Park Transform

Implement αβ to dq transformation

Since R2020a

• 

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

Description

The Park Transform block computes the Park transformation of two-phase orthogonal components in a stationary αβ reference frame.

The block accepts the following inputs:

• α-β axes components in the stationary reference frame.

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

It outputs orthogonal direct and quadrature axis components in the rotating dq reference frame. You can configure the block to align either the d- or the q-axis with the α-axis at time t = 0.

The figures show the α-β axes components in an αβ reference frame and a rotating dq 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 Park transformation.

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

  $$\left[\begin{array}{c}{f}_d\\ f_q\end{array}\right]=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]\left[\begin{array}{c}{f}_{\alpha }\\ f_{\beta }\end{array}\right]$$

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

  $$\left[\begin{array}{c}{f}_d\\ f_q\end{array}\right]=\left[\begin{array}{cc}\sin \theta & -\cos \theta \\ \cos \theta & \sin \theta \end{array}\right]\left[\begin{array}{c}{f}_{\alpha }\\ f_{\beta }\end{array}\right]$$

where:

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

• $$f_d$$ and $f_q$ are the direct and quadrature axis orthogonal components in the rotating dq reference frame.

Examples

Field-Oriented Control of Induction Motor Using Speed Sensor

Implements the field-oriented control (FOC) technique to control the speed of a three-phase AC induction motor (ACIM). The FOC algorithm requires rotor speed feedback, which is obtained in this example by using a quadrature encoder sensor. For details about FOC, see Field-Oriented Control (FOC).

Open Example

Field-Weakening Control (with MTPA) of PMSM

Implements the field-oriented control (FOC) technique to control the torque and speed of a three-phase permanent magnet synchronous motor (PMSM). The FOC algorithm requires rotor position feedback, which is obtained by a quadrature encoder sensor. For details about FOC, see Field-Oriented Control (FOC).

Open Example

Field-Oriented Control of PMSM Using Hall Sensor

Implements the field-oriented control (FOC) technique to control the speed of a three-phase permanent magnet synchronous motor (PMSM). The FOC algorithm requires rotor position feedback, which is obtained by a Hall sensor. For details about FOC, see Field-Oriented Control (FOC).

Open Example

Ports

Input

α — Axis component

scalar

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

Data Types: single | double | fixed point

β — Axis component

scalar

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

Data Types: single | double | fixed point

sin θ_e — Sine value of rotational angle

scalar

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

Data Types: single | double | fixed point

cos θ_e — Cosine value of rotational angle

scalar

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

Data Types: single | double | fixed point

Output

d — Axis component

scalar

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

Data Types: single | double | fixed point

q — Axis component

scalar

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

Data Types: single | double | fixed point

Parameters

Alpha (phase-a) axis alignment — dq reference frame alignment

D-axis (default) | Q-axis

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation

Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see OutputPipeline (HDL Coder).

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced in R2020a