given in [Уравнения в режиме с динамикой].

  • Specify equation parameters directly - the model accounts for dynamics, but it is necessary to specify values for rotor and stator inductances and maximum coupling coefficient instead of transformer ratio and measured total resistances. This model is valid for any input waveform. The equations are given in [Уравнения в режиме с динамикой].

Transformation ratio - ratio of peak output voltage to input voltage
0.5 (by default) | positive number

Transformation ratio defined as the ratio between peak output voltage and peak input voltage with negligible secondary voltage drop due to resistance and inductance.

Dependencies

To use this parameter, set the Parameterization parameter to Specify transformation ratio and omit dynamics or Specify transformation ratio and measured impedances. If `Specify transformation ratio and measured impedances' is selected, the transformation ratio will take into account the voltage drop due to the primary resistance.

Rotor resistance is the resistance of the primary winding
70 ohms (by default) | positive number.

The active resistance of the rotor. This resistance is also called primary resistance.

Dependencies

To use this parameter, set parameterization to Specify transformation ratio and measured impedances or Specify equation parameters directly.

Stator resistance - secondary winding resistance
180 ohms (by default) | positive number.

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

Dependencies

To use this parameter, set parameterization to Specify transformation ratio and measured impedances or Specify equation parameters directly.

Rotor reactance - primary winding reactance
100 ohms (by default) | positive number.

The rotor reactance when the secondary winding is open. This reactance is also referred to as the primary winding reactance.

Dependencies

To use this parameter, set parameterization to `Specify transformation ratio and measured impedances'.

Stator reactance is the secondary reactance of the secondary winding
300 ohms (by default) | positive number.

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

Dependencies

To use this parameter, set parameterization to `Specify transformation ratio and measured impedances'.

Frequency at which reactances and transformation ratio are specified is the frequency of the sinusoidal source
10 kHz (by default) | Positive number

The frequency of the sinusoidal source used in measuring reactances.

Dependencies

To use this parameter, set parameterization to `Specify transformation ratio and measured impedances'.

Rotor inductance - primary inductance
0.0016 Gn (by default) | positive number.

Rotor or primary inductance .

Dependencies

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

Stator inductance - secondary inductance
0.0048 Gn (by default) | positive number.

Stator or secondary inductance, .

Dependencies

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

Peak coefficient of coupling - maximum coupling coefficient
0.35 (by default) | `Number from zero to one'.

Maximum coupling coefficient between primary and secondary windings.

Dependencies

To use this parameter, set parameterization to `Specify equation parameters directly'.

Number of pole pairs - number of rotor pole pairs
1 (By default) | `positive number

Number of rotor pole pairs.