# Inverse Park Transform

Implement dq to αβ transformation

Since R2020a

Libraries:
Motor Control Blockset / Controls / Math Transforms
Motor Control Blockset HDL Support / Controls / Math Transforms

## Description

The Inverse Park Transform block computes the inverse Park transformation of the orthogonal direct (d) and quadrature (q) axes components or the multiplexed dq0 components in the rotating dq reference frame.

You can configure the block to align either the d- or q-axis with the α-axis at time t = 0.

The block accepts the following inputs:

• Either d-q axes components or multiplexed components dq0 in the rotating reference frame. Use the Number of inputs parameter to use either two or three inputs.

• Sine and cosine values of the corresponding angles of transformation.

When using two-input configuration, it outputs the two-phase orthogonal components in the stationary αβ reference frame. When using three-input configuration, it outputs multiplexed components αβ0.

For a balanced system, the zero component is equal to zero.

The figures show a rotating dq reference frame and the α-β axes components in an αβ reference frame for when:

• The d-axis aligns with the α-axis.

• The q-axis aligns with the α-axis.

In both cases, the angle θ = ωt, where:

• θ is the angle between the α- and d-axes for the d-axis alignment or the angle between the α- and q-axes for the q-axis alignment. It indicates the angular position of the rotating dq reference frame with respect to the α-axis.

• ω is the rotational speed of the d-q reference frame.

• t is the time, in seconds, from the initial alignment.

The figures show the time-response of the individual components of the αβ and dq reference frames when:

• The d-axis aligns with the α-axis.

• The q-axis aligns with the α-axis.

### Equations

The following equations describe how the block implements inverse Park transformation.

• When the d-axis aligns with the α-axis.

• When the q-axis aligns with the α-axis.

where:

• ${f}_{d}$ and ${f}_{q}$ are the direct and quadrature axis orthogonal components in the rotating dq reference frame.

• ${f}_{\alpha }$ and ${f}_{\beta }$ are the two-phase orthogonal components in the stationary αβ reference frame.

## Ports

### Input

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Direct axis component, d, in the rotating dq reference frame.

#### Dependencies

To enable this port, set the Number of inputs parameter to `Two inputs`.

Data Types: `single` | `double` | `fixed point`

Quadrature axis component, q, in the rotating dq reference frame.

#### Dependencies

To enable this port, set the Number of inputs parameter to `Two inputs`.

Data Types: `single` | `double` | `fixed point`

Multiplexed direct axis component, d, quadrature axis component, q, and the 0 component in the rotating dq reference frame.

#### Dependencies

To enable this port, set the Number of inputs parameter to `Three inputs`.

Data Types: `single` | `double` | `fixed point`

Sine value of the angle of transformation, θe. θe is the angle between the rotating reference frame and the α-axis.

Data Types: `single` | `double` | `fixed point`

Cosine value of the angle of transformation, θe. θe is the angle between the rotating reference frame and the α-axis.

Data Types: `single` | `double` | `fixed point`

### Output

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Alpha-axis component, α, in the stationary αβ reference frame.

#### Dependencies

To enable this port, set the Number of inputs parameter to `Two inputs`.

Data Types: `single` | `double` | `fixed point`

Beta-axis component, β, in the stationary αβ reference frame.

#### Dependencies

To enable this port, set the Number of inputs parameter to `Two inputs`.

Data Types: `single` | `double` | `fixed point`

Multiplexed alpha-axis component, α and beta-axis component, β and `0` component, in the stationary αβ reference frame.

#### Dependencies

To enable this port, set the Number of inputs parameter to `Three inputs`.

Data Types: `single` | `double` | `fixed point`

## Parameters

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Select the number of inputs that you can specify:

• `Two inputs` — Configure the block to accept two separate input signals d and q. The block generates two separate output signals α and β.

• `Three inputs` — Configure the block to accept a multiplexed input containing d,q, and 0 signals. The block generates a multiplexed output containing α, β, and 0 signals.

Align either the d- or q-axis of the rotating reference frame to the α-axis of the stationary reference frame.

Type of position (theta) input:

• `Sine and Cosine electrical position` — Configure the block to directly accept sinθe and cosθe inputs.

• `Electrical position` — Configure the block to accept the electrical position (θe) input. The block internally computes the sinθe and cosθe signals from the θe input.

Unit of the electrical position input (θe).

#### Dependencies

To enable this parameter, set Theta input to `Electrical position`.

Size of the lookup table array that the block uses to compute sinθe and cosθe signals from the θe input. You can specify a value between 125 and 4095.

#### Dependencies

To enable this parameter, set Theta input to `Electrical position`.

## Version History

Introduced in R2020a